80
,QWURGX Fa DR D DQ DOLVH H DR SURFHVVDPHQWR GH VLQDLV XVDQGR R 0$7/$%

Analise de Sinais

Embed Size (px)

DESCRIPTION

...

Citation preview

Page 1: Analise de Sinais

,QWURGX�FaDR �D DQ�DOLVH H DR

SURFHVVDPHQWR GH VLQDLV XVDQGR R

0$7/$%5� 6DPSDLR� (� &DWDOGR� 5� 5LTXHOPH

5LR GH -DQHLUR� VHWHPEUR GH �����

Page 2: Analise de Sinais

�,QGLFH

� ,QWURGX�FaDR �

� 6LQDLV &RQW��QXRV QR WHPSR �

��� ,QWURGX�FaDR � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ���� $Q�DOLVH GH )RXULHU � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

����� 6�HULH GH )RXULHU � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������ 2 HVSHFWUR FRPSOH[R GH )RXULHU � � � � � � � � � � � � � � � � � � � � � � � �

��� 7UDQVIRUPDGD GH )RXULHU � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� ,QWURGX�FaDR � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� $ WUDQVIRUPDGD GH )RXULHU � � � � � � � � � � � � � � � � � � � � � � � � � � ������� ([LVWAHQFLD GD WUDQVIRUPDGD GH )RXULHU � � � � � � � � � � � � � � � � � � � ������� 3URSULHGDGHV GD WUDQVIRUPDGD GH )RXULHU � � � � � � � � � � � � � � � � � � ��

��� &RQYROX�FaDR � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� ,QWURGX�FaDR � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� 3URSULHGDGHV � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

� 6LQDLV GLVFUHWRV QR WHPSR ��

��� 6HT¦XAHQFLDV � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� 2SHUD�FaRHV FRP VHT¦XAHQFLDV H VHT¦XAHQFLDV E�DVLFDV � � � � � � � � � � � � � � � � � � � ��

����� 2SHUD�FaRHV FRP VHT¦XAHQFLDV � � � � � � � � � � � � � � � � � � � � � � � � � � ������� 6HT¦XAHQFLDV E�DVLFDV � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

��� 6LVWHPDV GLVFUHWRV QR WHPSR � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� ,QWURGX�FaDR � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� $OJXQV WLSRV GH VLVWHPDV � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� 6LVWHPDV /LQHDUHV ,QYDULDQWHV QR 7HPSR � � � � � � � � � � � � � � � � � � ������� 3URSULHGDGHV GH 6LVWHPDV /LQHDUHV ,QYDULDQWHV QR 7HPSR � � � � � � � � � ������� (TXD�FaRHV OLQHDUHV GH GLIHUHQ�FD GH FRH�FLHQWHV FRQVWDQWHV � � � � � � � � � ������� 5HSUHVHQWD�FaDR QR GRP��QLR GD IUHT¦XAHQFLD GH VLQDLV GLVFUHWRV QR WHPSR � � ������� 5HSUHVHQWD�FaDR GH VHT� SHOD WUDQVIRUPDGD GH )RXULHU GLVFUHWD�7)'� � � � ������� 3URSULHGDGHV GD WUDQVIRUPDGD GH )RXULHU GLVFUHWD � � � � � � � � � � � � � ��

��� $PRVWUDJHP GH VLQDLV FRQW��QXRV � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� ,QWURGX�FaDR � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� $PRVWUDJHP SHUL�RGLFD � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

Page 3: Analise de Sinais

����� 5HSUHVHQWD�FaDR GDV DPRVWUDV QR GRP��QLR GD IUHT¦XAHQFLD � � � � � � � � � � � ������� 7HRUHPD GD DPRVWUDJHP � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� 5HFRQVWUX�FaDR GH XP VLQDO OLPLWDGR HP IDL[D D SDUWLU GH VXDV DPRVWUDV � � ������� 3URFHVVDPHQWR GLVFUHWR GH VLQDO FRQW��QXR � � � � � � � � � � � � � � � � � � ��

��� &RQVLGHUD�FaRHV SU�DWLFDV � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� ,QWURGX�FaDR � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� 3U�H��OWUDJHP SDUD HYLWDU PDVFDUDPHQWR � � � � � � � � � � � � � � � � � � � ������� &RQYHUVaDR DQDO�RJLFD�GLJLWDO � � � � � � � � � � � � � � � � � � � � � � � � � ������� &RQYHUVaDR GLJLWDO�DQDO�RJLFD � � � � � � � � � � � � � � � � � � � � � � � � � ��

��� $ 7UDQVIRUPDGD 'LVFUHWD GH )RXULHU �7')� � � � � � � � � � � � � � � � � � � � � ������� ,QWURGX�FaDR � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� $ V�HULH GLVFUHWD GH )RXULHU � � � � � � � � � � � � � � � � � � � � � � � � � � ������� $ WUDQVIRUPDGD GLVFUHWD GH )RXULHU �7')� � � � � � � � � � � � � � � � � � ������� $ WUDQVIRUPDGD U�DSLGD GH )RXULHU � � � � � � � � � � � � � � � � � � � � � � ������� ([HPSORV � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

��� $Q�DOLVH GH VLQDLV XVDQGR 7') � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� ,QWURGX�FaDR � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� -DQHODV � 2 YD]DPHQWR � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� &RQVHTXAHQFLD GD DSOLFD�FaDR GH MDQHODV � � � � � � � � � � � � � � � � � � � � ������� 7LSRV GH MDQHODV � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

� 'XDV DSOLFD�FaRHV ��

��� 0XOWLSOH[D�FaDR � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� &RQFHLWR � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� 7LSRV GH PXOWLSOH[D�FaDR � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

��� 7UDQVOD�FaDR GH IUHT¦XAHQFLDV � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� 0RGXOD�FaDR H GHPRGXOD�FaDR � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

����� 7LSRV GH PRGXOD�FaDR � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� 0RGXOD�FaDR HP DPSOLWXGH � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

��� 'HPRGXOD�FaDR � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� $SOLFD�FaDR �D (QJHQKDULD 0HFADQLFD� SURFHVVDPHQWR GH VLQDLV SURYHQLHQWHV GH DFHO�

HUARPHWURV H WUDQVGXWRUHV GH IRU�FD � � � � � � � � � � � � � � � � � � � � � � � � � � ��

Page 4: Analise de Sinais

&DS��WXOR �

,QWURGX�FaDR

(VWH �H XP FXUVR GH DQ�DOLVH H SURFHVVDPHQWR GH VLQDLV� 7UDWD�VH GH XP FXUVR IRUPDWLYR� HVVHQFLDOSDUD TXH VH WHQKD XPD FRPSUHHQVaDR P��QLPD GRV GHVHQYROYLPHQWRV WHFQRO�RJLFRV PRGHUQRV�U�DGLR� WHOHYLVaDR� WHOHIRQLD� &'� UDGDU� VLVWHPDV GH FRQWUROH� VLVWHPDV GH PHGLGD� HWF� 2 FXUVRFRPH�FD FRP R FRQFHLWR GH VLQDO� TXH VHU�D H[HPSOL�FDGR PDV QaDR GH�QLGR� $ GHVFUL�FaDR GH XPVLQDO� VXD DQ�DOLVH� �H IHLWD GHFRPSRQGR�R QXPD EDVH FXMDV FRPSRQHQWHV VaDR VLQDLV HOHPHQWDUHV�H[SRQHQFLDLV GR WLSR H��M�W� $V FRPSRQHQWHV GR VLQDO QD EDVH GH H[SRQHQFLDLV GHVFUHYH RHVSHFWUR GR VLQDO� RX VHMD� VXD FRPSRVL�FaDR IUHT¦XHQFLDO� $ PHOKRU PDQHLUD GH LQLFLDU�VH QRHVWXGR GH VLQDLV �H YHQGR H RXYLQGR VLQDLV� H SDUDOHODPHQWH YHQGR VXD FRPSRVL�FaDR IUHT¦XHQFLDO�$ PRQWDJHP GD �JXUD IRL FRQVWUX��GD FRP HVVH �P�

1�RV YHUHPRV QR FXUVR Y�DULRV H[HPSORV GH VLQDLV H GH FRPR �H IHLWD VXD DQ�DOLVH� $V LG�HLDVE�DVLFDV VaDR DV GD �$OJHEUD /LQHDU� PDV �H QHFHVV�DULR DQWHV EXVFDU XP HVSD�FR GH UHSUHVHQWD�FaDRDGHTXDGR H� VREUHWXGR� XPD EDVH DSURSULDGD �QR QRVVR FXUVR VHU�D VHPSUH IRUPDGD SRU H[�SRQHQFLDLV� PDV QDV DXODV GLVFXWLUHPRV DV OLPLWD�FaRHV GHVVH SRQWR GH YLVWD�� 9HUHPRV TXH DHVFROKD GH XPD ERD EDVH GHVHPSHQKD XP SDSHO IXQGDPHQWDO H UHTXHU IDPLOLDULGDGH FRP VLQDLVH FRP DV DSOLFD�FaRHV GHVHMDGDV� (VWXGDUHPRV VLQDLV GH GRLV SRQWRV GH YLVWD LQGHSHQGHQWHV� PDVFRPSOHPHQWDUHV � FRQW��QXR H GLVFUHWR�$R ODGR GD DQ�DOLVH GH XP VLQDO� WHPRV R VHX SURFHVVDPHQWR� TXH �H D WUDQVIRUPD�FaDR GH XP

VLQDO HP RXWUR �GLUHPRV TXH HVWD WUDQVIRUPD�FaDR �H IHLWD WUDY�HV GH XP VLVWHPD�� (VWXGDUHPRVVLVWHPDV HVSHFLDLV� TXH FKDPDUHPRV GH �OWURV� TXH VHUaDR DV HVWUHODV GR FXUVR�'HYLGR D OLPLWD�FaRHV GH HVSD�FR� QaDR FREULPRV QHVVDV 1RWDV D SDUWH RSHUDFLRQDO TXH VHU�D IHLWD

FRP R 0$7/$%� $Q�DOLVH H 3URFHVVDPHQWR GH 6LQDLV �H XP DVVXQWR GH UD]R�DYHO FRPSOH[LGDGH�0HVPR RV F�DOFXORV PDLV VLPSOHV VaDR PXLWR WUDEDOKRVRV SDUD VHUHP IHLWRV D PaDR� 6HP XPD

Page 5: Analise de Sinais

IHUUDPHQWD FRPR R 0$7/$% D WHRULD SHUGH XP SRXFR R VHQWLGR H� FRPR FDGD XP YHU�D SRU VLPHVPR� D JUD�FD�+�D Y�DULDV DSOLFD�FaRHV GH $Q�DOLVH H 3URFHVVDPHQWR GH 6LQDLV HP GLYHUVDV �DUHDV� WDLV FRPR

HQJHQKDULD HO�HWULFD� HQJHQKDULD PHFADQLFD� SURFHVVDPHQWR GH LPDJHQV� FRPXQLFD�FaDR� FRPSX�WD�FaDR JU�D�FD H RXWUDV� 'LVFXWLUHPRV D VHJXLU XP SRXFR VREUH DV DSOLFD�FaRHV HP GXDV �DUHDV �FRPXQLFD�FaRHV H HQJHQKDULD PHFADQLFD�$ KLVW�RULD GD FRPXQLFD�FaDR QDVFH TXDQGR R KRPHP VHQWH D QHFHVVLGDGH GH H[SUHVVDU R VHX

SHQVDPHQWR D XP VHPHOKDQWH� ,VVR SRGH VHU IHLWR GH Y�DULDV IRUPDV � SHOD SDODYUD� SHOD P��PLFD�SRU GHVHQKRV� HWF� 3RU�HP� TXDQGR RV KRPHQV HVWaDR GLVWDQWHV� D FRPXQLFD�FaDR WRUQD�VH GLI��FLO RXPHVPR LPSRVV��YHO� 6ROX�FaRHV W�HFQLFDV GHVVH SUREOHPD VXUJLUDP FRP R LQYHQWR GD WHOHJUD�D� GDFRPXQLFD�FaDR YLD U�DGLR� GD WHOHIRQLD� H RXWURV� 0DLV UHFHQWHPHQWH� GD ,QWHUQHW� 3DUD GLVFXWLUPRVD FRPXQLFD�FaDR �D GLVWADQFLD GH PRGR JHUDO FRPH�FDUHPRV GLVFXWLQGR XP SRXFR DV FDUDFWHU��VWLFDVE�DVLFDV GH XPD OLJD�FaDR WHOHIARQLFD� EHP FRQKHFLGD QRVVD�3DUD HQWHQGHUPRV HVVD FRPXQLFD�FaDR GLVFXWLUHPRV RV IDWRUHV TXH D LQ�XHQFLDP� R VRP� D

YR]� R RXYLGR� D IDL[D GH IUHT¦XAHQFLDV XWLOL]DGDV� D WUDQVIRUPD�FaDR GH HQHUJLD DF�XVWLFD HP HQHUJLDHO�HWULFD H YLFH�YHUVD� D OLJD�FaDR WHOHIARQLFD HOHPHQWDU� HQWUH RXWURV�2 VRP VH SURGX] SRU YLEUD�FaRHV PHFADQLFDV� GH IUHT¦XAHQFLDV SHUFHSW��YHLV SHOR RXYLGR KXPDQR�

QXP PHLR HO�DVWLFR�$V FRUGDV YRFDLV GR VHU KXPDQR VaDR FDSD]HV GH SURGX]LU YLEUD�FaRHV VRQRUDV GHQWUR GH XPD

IDL[D GH ��� D ����� +]� &DGD VRP HPLWLGR SRGH VHU SHQVDGR FRPR FRPSRVWR GH YLEUD�FaRHVHOHPHQWDUHV GH GLYHUVDV IUHT¦XAHQFLDV� P�XOWLSODV GH XPD IUHT¦XAHQFLD IXQGDPHQWDO� 3DUD R KRPHPHVVD IUHT¦XAHQFLD IXQGDPHQWDO �H GH ��� +] H SDUD D PXOKHU �H GH ��� +]�$ IDL[D GH IUHT¦XAHQFLDV DXG��YHLV SHOR RXYLGR KXPDQR YDL GHVGH �� +] DW�H ����� +]� H R OLPLWH

VXSHULRU YDULD GH SHVVRD SDUD SHVVRD�'LYHUVRV HVWXGRV IRUDP UHDOL]DGRV SDUD GHWHUPLQDU TXDO D IDL[D GH IUHT¦XAHQFLDV PDLV DSUR�

SULDGD SDUD DV FRPXQLFD�FaRHV� VRE R SRQWR GH YLVWD HFRQARPLFR H GH TXDOLGDGH� 3DUD IRQLD IRUDPOHYDGRV HP FRQWD RV IDWRUHV FDUDFWHU��VWLFRV GD YR] H GR RXYLGR KXPDQR� LQWHOLJLELOLGDGH H HQ�HUJLD GD YR]� 'HVVD IRUPD IRL HVFROKLGD D IDL[D GH IUHT¦XAHQFLD HQWUH ��� +] H ���� +] SDUDFRPXQLFD�FaRHV WHOHIARQLFDV� 3DUD WUDQVPLVVaDR GH P�XVLFD� D IDL[D YDL GH �� D ����� +]�$ HQHUJLD DF�XVWLFD SURGX]LGD SHOD YR] �H WUDQVIRUPDGD HP HQHUJLD HO�HWULFD SRU LQWHUP�HGLR

GH XP PLFURIRQH� 3DUD D WUDQVIRUPD�FaDR GD HQHUJLD HO�HWULFD HP HQHUJLD DF�XVWLFD JHUDOPHQWHXWLOL]DP�VH F�DSVXODV PDJQ�HWLFDV H GLQADPLFDV�$ OLJD�FaDR WHOHIARQLFD HOHPHQWDU� HQWUH GXDV SHVVRDV� GLJDPRV $ H %� FRQVLVWH GH GRLV DSDUHOKRV

WHOHIARQLFRV LQWHUOLJDGRV SRU XP SDU GH �RV HP TXH D GLVWADQFLD HQWUH RV DSDUHOKRV �H SHTXHQD�1D UHDOLGDGH D OLJD�FaDR �H XP SRXFR PDLV FRPSOH[D� SRLV R LQWHUORFXWRU $ GHYHULD WHU GRLV

FRQGXWRUHV OLJDQGR VXD F�DSVXOD WUDQVPLVVRUD FRP D UHFHSWRUD GH %� H YLFH�YHUVD�3RU�HP� HVVD OLJD�FaDR HQYROYH VRPHQWH D QHFHVVLGDGH GH FRPXQLFD�FaDR HQWUH GXDV SHVVRDV� 6H

R LQWHUORFXWRU $ GHVHMD VH FRPXQLFDU FRP RXWUDV SHVVRDV� R Q�XPHUR GH FRQGXWRUHV LULD FUHVFHUPXLWR� &RPR SRGHPRV SHUFHEHU� D TXDQWLGDGH GH FRQGXWRUHV SDUD XP Q�XPHUR JUDQGH GHOLJD�FaRHV� WRUQD R VLVWHPD HFRQRPLFDPHQWH LQYL�DYHO� 'HVVD IRUPD� SDUD VROXFLRQDU HVVH SUREOHPD�RV LQWHUORFXWRUHV� FKDPDGRV DVVLQDQWHV� HVWaDR OLJDGRV D XP FHQWUR WHOHIARQLFR RQGH �H H[HFXWDGDD LQWHUOLJD�FaDR HQWUH RV DVVLQDQWHV TXH VH GHVHMDP FRPXQLFDU� RSHUD�FaDR FKDPDGD GH FRPXWD�FaDRWHOHIARQLFD�

Page 6: Analise de Sinais

$JRUD TXH M�D GLVFXWLPRV RV FRQFHLWRV E�DVLFRV GH FRPXQLFD�FaDR WHOHIARQLFD GHVHMDPRV VDEHUFRPR� DWUDY�HV GH XP PHVPR SDU GH �RV� Y�DULDV SHVVRDV SRGHP VH FRPXQLFDU� $ W�HFQLFD D VHUGLVFXWLGD �H D PXOWLSOH[D�FaDR TXH SRGH VHU WDQWR DQDO�RJLFD FRPR GLJLWDO H VHU�D PHOKRU GLVFXWLGDQR �XOWLPR FDS��WXOR� DS�RV WHUPRV HVWXGDGR FRQFHLWRV E�DVLFRV GH VLQDLV H UHOD�FaDR HQWUH R GRP��QLRGR WHPSR H GD IUHT¦XAHQFLD�8PD RXWUD XWLOL]D�FaDR GH $Q�DOLVH H 3URFHVVDPHQWR GH 6LQDLV HVW�D OLJDGD D YLEUD�FaRHV PHFADQL�

FDV� $ DQ�DOLVH GH YLEUD�FaRHV HP P�DTXLQDV �H FDUDFWHUL]DGD SRU XP Q�XPHUR GH �DUHDV GLVWLQWDV GHDSOLFD�FaRHV� 'H PRGR JHUDO� D DQ�DOLVH GH YLEUD�FaRHV HP P�DTXLQDV YLVD XP GRV VHJXLQWHV REMHWLYRV� SHVTXLVD H GHVHQYROYLPHQWR GH P�DTXLQDV� FRQWUROH GH SURGX�FaDR H GH TXDOLGDGH H PDQXWHQ�FaDRH PRQLWRUDPHQWR GDV P�DTXLQDV HP VHUYL�FR�$ LPSOHPHQWD�FaDR GD DQ�DOLVH GH YLEUD�FaRHV HP P�DTXLQDV �H IHLWD DWUDY�HV GH LQVWUXPHQWRV GH

DQ�DOLVHV FKDPDGRV GH $QDOLVDGRUHV 'LQADPLFRV GH VLQDLV� $V YLEUD�FaRHV PHFADQLFDV VaDR FRPEL�QD�FaRHV GH VLQDLV FDXVDGRV SRU XPD JUDQGH YDULHGDGH GH IRQWHV LQWHUQDV GH YLEUD�FaDR� FRPR SRUH[HPSOR� GHVEDODQFHDPHQWR GR URWRU GH XPD P�DTXLQD URWDWLYD� RX GHIHLWR HP URODPHQWRV� HQWUHRXWURV� $S�RV D FRQYHUVaDR GR PRYLPHQWR PHFADQLFR HP VLQDO HO�HWULFR� DWUDY�HV GH XP GLVSRVLWLYRFKDPDGR GH WUDQVGXWRU SRGHPRV HVWXGDU HVVH VLQDO� YLVDQGR� SRU H[HPSOR� RV REMHWLYRV� UH�GX]LU RV GDGRV GH YLEUD�FaDR D XPD PDQHLUD I�DFLO GH VHU LQWHUSUHWDGD� SUHYHU SRVV��YHLV IDOKDV QRIXQFLRQDPHQWR GD P�DTXLQD H YHUL�FDU VH K�D FKRTXH HQWUH FRPSRQHQWHV GD P�DTXLQD�1R VHJXQGR FDS��WXOR HVWXGDUHPRV VLQDLV FRQW��QXRV QR WHPSR� 7UDWDUHPRV GD 6�HULH H GD

7UDQVIRUPDGD GH )RXULHU H PRVWUDUHPRV DOJXQV H[HPSORV� 'HSRLV GLVFXWLPRV VREUH �OWURVDQDO�RJLFRV H VXDV )XQ�FaRHV 5HVSRVWD HP )UHT¦XAHQFLD �)5)�� 1R WHUFHLUR FDS��WXOR WUDWDPRV GHVLQDLV GLJLWDLV� (VWXGDPRV QHVVHV FDS��WXOR D 7UDQVIRUPDGD GH )RXULHU 'LVFUHWD� D 6�HULH 'LVFUH�WD GH )RXULHU H D 7UDQVIRUPDGD 'LVFUHWD GH )RXULHU� 'LVFXWLPRV RV SUREOHPDV GH YD]DPHQWR�/HDNDJH� PDVFDUDPHQWR� $OLDVLQJ� H WDPE�HP D XWLOL]D�FaDR GH MDQHODV WHPSRUDLV� )LQDOPHQWH QRTXDUWR FDS��WXOR HVWXGDPRV XP SRXFR PDLV D PXOWLSOH[D�FaDR H DSOLFD�FaRHV �D (QJHQKDULD 0HFADQLFD�

Page 7: Analise de Sinais

&DS��WXOR �

6LQDLV &RQW��QXRV QR WHPSR

��� ,QWURGX�FaDR

'H PRGR JHUDO� XP VLQDO �H XPD JUDQGH]D I��VLFD YDUL�DYHO QR WHPSR� WDO FRPR WHQVaDR� FRUUHQWH�DFHOHUD�FaDR GH XP SRQWR GH XP FRUSR� SUHVVaDR QXP SRQWR GR HVSD�FR� S+ QXP SRQWR GH XPDVROX�FaDR� FRU QXP SL[HO GH XPD WHOD GH 79���� H TXH FRQW�HP DOJXP WLSR GH LQIRUPD�FaDR� JHUDO�PHQWH VREUH R HVWDGR RX FRPSRUWDPHQWR GH XP VLVWHPD I��VLFR� 2V VLQDLV VaDR UHSUHVHQWDGRVPDWHPDWLFDPHQWH SRU XPD IXQ�FaDR GH XPD RX PDLV YDUL�DYHLV� 7UDWDUHPRV DSHQDV GH IXQ�FaRHVGH XPD YDUL�DYHO� $ YDUL�DYHO FRQVLGHUDGD SRGH VHU FRQW��QXD RX GLVFUHWD� H FKDPDUHPRV GHVLQDLV FRQW��QXRV QR WHPSR TXDQGR D YDUL�DYHO IRU GH�QLGD SDUD XP LQWHUYDOR FRQW��QXR GH WHPSR�0XLWDV YH]HV �H LPSRUWDQWH TXH DQDOLVHPRV R VLQDO� QaDR QR GRP��QLR GR WHPSR PDV QR GRP��QLRGD IUHT¦XAHQFLD� (VWULWDPHQWH IDODQGR� LPDJLQDPRV XPD IXQ�FaDR WHPSRUDO FRPR VHQGR FRPSRVWDGH Y�DULDV FRPSRQHQWHV GH IUHT¦XAHQFLD� &RQVHT¦XHQWHPHQWH� HQTXDQWR R VLQDO H[LVWH �VLFDPHQWHQR GRP��QLR GR WHPSR� SRGHUHPRV D�UPDU TXH HOH FRQVLVWH GHVVDV FRPSRQHQWHV QR GRP��QLR GDIUHT¦XAHQFLD� $ DQ�DOLVH GRV VLQDLV QR GRP��QLR GD IUHT¦XAHQFLD VHU�D IHLWD SRU LQWHUP�HGLR GD DQ�DOLVHGH )RXULHU� EDVHDGD QDV V�HULHV H WUDQVIRUPDGDV GH )RXULHU�(VWH FDS��WXOR �H GHYRWDGR D XPD UHYLVaDR GD DQ�DOLVH GH )RXULHU H D HVWXGDU FRPR XP VLQDO QR

GRP��QLR GR WHPSR SRGH VHU UHSUHVHQWDGR QR GRP��QLR GD IUHT¦XAHQFLD�

��� $Q�DOLVH GH )RXULHU

����� 6�HULH GH )RXULHU

&RQVLGHUHPRV I � ,5 � ,5 XPD IXQ�FaDR TXH VDWLVID] DV VHJXLQWHV FRQGL�FaRHV�

�L� I �H SHUL�RGLFD GH SHU��RGR 7�

�LL� I �H GH FODVVH &� SRU SDUWHV HP �W�� W� � 7 ��

Page 8: Analise de Sinais

(P WRGR SRQWR GH FRQWLQXLGDGH GH I � SRGHPRV HVFUHYHU�

I�W� DR��

�;Q �

>DQFRV��Q�W

7� � EQVHQ�

�Q�W

7�@ �����

RQGH �!!!!!!!!!!!�!!!!!!!!!!!�

DR �

7

= WR�7

WR

I�W�GW �

DQ �

7

= WR�7

WR

I �W�FRV��Q�W

7�GW H

EQ �

7

= WR�7

WR

I �W�VHQ��Q�W

7�GW�

�����

1XP SRQWR GH GHVFRQWLQXLGDGH R ODGR HVTXHUGR GH ��� �H VXEVWLWX��GR SRU �

OLP��R�

�>I�W� �� � I�W� ��@� �����

$ V�HULH ��� FRP FRH�FLHQWHV GDGRV SRU ��� �H FKDPDGD GH V�HULH GH )RXULHU GH I QD IRUPD

WULJRQRP�HWULFD�$V FRQGL�FaRHV �L� H �LL� VaDR PXLWDV YH]HV FKDPDGDV FRQGL�FaRHV GH 'LULFKOHW H VaDR VX�FLHQWHV

�PDV QaDR QHFHVV�DULDV� SDUD D FRQYHUJAHQFLD GD V�HULH GH )RXULHU�(P QRWD�FaDR H[SRQHQFLDO �RX FRPSOH[D� D V�HULH GH )RXULHU GH I SRGH VHU HVFULWD FRPR

I�W�

��;Q ��

)QHM �Q�W

7 �����

RQGH

)Q �

7

= WR�7

WR

I�W�H�M�Q�W7 GW� �����

)D]HQGR �R ��

7� WHPRV

)Q �

7

= WR�7

WR

I �W�H�MQ�RWGW� �����

2EVHUYDPRV TXH� FRQKHFLGR I � RV FRH�FLHQWHV GH ��� SRGHP VHU FDOFXODGRV H� UHFLSURFDPHQWH�FRQKHFLGRV RV FRH�FLHQWHV I)QJQ�==� I SRGH VHU VLQWHWL]DGD SRU ���� 'HVVD IRUPD� I H I)QJQ�==IRUQHFHP D PHVPD LQIRUPD�FaDR� 0XGD V�R R SRQWR GH YLVWD � XP WHPSRUDO� RXWUR IUHT¦XHQFLDO�

Page 9: Analise de Sinais

)LJXUD ���� ([HPSOR GH XPD IXQ�FaDR SHUL�RGLFD�

([HPSOR

&RQVLGHUHPRV D IXQ�FaDR I � ,5 � ,5� SHUL�RGLFD GH SHU��RGR �� GDGD SRU

I�W� W � � � W � �� �����

2 JU�D�FR GHVVD IXQ�FaDR �H PRVWUDGR QD �JXUD ����

6�HULH GH )RXULHU GH I QD IRUPD WULJRQRP�HWULFD

&�DOFXOR GRV FRH�FLHQWHV

DR �

7

= �

I�W�GW

= �

WGW ��

DQ �

7

= �

I �W�FRV��Q�W

7�GW

= �

WFRV��Q�W

7�GW

= �

WFRV�Q�W�GW ��

EQ �

7

= �

I�W�VHQ��Q�W

7�GW

= �

WVHQ��Q�W

7�GW

= �

WVHQ�Q�W�GW ��

Q��

$VVLP�

I�W� � �

��;Q �

��

Q�VHQ�Q�W��

6�HULH GH )RXULHU GH I QD IRUPD H[SRQHQFLDO

&�DOFXOR GRV FRH�FLHQWHV

)Q �

7

= �

I �W�H�M�Q�W7 GW

= �

WH�MQ�WGW �

Q�M � Q � �

H

)R �

7

= �

I �W�GW �

= �

WGW ��

Page 10: Analise de Sinais

$VVLP�

)Q

�� � Q ��

Q�M � Q � ��

7HPRV�

I �W� � �

��;Q ��

Q�MHMQ�W � Q � ��

����� 2 HVSHFWUR FRPSOH[R GH )RXULHU

$ H[SDQVaDR HP V�HULH GH )RXULHU GH XPD IXQ�FaDR SHUL�RGLFD �H D GHFRPSRVL�FaDR GD IXQ�FaDR HPWHUPRV GDV VXDV FRPSRQHQWHV GH Y�DULDV IUHT¦XAHQFLDV� 8PD IXQ�FaDR SHUL�RGLFD GH SHU��RGR 7 WHPFRPSRQHQWHV GH IUHT¦XAHQFLDV GDGDV SRU Q�� RQGH � �

7H Q � ==� (P WHUPRV GDV IUHT¦XAHQFLDV

DQJXODUHV �RX SXOVD�FaRHV�� DV FRPSRQHQWHV VaDR GDGDV SRU Q�R RQGH �R ��7 ��� H Q � ==�

&KDPDPRV GH HVSHFWUR GD IXQ�FaDR I R FRQMXQWR GH WRGRV RV FRH�FLHQWHV GH )RXULHU )Q � Q �==� 6H HVSHFL�FDUPRV I SRGHPRV HQFRQWUDU VHX HVSHFWUR� 5HFLSURFDPHQWH� VH R HVSHFWUR IRUFRQKHFLGR SRGHPRV HQFRQWUDU D IXQ�FaDR I FRUUHVSRQGHQWH�3RUWDQWR� SRGHPRV HVSHFL�FDU I GH GXDV IRUPDV� D UHSUHVHQWD�FaDR QR GRP��QLR GR WHPSR�

RQGH I �H H[SUHVVD FRPR IXQ�FaDR GR WHPSR H D UHSUHVHQWD�FaDR QR GRP��QLR GD IUHT¦XAHQFLD� RQGH RHVSHFWUR �H HVSHFL�FDGR�2EVHUYDPRV TXH R HVSHFWUR GH XPD IXQ�FaDR SHUL�RGLFD QaDR �H XPD FXUYD FRQW��QXD� PDV H[LVWH

DSHQDV SDUD YDORUHV GLVFUHWRV GH �� P�XOWLSORV GH XPD IUHT¦XAHQFLD E�DVLFD �R ��7� � Q�R� Q �

==�� 2V FRH�FLHQWHV )Q VaDR FRPSOH[RV H� VaDR GHVFULWRV SRU XPD PDJQLWXGH H XPD IDVH�&RQVLGHUHPRV D IXQ�FaDR GDGD SRU ���� 7HPRV TXH

)Q

�� � Q ��

Q�M � Q � ��

$VVLP�

M )Q M

���� � Q ��

M Q� M� Q � �

H ?)Q

�!!�!!�� � Q ��

�� Q SRVLWLYR

��

�� Q QHJDWLYR�

)D]HQGR � Q�� Q��

7 Q�� WHPRV �

M )Q M

���� � � ��

M � M� � � �

H ?)Q

�!!�!!�� � � ��

�� � SRVLWLYR

��

�� � QHJDWLYR�

Page 11: Analise de Sinais

)LJXUD ���� $PSOLWXGH H IDVH GRV FRH�FLHQWHV GD V�HULH GH )RXULHU�

)LJXUD ���� )XQ�FaDR SRUWD SHUL�RGLFD�

&RQVWUX��PRV RV JU�D�FRV GH M )Q M H ?)Q� HP WHUPRV GD IUHT¦XAHQFLD �� DSUHVHQWDQGR�RV QD�JXUD ����&RQVLGHUHPRV� DJRUD� D IXQ�FaDR I � ,5 � ,5� SHUL�RGLFD GH SHU��RGR 7 � GDGD SRU �

I �W�

��� �¡

�� W � ¡

�� ¡�� W � 7 � ¡

��

�����

(VVD IXQ�FaDR �H FRQKHFLGD FRPR SRUWD �JDWH� SHUL�RGLFD� 0RVWUDPRV R VHX JU�D�FR QD �JXUD ����2V FRH�FLHQWHV )Q GD V�HULH GH )RXULHU QD IRUPD H[SRQHQFLDO VaDR GDGRV SRU�

)Q �

7

= 7�¡ �

�¡ �

I �W�H�M�Q�W7 GW

7

= ¡ �

�¡ �

H�MQ�RWGW

¡

7>VHQ�Q�R¡ ��

Q�R¡ �@ � Q � ��

�����

H

)R �

7

= 7� ¡�

� ¡�

I�W�GW �

7

= ¡�

� ¡�

GW ¡

7� ������

'HVVD IRUPD�

)Q

�!�!�

¡

7� Q �

¡

7

�VHQ�Q��¡ ��

Q��¡ �

�� Q � ��

������

��

Page 12: Analise de Sinais

)LJXUD ���� 5HSUHVHQWD�FaDR GR HVSHFWUR GD IXQ�FaDR SRUWD SHUL�RGLFD�

'H�QLQGR D IXQ�FaDR 6D� FRQKHFLGD FRPR IXQ�FaDR GH DPRVWUDJHP� SRU

6D � ,5 � ,5

W�

�� � W �VHQW

W� W � �

������

H ID]HQGR � ��

7� WHPRV�

)Q ¡

76D�

Q�¡

7�� ������

$ IUHT¦XAHQFLD IXQGDPHQWDO �H �R ��

7� 6H � Q�R� HQWaDR

)Q ¡

76D�

�¡

��� ������

0RVWUDPRV R JU�D�FR GH )Q HP WHUPRV GD IUHT¦XAHQFLD � QD �JXUD ����3RGHPRV REVHUYDU TXH �D PHGLGD TXH 7 DXPHQWD� D IUHT¦XAHQFLD IXQGDPHQWDO ��

7VH WRUQD

PHQRU H R HVSHFWUR WRUQD�VH� HQWaDR� PDLV GHQVR� ,QWXLWLYDPHQWH� VRPRV OHYDGRV D SHQVDU TXHTXDQGR 7 WHQGH DR LQ�QLWR WHPRV� QR GRP��QLR GR WHPSR� XP �XQLFR SXOVR UHWDQJXODU GH ODUJXUD¡ H QR GRP��QLR GD IUHT¦XAHQFLD XP HVSHFWUR FRQW��QXR FRP FRPSRQHQWHV HP WRGDV DV IUHT¦XAHQFLDV�,VVR SRGH VHU SURYDGRU ULJRURVDPHQWH�

��� 7UDQVIRUPDGD GH )RXULHU

����� ,QWURGX�FaDR

4XDQGR R VLQDO FRP R TXDO HVWDPRV WUDEDOKDQGR IRU QaDR�SHUL�RGLFR HOH SRGH VHU H[SUHVVR FRPRXPD VRPD FRQW��QXD �LQWHJUDO� GH VLQDLV H[SRQHQFLDLV� HP FRQWUDVWH FRP VLQDLV SHUL�RGLFRV� TXHSRGHP VHU UHSUHVHQWDGRV SRU XPD VRPD GLVFUHWD GH VLQDLV H[SRQHQFLDLV �V�HULH GH )RXULHU � FRPRM�D YLVWR�� 9HMDPRV XPD PRWLYD�FaDR SDUD HVVD D�UPD�FaDR�

��

Page 13: Analise de Sinais

����� $ WUDQVIRUPDGD GH )RXULHU

&RQVLGHUHPRV XPD IXQ�FaDR I FRPR PRVWUD D �JXUD ��� �

)LJXUD ���� *U�D�FR GH XPD IXQ�FaDR I �

&RQVWUX��PRV XPD QRYD IXQ�FaDR� SHUL�RGLFD� I7 FRP SHU��RGR 7� GH DFRUGR FRP D �JXUD ����

)LJXUD ���� &RQVWUX�FaDR GH XPD IXQ�FaDR SHUL�RGLFD D SDUWLU GH XPD IXQ�FaDR I GDGD�

7RUQDPRV R SHU��RGR 7 JUDQGH R VX�FLHQWH SDUD TXH QaDR KDMD VXSHUSRVL�FaDR HQWUH RV SXOVRVGD IRUPD GH I � (VVD QRYD IXQ�FaDR I7 �H XPD IXQ�FaDR SHUL�RGLFD H SRGH VHU UHSUHVHQWDGD SRU XPDV�HULH H[SRQHQFLDO GH )RXULHU�1XPD WRSRORJLD DGHTXDGD� TXDQGR 7 � �� I7 � I � 'HVVH PRGR� D V�HULH GH )RXULHU TXH

UHSUHVHQWD I7 WDPE�HP UHSUHVHQWDU�D I �$ V�HULH GH )RXULHU GH I7 �H GDGD SRU

I7 �W�

��;Q ��

)Q HMQ�RW ������

RQGH �R ��7H

)Q �

7

= 7 �

�7 �

I7 �W�H�MQ�RWGW� ������

)D�FDPRV Q�R �Q� $VVLP� )Q )Q��Q��&RQVLGHUHPRV 7)Q��Q� ) ��Q�� TXH �H REYLDPHQWH OLPLWDGR �SRU FRQVWUX�FaDR�� 7HPRV�

I7 �W� �

7

��;Q ��

) ��Q�HM�QW� ������

��

Page 14: Analise de Sinais

6XEVWLWXLQGR 7 ��

�R

HP ���� WHPRV

I7 �W� �

��

��;Q ��

) ��Q�HM�QW�R� ������

4XDQGR 7 �� � I7 � I H REWHPRV �

I �W� �

��

= ��

��

) ���HM�WG� ������

H

) ���

= ��

��

I�W�H�M�WGW� ������

2 HVSHFWUR GH I VHU�D FRQW��QXR H UHSUHVHQWDGR SHOD IXQ�FaDR ) �$ HTXD�FaDR ���� �H FRQKHFLGD FRPR WUDQVIRUPDGD �GLUHWD� GH )RXULHU GH I H D HTXD�FaDR ����

FRPR WUDQVIRUPDGD LQYHUVD GH )RXULHU GH ) �6LPEROLFDPHQWH SRGHPRV HVFUHYHU

) ��� ) >I �W�@ ������

H

I�W� )��>) ���@� ������

)D]HQGR � ��� HP ���� H ���� FKHJDPRV D XPD IRUPXOD�FaDR VLP�HWULFD� R IDWRU �� QaDR DSDUHFH�

I�W�

= ��

��

A)���HM���WG� ������

H

A)���

= ��

��

I�W�H�M���WGW� ������

����� ([LVWAHQFLD GD WUDQVIRUPDGD GH )RXULHU

2 HVSD�FR /��5�

2 HVSD�FR /��5� �H R HVSD�FR GH WRGDV DV IXQ�FaRHV I � ,5� & WDLV TXH=5

NINGW ��� ������

��

Page 15: Analise de Sinais

2 HVSD�FR /��5�

2 HVSD�FR /��5� �H R HVSD�FR GH WRGDV DV IXQ�FaRHV I � ,5 � &� WDLV TXH=5

NIN�GW ��� ������

7HRUHPD�

6H D IXQ�FaDR I SHUWHQFH DR HVSD�FR /��5� HQWaDR D WUDQVIRUPDGD GH I H[LVWH�

7HRUHPD�

6H D IXQ�FaDR I SHUWHQFH DR HVSD�FR /��5� HQWaDR D WUDQVIRUPDGD )� GH I � H[LVWH H ) � /��5��

([HPSORV

�� &RQVLGHUHPRV D IXQ�FaDR *¡ �FRQKHFLGD FRPR IXQ�FaDR SRUWD� GH�QLGD SRU

*¡ �W�

��� M W M� ¡

�� M W M! ¡��

������

)LJXUD ���� IXQ�FaDR SRUWD�

&DOFXODQGR D WUDQVIRUPDGD GH )RXULHU GHVVD IXQ�FaDR� WHPRV �

) ��� )I*¡�W�J

= ¡ �

�¡ �

H�M�WGW ¡6HQ��¡

��

�¡�

� � � �� ������

3DUD � � WHPRV �

)I*¡ �W�J M� �

= ¡ �

�¡ �

GW ¡�

/RJR�

)I*¡�W�J ¡6D��¡

���

$ �JXUD ��� PRVWUD D UHSUHVHQWD�FaDR GR HVSHFWUR GD IXQ�FaDR SRUWD� 1HVWH FDVR ) �H XPDIXQ�FaDR UHDO�

��

Page 16: Analise de Sinais

)LJXUD ���� 5HSUHVHQWD�FaDR GR HVSHFWUR GD IXQ�FaDR SRUWD�

�� &RQVLGHUHPRV D IXQ�FaDR I � ,5 � ,5 GH�QLGD SRU

I�W� H�MWM�

&DOFXODQGR VXD WUDQVIRUPDGD GH )RXULHU� REWHPRV �

)IH�MWMJ

= ��

��

H�MWMH�M�WGW �

� � ���

�� &RQVLGHUHPRV D IXQ�FaDR I � ,5 � ,5 GH�QLGD SRU

I �W�

�H�W� W ! ��� W � ��

$ VXD WUDQVIRUPDGD GH )RXULHU �H GDGD SRU�

)II�W�J

= ��

H�WH�M�WGW �

� � M��

�� &RQVLGHUHPRV D IXQ�FaDR *¡ � ,5 � ,5 GH�QLGD SRU

*¡ ���

��� M � M� ¡ ��� M � M! ¡ ��

'HVHMDPRV FDOFXODU VXD WUDQIRUPDGD GH )RXULHU LQYHUVD� $VVLP�

)��I*¡ ���J �

��

= ¡ �

�¡ �

HM�WG� ¡

��

6HQ� W¡��

W¡�

� W � ��

3DUD W � WHPRV �

)��I*¡���J MW � �

��

= ¡ �

�¡ �

G� �

��¡�

$VVLP�

)��I*¡���J ¡

��6D�

¡ W

���

/RJR� D WUDQVIRUPDGD GH I�W� 6D� W¡�� �H LJXDO D ��

¡*¡���� (P SDUWLFXODU�

)I6D�W�J �*�����

��

Page 17: Analise de Sinais

����� 3URSULHGDGHV GD WUDQVIRUPDGD GH )RXULHU

$V SURSULHGDGHV GD WUDQVIRUPDGD GH )RXULHU HVWaDR DSUHVHQWDGDV QD VHJXLQWH WDEHOD ����

)81&� a$2 75$16)250$'$

I �W� ) �Z�

6LPHWULD ) �W� ��I ��Z�

/LQHDULGDGH D�I��W� � I��W� D�)��Z� � D�)��Z�

0XGDQ�FD GH HVFDOD I �DW��

M D M)�ZD

�I �W�HMZ�W ) �Z � Z��

7UDQVOD�FaDR HP IUHT¦XAHQFLD I �W� FRV�Z�W��

�>) �Z � Z�� � ) �Z � Z��@

I�W� VHQ�Z�W�M

�>) �Z � Z��� ) �Z � Z��@

7UDQVOD�FaDR QR WHPSR I �W� W�� H�MZW�) �Z�

'XDOLGDGH ) �W� I�Z�

&RQMXJD�FaDR I ��W� ) ���Z�

'LIHUHQFLD�FaDR QR WHPSRGQI

GWQ�MZ�Q) �Z�

,QWHJUD�FaDR QR WHPSR

= W

��

I�¡ �G¡�

MZ) �Z�

'LIHUHQFLD�FaDR QD IUHT¦XAHQFLD ��MW�QI�W�GQI

GZQ

I�W� UHDO ) �Z� ) ���Z�I�W� UHDO 5I) �Z�J 5I) ���Z�JI�W� UHDO ,I) �Z�J �,I) ���Z�J

6LPHWULD I�W� UHDO M) �Z�M M) ��Z�MI�W� UHDO ?) �Z� �?) ��Z�

I �W� UHDO� SDU HP W ) �Z� UHDO� SDU HP ZI �W� UHDO� LPSDU HP W ) �Z� LPDJLQ�DULD� LPSDU HP Z

7DEHOD ���� 3URSULHGDGHV GD WUDQVIRUPDGD GH )RXULHU

��� &RQYROX�FaDR

����� ,QWURGX�FaDR

'DGDV GXDV IXQ�FaRHV I� H I� IRUPDPRV D LQWHJUDO

I �W�

= ��

��

I��¡�I��W� ¡�G¡� ������

��

Page 18: Analise de Sinais

(VVD LQWHJUDO GH�QH D FRQYROX�FaDR GDV IXQ�FaRHV I� H I�� 6LPEROLFDPHQWH HVFUHYHPRV

I I� � I��

9HUHPRV TXH FRQYROX�FaDR HVW�D LQWLPDPHQWH DVVRFLDGR D SURGXWR�

����� 3URSULHGDGHV

&RPXWDWLYLGDGH

I� � I� I� � I�� ������

'LVWULEXWLYLGDGH

I� � >I� � I�@ I� � I� � I� � I�� ������

$VVRFLDWLYLGDGH

I� � >I� � I�@ >I� � I�@ � I�� ������

7HRUHPD GD FRQYROX�FaDR QR WHPSR

6H I��W�� )���� H I��W�� )���� HQWaDR

I� � I� � )�)�� ������

6H I��W�� A)���� H I��W�� A)���� HQWaDR

I� � I� � A)�A)�� ������

7HRUHPD GD FRQYROX�FaDR QD IUHT¦XAHQFLD

6H I��W�� )���� H I��W�� )���� HQWaDR

I�I� ��

��>)� � )�@� ������

6H I��W�� A)���� H I��W�� A)���� HQWaDR

I�I� � A)� � A)�� ������

$SUHVHQWDPRV QD WDEHOD ��� DOJXPDV WUDQVIRUPDGDV TXH HQYROYHP R LPSXOVR XQLW�DULR �'HOWDGH 'LUDF� GHQRWDGR SRU ��0RVWUDPRV� QD WDEHOD ��� DV RUGHQV GH JUDQGH]D GH DOJXQV VLQDLV�

��

Page 19: Analise de Sinais

)81&� a$2 75$16)250$'$

I�W� ) �Z�

$ ��$�

HM��W ����� � ���

FRV���W� �>��� � ��� � ��� � ���@

I�W� VHQ���W� M�>��� � ���� ��� � ���@

7DEHOD ���� $OJXPDV WUDQIRUPDGDV TXH HQYROYHP R LPSXOVR XQLW�DULR�

7,32 '( 6,1$/ %$1'$ (0 +]

FRUUHQWH GRP�HVWLFD ��

TXDUW]R GH UHO�RJLR ���

RQGD GH UDGDU ����

YLEUD�FaDR GH XP �DWRPR GH &�HVLR ����

21'$6 +(57=,$1$6�

PXLWR ORQJDV �WHO�HJUDIR� �� � � ��� D �� ���

ORQJDV �U�DGLR� �� ��� D �� ���

P�HGLDV �U�DGLR� �� ��� D �� ���

FXUWDV �U�DGLR� �� ��� D �� ���

P�HWULFDV �WHOHYLVaDR� �� ��� D �� ���

FHQWLP�HWULFDV �UDGDU� �� ��� D ����

OX] YLV��YHO �� � � ���� D �� �� ����

7DEHOD ���� 2UGHQV GH JUDQGH]D GH VLQDLV�

��

Page 20: Analise de Sinais

&DS��WXOR �

6LQDLV GLVFUHWRV QR WHPSR

��� 6HT¦XAHQFLDV

6LQDLV GLVFUHWRV QR WHPSR VaDR UHSUHVHQWDGRV PDWHPDWLFDPHQWH FRPR VHT¦XAHQFLDV GH Q�XPHURV� [�FXMR Q��HVLPR Q�XPHUR �H [>Q@� H QRWDPRV SRU [ I[>Q@J � Q � ==� 3RGH VHU TXH XPD VHT¦XAHQFLDGHVWH WLSR RULJLQRX�VH GD DPRVWUDJHP GH XP VLQDO FRQW��QXR� 6H R VLQDO FRQW��QXR IRU [D�W�SRGHPRV GL]HU TXH [>Q@ [D�Q7 � � Q � ==� 7 �H FKDPDGR GH SHU��RGR GH DPRVWUDJHP H �

7�H D

IUHT¦XAHQFLD GH DPRVWUDJHP� 8VDUHPRV� DV YH]HV� D QRWD�FaDR [>Q@ SDUD QRV UHIHULU �D VHT¦XAHQFLD�

��� 2SHUD�FaRHV FRP VHT¦XAHQFLDV H VHT¦XAHQFLDV E�DVLFDV

����� 2SHUD�FaRHV FRP VHT¦XAHQFLDV

2 SURGXWR H D VRPD GH GXDV VHT¦XAHQFLDV [>Q@ H \>Q@ VaDR GH�QLGRV FRPR R SURGXWR H D VRPD GHFDGD HOHPHQWR GH [>Q@ SRU FDGD HOHPHQWR GH \>Q@� $ PXOWLSOLFD�FaDR GH XPD VHT¦XAHQFLD [>Q@ SRUXP Q�XPHUR � �H GH�QLGD FRPR D PXOWLSOLFD�FaDR GH FDGD HOHPHQWR GH [>Q@ SRU ��

����� 6HT¦XAHQFLDV E�DVLFDV

,PSXOVR XQLW�DULR

$ VHT¦XAHQFLD LPSXOVR XQLW�DULR �H GH�QLGD SRU

�>Q@

�� � Q � �� � Q ��

�����

4XDOTXHU VHT¦XAHQFLD SRGH VHU H[SUHVVD SRU

[>Q@

��;N ��

[>N@�>Q � N@� �����

��

Page 21: Analise de Sinais

'HJUDX 8QLW�DULR

$ VHT¦XAHQFLD GHJUDX XQLW�DULR �H GH�QLGD SRU

X>Q@

��� Q � ��� Q � ��

�����

3RGHPRV HVFUHYHU

X>Q@

Q;N ��

�>N@ �����

RX

X>Q@

�;N �

�>Q� N@� �����

6HT¦XAHQFLD ([SRQHQFLDO

'H�QLPRV D VHT¦XAHQFLD H[SRQHQFLDO SRU

[>Q@ $�Q� �����

RQGH $ H � VaDR FRQVWDQWHV�

6HT¦XAHQFLD 6HQRLGDO

8PD VHT¦XAHQFLD VHQRLGDO WHP D IRUPD

[>Q@ $FRV��RQ � £� � �����

RQGH $� �R H £ VaDR FRQVWDQWHV�

6HT¦XAHQFLD 3HUL�RGLFD

8PD VHT¦XAHQFLD SHUL�RGLFD �H DTXHOD QD TXDO

[>Q@ [>Q�1 @ � SDUD WRGR Q H 1 � ==� �����

'HYHPRV REVHUYDU TXH VHT¦XAHQFLDV VHQRLGDLV H H[SRQHQFLDLV QaDR VaDR QHFHVVDULDPHQWH SHUL�R�GLFDV�2EVHUYDPRV� SRU H[HPSOR� TXH D FRQGL�FaDR GH SHULRGLFLGDGH SDUD XP VLQDO VHQRLGDO �H REWLGD

GD VHJXLQWH IRUPD �

$FRV��RQ� £� $FRV��RQ� �R1 � £�� �����

5HTXHUHQGR TXH�

�R1 �N� � N � ==� ������

��

Page 22: Analise de Sinais

$QDORJDPHQWH� DV VHT¦XAHQFLDV H[SRQHQFLDLV FRPSOH[DV GD IRUPD &HM�RQ VHUaDR SHUL�RGLFDV VHHM�R�Q�1� HM�RQ� ,VWR V�R �H YHUGDGH VH �R1 �N�� &RQVHT¦XHQWHPHQWH� H[SRQHQFLDLV FRP�SOH[DV H VHT¦XAHQFLDV VHQRLGDLV QaDR VaDR QHFHVVDULDPHQWH SHUL�RGLFDV� GHSHQGHQGR GR YDORU GH �R �3RU H[HPSOR� SDUD �R

���� R PHQRU YDORU GH 1 TXH VDWLVID] ����� FRP N LQWHLUR� �H 1 � � FRUUHV�

SRQGHQGR D N �� � 3DUD �R �� QaDR H[LVWHP YDORUHV LQWHLURV GH 1 RX N TXH VDWLVID�FDP �����'R TXH IRL YLVWR� SDUD VLQDLV GLVFUHWRV� D LQWHUSUHWD�FaDR GR TXH VHMDP DOWDV H EDL[DV IUHT¦XAHQFLDV�H GLVWLQWD GR TXH IRL YLVWR TXDQGR WUDWDPRV GH VLQDLV VHQRLGDLV H H[SRQHQFLDLV FRPSOH[DV SDUDVLQDLV FRQW��QXRV� 3DUD XP VLQDO VHQRLGDO FRQW��QXR [�W� $FRV��RW � £�� �D PHGLGD TXH �R

FUHVFH� [�W� RVFLOD PDLV UDSLGDPHQWH� 3DUD XP VLQDO VHQRLGDO GLVFUHWR [>Q@ $FRV��RQ � £���D PHGLGD TXH �R YDULD GH �R � DW�H �R �� [>Q@ RVFLOD PDLV U�DSLGR� 0DV� �D PHGLGD TXH �R

YDULD GH �R � DW�H �R �� DV RVFLOD�FaRHV WRUQDP�VH PDLV OHQWDV� 'HVVD IRUPD� YDORUHV GH �R QDYL]LQKDQ�FD GH �R �N�� SDUD N � ==� VaDR GLWDV EDL[DV IUHT¦XAHQFLDV H YDORUHV GH �R QD YL]LQKDQ�FDGH �R ��N � ��� SDUD N � == VaDR GLWDV DOWDV IUHT¦XAHQFLDV�

��� 6LVWHPDV GLVFUHWRV QR WHPSR

����� ,QWURGX�FaDR

8P VLVWHPD GLVFUHWR QR WHPSR �H GH�QLGR PDWHPDWLFDPHQWH SRU XP RSHUDGRU TXH WUDQVIRUPDXPD VHT¦XAHQFLD GH HQWUDGD QXPD VHT¦XAHQFLD GH VD��GD�6H [ �H D VHT¦XAHQFLD GH HQWUDGD H \ D GH VD��GD H 7 R RSHUDGRU TXH UHSUHVHQWD R VLVWHPD� WHPRV

\ 7I[J� ������

&RPR H[HPSOR FRQVLGHUHPRV R FRQKHFLGR VLVWHPD LGHDO GH DWUDVR GH�QLGR SHOD HTXD�FaDR

\>Q@ [>Q� QG@ � Q � == ������

RQGH QG �H XP LQWHLUR �[R FKDPDGR GH DWUDVR GR VLVWHPD�

����� $OJXQV WLSRV GH VLVWHPDV

6LVWHPDV VHP PHP�RULD

8P VLVWHPD �H GLWR VHP PHP�RULD VH D VD��GD \>Q@ GHSHQGH VRPHQWH GD HQWUDGD [>Q@ SDUD R PHVPRYDORU GH Q�

6LVWHPDV /LQHDUHV

6H \� H \� VaDR DV UHVSRVWDV GH XP VLVWHPD TXDQGR [� H [� VaDR DV UHVSHFWLYDV HQWUDGDV HQWaDR RVLVWHPD �H GLWR OLQHDU VH H V�R VH

7ID�[� � D�[�J D�7I[�J� D�7I[�J� ������

��

Page 23: Analise de Sinais

6LVWHPDV LQYDULDQWHV QR WHPSR

8P VLVWHPD �H GLWR LQYDULDQWH QR WHPSR VH XP GHVORFDPHQWR QR WHPSR QD VHT¦XAHQFLD GH HQWUDGDFDXVD XP LJXDO GHVORFDPHQWR QR WHPSR QD VHT¦XAHQFLD GH VD��GD � LVWR �H� VH SDUD WRGR QR D VHT¦XAHQFLDGH HQWUDGD [�>Q@ [>Q � QR@ SURGX] XPD VHT¦XAHQFLD GH VD��GD \�>Q@ \>Q� QR@�

(VWDELOLGDGH

8P VLVWHPD �H GLWR HVW�DYHO VH H VRPHQWH VH WRGD VHT¦XAHQFLD GH HQWUDGD OLPLWDGD SURGX] XPDVHT¦XAHQFLD GH VD��GD WDPE�HP OLPLWDGD�$ HQWUDGD [ �H OLPLWDGD VH H[LVWLU XP YDORU SRVLWLYR �QLWR 0 WDO TXH

M [>Q@ M�0 SDUD WRGR Q� ������

(VWDELOLGDGH UHTXHU TXH SDUD WRGD HQWUDGD OLPLWDGD H[LVWD XP YDORU SRVLWLYR �QLWR 1 �[RWDO TXH

M \>Q@ M� 1 SDUD WRGR Q� ������

����� 6LVWHPDV /LQHDUHV ,QYDULDQWHV QR 7HPSR

8PD FODVVH LPSRUWDQWH GH VLVWHPDV FRQVLVWH GDTXHOHV TXH VaDR OLQHDUHV H LQYDULDQWHV QR WHPSR�&RQVLGHUH TXH KN>Q@ �H D UHVSRVWD GR VLVWHPD FXMD HQWUDGD �H �>Q� N@�&RQVLGHUHPRV � DJRUD� D HQWUDGD [� $VVLP� D VD��GD \ VHU�D GDGD SRU

\>Q@ 7I

��;N ��

[>N@�>Q� N@J� ������

'D FRQGL�FaDR GH OLQHDULGDGH� WHPRV

\>Q@

��;N ��

[>N@7I�>Q� N@J

��;N ��

[>N@KN>Q@� ������

$ SURSULHGDGH GH LQYDULADQFLD QR WHPSR LPSOLFD TXH VH K>Q@�UHVSRVWD DR LPSXOVR� �H D UHVSRVWDSDUD �>Q@ HQWaDR D UHVSRVWD SDUD �>Q� N@ �H K>Q� N@� $VVLP�

\>Q@

��;N ��

[>N@K>Q� N@

��;N ��

[>Q� N@K>Q@� ������

3RUWDQWR� XP VLVWHPD OLQHDU LQYDULDQWH QR WHPSR �DEUHYLDGR FRPR /,7� �H FRPSOHWDPHQWHFDUDFWHUL]DGR SRU VXD UHVSRVWD DR LPSXOVR�$ HTXD�FaDR ���� �H FKDPDGD GH FRQYROX�FaDR HQWUH [ H K H UHSUHVHQWDPRV QD IRUPD

\ [ � K� ������

��

Page 24: Analise de Sinais

����� 3URSULHGDGHV GH 6LVWHPDV /LQHDUHV ,QYDULDQWHV QR 7HPSR

&RPR WRGRV RV VLVWHPDV OLQHDUHV LQYDULDQWHV QR WHPSR VaDR GHVFULWRV SHOD RSHUD�FaDR GH FRQYROX�FaDR�DV SURSULHGDGHV GHVVD FODVVH GH VLVWHPDV VaDR GH�QLGDV SHODV SURSULHGDGHV GD FRQYROX�FaDR GLVFUHWDQR WHPSR�

&RPXWDWLYLGDGH

[ � K K � [� ������

'LVWULEXWLYLGDGH

[ � �K� � K�� [ � K� � [ � K�� ������

����� (TXD�FaRHV OLQHDUHV GH GLIHUHQ�FD GH FRH�FLHQWHV FRQVWDQWHV

8PD VXEFODVVH GH VLVWHPDV OLQHDUHV LQYDULDQWHV QR WHPSR FRQVLVWH GH VLVWHPDV QRV TXDLV DHQWUDGD H D VD��GD VDWLVID]HP XPD HTXD�FaDR GH GLIHUHQ�FD OLQHDU GH Q��HVLPD RUGHP GH FRH�FLHQWHVFRQVWDQWHV GD IRUPD

1;N �

DN\>Q � N@

0;O �

EO[>Q� O@� ������

&RPR H[HPSOR FRQVLGHUHPRV R VLVWHPD FRQKHFLGR FRPR DFXPXODGRU� QR TXDO D VD��GD QR LQVWDQWHQ �H LJXDO �D VRPD GD HQWUDGD QR LQVWDQWH Q H GR YDORU GD VD��GD QR LQVWDQWH DQWHULRU Q� ��

)LJXUD ���� 'LDJUDPD GH EORFR GH XPD HTXD�FaDR GH GLIHUHQ�FD UHFXUVLYD UHSUHVHQWDQGR XP DFX�PXODGRU�

$ HTXD�FaDR GH GLIHUHQ�FD TXH UHSUHVHQWD HVVH VLVWHPD �H GDGD SRU

\>Q@ \>Q� �@ � [>Q@� ������

��

Page 25: Analise de Sinais

����� 5HSUHVHQWD�FaDR QR GRP��QLR GD IUHT¦XAHQFLD GH VLQDLV GLVFUHWRV QRWHPSR

6HT¦XAHQFLDV H[SRQHQFLDLV FRPSOH[DV WAHP XP OXJDU GH GHVWDTXH QD UHSUHVHQWD�FaDR GH VLQDLV GLVFUH�WRV QR WHPSR� ,VWR GHYH�VH DR IDWR GH TXH H[SRQHQFLDLV FRPSOH[DV VaDR DXWRIXQ�FaRHV GH VLVWHPDVOLQHDUHV LQYDULDQWHV QR WHPSR� (VWD SURSULHGDGH SHUPLWH TXH VLQDLV GLVFUHWRV SRVVDP VHU UHSUH�VHQWDGRV HP WHUPRV GH H[SRQHQFLDLV FRPSOH[DV�3DUD GHPRQVWUDU D SURSULHGDGH GH DXWRIXQ�FaDR GH H[SRQHQFLDLV FRPSOH[DV SDUD VLVWHPDV

GLVFUHWRV FRQVLGHUH XPD HQWUDGD [>Q@ HM�Q � Q � ==� $ VD��GD FRUUHVSRQGHQWH GH XP VLVWHPDOLQHDU LQYDULDQWH QR WHPSR FRP UHVSRVWD DR LPSXOVR K>Q@ �H

\>Q@

��;N ��

K>N@HM��Q�N� HM�Q�

��;N ��

K>N@H�M�N�� ������

'H�QLQGR

+�HM��

��;N ��

K>N@H�M�N � ������

SRGHPRV HVFUHYHU

\>Q@ +�HM��HM�Q� ������

&RQVHT¦XHQWHPHQWH� HM�Q �H XPD DXWRIXQ�FaDR GR VLVWHPD H R DXWRYDORU DVVRFLDGR �H +�HM���$ IXQ�FaDR Z �� +�HM�� �H FKDPDGD GH IXQ�FaDR UHVSRVWD HP IUHT¦XAHQFLD �)5)� GR VLVWHPD OLQHDULQYDULDQWH QR WHPSR� 2 FRQFHLWR GH IXQ�FaDR GH UHVSRVWD HP IUHT¦XAHQFLD �H SUDWLFDPHQWH R PHVPRVHMD R VLVWHPDV FRQW��QXR RX GLVFUHWR QR WHPSR� 3RU�HP� SDUD VLVWHPDV GLVFUHWRV OLQHDUHV LQYDUL�DQWHV QR WHPSR� D IXQ�FaDR UHVSRVWD HP IUHT¦XAHQFLD �H VHPSUH XPD IXQ�FaDR SHUL�RGLFD GD IUHT¦XAHQFLDFRP SHU��RGR ��� &RP HIHLWR�

+�HM�������

�;Q ��

K>Q@H�M������Q�

0DV�

H�M��Q � SDUD Q � ==�

$VVLP�

H�M������Q H�M�Q � H�M��Q H�M�Q�

/RJR�

+�HM������� +�HM���

��

Page 26: Analise de Sinais

)LJXUD ���� 5HVSRVWD HP IUHT¦XAHQFLD GR �OWUR LGHDO SDVVD�EDL[D�

'H PRGR JHUDO�

+�HM�����U�� +�HM�� � U � ==�

LVWR �H� +�HM�� �H SHUL�RGLFD FRP SHU��RGR ���&RPR+�HM�� �H SHUL�RGLFD FRP SHU��RGR �� � V�R SUHFLVDPRV HVSHFL�FDU+�HM�� QXP LQWHUYDOR GH

FRPSULPHQWR ��� 1RUPDOPHQWH HVSHFL�FDPRV +�HM�� QR LQWHUYDOR �� � � � �� &RP UHOD�FaDR DHVVH LQWHUYDOR� DV EDL[DV IUHT¦XAHQFLDV VaDR DV IUHT¦XAHQFLDV SU�R[LPDV GH ]HUR H DV DOWDV IUHT¦XAHQFLDVVaDR DV IUHT¦XAHQFLDV SU�R[LPDV GH � RX ���&KDPDUHPRV RV VLVWHPDV OLQHDUHV LQYDULDQWHV QR WHPSR GH �OWURV�8PD FODVVH LPSRUWDQWH GH VLVWHPDV OLQHDUHV LQYDULDQWHV QR WHPSR VaDR DTXHOHV FXMD UHVSRVWD

HP IUHT¦XAHQFLD YDOH � QXPD GHWHUPLQDGD IDL[D GH IUHT¦XAHQFLDV H ]HUR IRUD GHVVD IDL[D� (VVHV VaDRRV FKDPDGRV �OWURV VHOHWLYRV LGHDLV�&RQVLGHUHPRV� FRPR H[HPSOR� D UHVSRVWD HP IUHT¦XAHQFLD GH XP �OWUR LGHDO SDVVD�EDL[D�'HYLGR �D SHULRGLFLGDGH GD UHVSRVWD HP IUHT¦XAHQFLD SDUHFH TXH R �OWUR IXQFLRQD FRPR XP

�OWUR PXOWLIDL[D� 3RU�HP� R �OWUR UHMHLWD DOWDV IUHT¦XAHQFLDV H V�R SHUPLWH D SDVVDJHP GH EDL[DVIUHT¦XAHQFLDV� &RPR D UHVSRVWD HP IUHT¦XAHQFLD �H FRPSOHWDPHQWH HVSHFL�FDGD QR LQWHUYDOR �� �� � �� D DPSOLWXGH GD UHVSRVWD HP IUHT¦XAHQFLD GR �OWUR LGHDO SDVVD�EDL[D �H WLSLFDPHQWH PRVWUDGRVRPHQWH QHVVH LQWHUYDOR FRPR LQGLFD D �JXUD ����$V DPSOLWXGHV GDV UHVSRVWDV HP IUHT¦XAHQFLD SDUD �OWURV LGHDLV SDVVD�DOWD H SDVVD�IDL[D VaDR

PRVWUDGRV QD �JXUD ���� 0RVWUDPRV VRPHQWH XP SHU��RGR GD UHVSRVWD HP IUHT¦XAHQFLD�

����� 5HSUHVHQWD�FaDR GH VHT¦XAHQFLDV SHOD WUDQVIRUPDGD GH )RXULHU'LVFUHWD�7)'�

'H�QLPRV D WUDQVIRUPDGD GH )RXULHU GLVFUHWD GH XPD VHT¦XAHQFLD [ SRU

;�HM��

��;Q ��

[>Q@H�M�Q ������

H D WUDQVIRUPDGD LQYHUVD GH ;�HM�� SRU

[>Q@ �

��

= �

��

;�HM��HM�QG�� ������

��

Page 27: Analise de Sinais

)LJXUD ���� 5HVSRVWDV HP IUHT¦XAHQFLD SDUD �OWURV LGHDLV� �D�)LOWUR LGHDO SDVVD�DOWD �E�)LOWUR LGHDOSDVVD�IDL[D�

3RGHU��DPRV WHU HVFROKLGR TXDOTXHU LQWHUYDOR GH FRPSULPHQWR ���'H PRGR JHUDO ;�HM�� �H FRPSOH[R H SRGHPRV HVFUHYAH�OR QD IRUPD

;�HM�� M ;�HM�� M HM?;�HM�� ������

RQGH M ;�HM�� M H ?;�HM�� VaDR � UHVSHFWLYDPHQWH� D PDJQLWXGH H D IDVH GH ;�HM���2EVHUYDQGR DV HTXD�FaRHV ����� ���� H ���� SRGHPRV YHU TXH D UHVSRVWD HP IUHT¦XAHQFLD GH XP

VLVWHPD OLQHDU LQYDULDQWH QR WHPSR �H D WUDQVIRUPDGD GH )RXULHU GLVFUHWD GD UHVSRVWD DR LPSXOVRH D UHVSRVWD DR LPSXOVR SRGH VHU REWLGD FDOFXODQGR D WUDQVIRUPDGD LQYHUVD GH )RXULHU GD IXQ�FaDRUHVSRVWD HP IUHT¦XAHQFLD� LVWR �H�

K>Q@ �

��

= �

��

+�HM��HM�QG�� ������

3RGHPRV REVHUYDU TXH D HTXD�FaDR ���� �H XPD V�HULH GH )RXULHU FRPSOH[D SDUD XPD IXQ�FaDRSHUL�RGLFD GH YDUL�DYHO FRQW��QXD H TXH ���� IRUQHFH RV FRH�FLHQWHV QD V�HULH GH )RXULHU�'HVHMDPRV� DJRUD� HVWXGDU D FRQYHUJAHQFLD GD V�HULH

�;��

[>Q@H�M�Q

LVWR �H� GHVHMDPRV HQFRQWUDU DV FRQGL�FaRHV WDLV TXH

M ;�HM�� M�� SDUD WRGR ��

8PD FRQGL�FaDR VX�FLHQWH SDUD D FRQYHUJAHQFLD �H HQFRQWUDGD GD VHJXLQWH IRUPD �

M ;�HM�� M M

��;Q ��

[>Q@H�M�QM

��;Q ��

M [>Q@ MM H�M�Q M

��;Q ��

M [>Q@ M���

��

Page 28: Analise de Sinais

$VVLP� VH [>Q@ IRU DEVROXWDPHQWH VRP�DYHO� HQWaDR ;�HM�� H[LVWH� 1HVWH FDVR SRGHPRV PRVWUDUTXH D V�HULH FRQYHUJH SDUD XPD IXQ�FaDR FRQW��QXD GH ��&RPR XPD VHT¦XAHQFLD HVW�DYHO �H� SRU GH�QL�FaDR� DEVROXWDPHQWH VRP�DYHO� WRGDV DV VHT¦XAHQFLDV

HVW�DYHLV SRVVXHP WUDQVIRUPDGD GH )RXULHU� (� WDPE�HP� TXDOTXHU VLVWHPD HVW�DYHO WHU�D UHVSRVWDHP IUHT¦XAHQFLD �QLWD H FRQW��QXD�$ VRPDELOLGDGH DEVROXWD �H XPD FRQGL�FaDR VX�FLHQWH SDUD D H[LVWAHQFLD GD WUDQVIRUPDGD GH

)RXULHU H WDPE�HP JDUDQWH D FRQYHUJAHQFLD XQLIRUPH� LVWR �H�VH

;�HM��

��;��

[>Q@H�M�Q

H

;0�HM��

0;Q �0

[>Q@H�M�Q

HQWaDR

OLP0���

= ��

��

M ;�HM���;0 �HM�� M G� ��

$OJXPDV VHT¦XAHQFLDV� SRU�HP� QaDR VaDR DEVROXWDPHQWH VRP�DYHLV� PDV VaDR TXDGUDGR VRP�DYHLV�LVWR �H�

��;Q ��

M [>Q@� M���

7DLV VHT¦XAHQFLDV SRGHP VHU UHSUHVHQWDGDV SRU XPD WUDQVIRUPDGD GH )RXULHU GLVFUHWD VH Q�RVCUHOD[DPRV D FRQGL�FaDR GH FRQYHUJAHQFLD XQLIRUPH� 7HPRV� DVVLP� R FDVR GH FRQYHUJAHQFLD P�HGLD�TXDGU�DWLFD� LVWR �H� VH

;�HM��

��;Q ��

[>Q@H�M�Q

H

;0�HM��

0;Q �0

[>Q@H�M�Q

HQWaDR

OLP0���

= ��

��

M ;�HM���;0 �HM�� M� G� ��

��

Page 29: Analise de Sinais

&RPR H[HPSOR FDOFXOHPRV D UHVSRVWD DR LPSXOVR GR �OWUR LGHDO SDVVD�EDL[D FXMD UHVSRVWDHP IUHT¦XAHQFLD �H

+�HM��

��� M � M� �F

�� �F �M � M� �������

FRP SHULRGLFLGDGH ���$VVLP�

K>Q@ �

��

= �F

��F

HM�QG� VHQ��FQ�

�Q� Q � ��

3DUD Q � WHPRV

K>�@ �

��

= �F

��F

G� �F

��

'H�QLQGR� 6D>Q@ VHQ�Q�

Q� WHPRV

K>Q@ �F

�6D��FQ��

2EVHUYDPRV TXH FRPR K>Q@ �H QaDR QXOD SDUD Q � �� 2EVHUYDPRV WDPE�HP TXH K>Q@ QaDR �HDEVROXWDPHQWH VRP�DYHO� ,VWR RFRUUH SRLV +�HM�� �H GHVFRQW��QXD HP � �F� &RPR K>Q@ QaDR �HDEVROXWDPHQWH VRP�DYHO�

��;Q ��

�F

�6D��FQ�H

�M�Q

QaDR FRQYHUJH XQLIRUPHPHQWH SDUD WRGRV RV YDORUHV GH ��3RGHPRV GDU XPD QR�FaDR LQWXLWLYD SDUD HVWH IDWR FRQVLGHUDQGR

+0 �HM��

0;Q �0

�F

�6D��FQ�H

�M�Q�

$ IXQ�FaDR +0 �HM�� �H PRVWUDGD QD �JXUD ��� SDUD Y�DULRV YDORUHV GH 0 H ZF � �� 1RWH TXH

�D PHGLGD TXH 0 DXPHQWD� R FRPSRUWDPHQWR RVFLODW�RULR HP � �F �FKDPDGR GH IHQARPHQR GH*LEEV� �H PDLV DFHQWXDGR� 3RGHPRV PRVWUDU TXH TXDQGR 0 � � D DPSOLWXGH P�D[LPD GDVRVFLOD�FaRHV QaDR YDL D ]HUR� $ VRPD LQ�QLWD QaDR FRQYHUJH XQLIRUPHPHQWH SDUD +�HM��� SRU�HP K>Q@�H TXDGUDGR VRP�DYHO H +0�H

M�� FRQYHUJH QR VHQWLGR P�HGLR�TXDGU�DWLFR SDUD +�HM��� LVWR �H�

OLP0���

= ��

��

M +�HM���+0 �HM�� M� G� ��

(PERUD D GLIHUHQ�FD HQWUH OLP0��

+0 �HM�� H +�HM�� QaDR SDUH�FD LPSRUWDQWH� HOD GHYH VHU FRQ�

VLGHUDGR QD FRQVWUX�FaDR GH �OWURV�

��

Page 30: Analise de Sinais

)LJXUD ���� *U�D�FRV GH +0�HM���

����� 3URSULHGDGHV GD WUDQVIRUPDGD GH )RXULHU GLVFUHWD

7HRUHPD GH 3DUVHYDO

(

��;Q ��

M [>Q@ M� �

��

= ��

��

M ;�HM�� M�G�� ������

$ IXQ�FaDR M ;�HM�� M��H FKDPDGD GH HVSHFWUR GH GHQVLGDGH GH HQHUJLD H V�R �H GH�QLGD SDUD VLQDLV

GH HQHUJLD �QLWD�

35235,('$'( '20�,1,2 '2 7(032 '20�,1,2 '$ )5(4¦8A(1&,$

/LQHDULGDGH D�[�>Q@ � D�[�>Q@ D�;��HM�� � D�;��H

M��

'HVORFDPHQWR QR WHPSR [>Q� QG@� H�M�Q;�HM�� HM�GQ[>Q@� ;�HM����G��H QD IUHT¦XAHQFLD

'LIHUHQFLD�FaDR QD IUHT¦XAHQFLD Q[>Q@ MG;

G��HM��

7DEHOD ���� 3URSULHGDGHV GD WUDQVIRUPDGD GH )RXULHU 'LVFUHWD�

��

Page 31: Analise de Sinais

7HRUHPD GD &RQYROX�FaDR

6H

[>Q@� ;�HM�� � K>Q@� +�HM�� �

\>Q@

��;N ��

[>N@K>Q� N@ [>Q@ � K>Q@� < �HM��

HQWaDR

< �HM�� ;�HM��+�HM��� ������

3HULRGLFLGDGH

$ WUDQVIRUPDGD GH )RXULHU ;�HM�� �H SHUL�RGLFD HP �� FRP SHU��RGR ��� 3RLV�

;�HM�������

��;Q ��

[>Q@H�M������Q

��;Q ��

[>Q@H�M�Q � H�M��Q

��;Q ��

[>Q@H�M�Q

;�HM���

'HVVD IRUPD V�R SUHFLVDPRV HVSHFL�FDU RV YDORUHV GH ;�HM�� HP XP SHULRGR�

6LPHWULD

3DUD [>Q@ UHDO�

;�H�M�� ;��HM��

RQGH VLJQL�FD FRQMXJDGR FRPSOH[R�$VVLP� SDUD WUD�FDUPRV RV JU�D�FRV UHSUHVHQWDWLYRV GH;�HM�� V�R SUHFLVDPRV FRQVLGHUDU PHWDGH

GH VHX SHU��RGR� *HUDOPHQWH� HVFROKHPRV � � >�� �@�6H [>Q@ IRU GH GXUD�FaDR �QLWD� HQWaDR SRGHPRV ID]HU XP SURJUDPD SDUD FDOFXODU ;�HM��

QXPHULFDPHQWH SDUD TXDOTXHU IUHT¦XAHQFLD �� 9DPRV VXSRU TXH [>Q@ WHQKD 1 DPRVWUDV HQWUHQ� � Q � Q1 �'HVHMDPRV FDOFXODU ;�HM�� SDUD �N

�0N � N �� �� � � � �0 TXH VaDR �0��� IUHT¦XAHQFLDV

LJXDOPHQWH HVSD�FDGDV HQWUH >�� �@� 'HVVD IRUPD� SRGHPRV HVFUHYHU

;�HM�N�

1;O �

H�M�� 0�NQO[�QO� � N �� �� � � � �0�

��

Page 32: Analise de Sinais

4XDQGR [>QO@ H ;�HM�N� VaDR FRORFDGDV FRPR YHWRUHV FROXQD [ H ;� UHVSHFWLYDPHQWH� 7HPRV�

; :[

RQGH : �H XPD PDWUL] �0 � ���1 GDGD SRU

: IH�M�� 0�NQO � Q� � Q � Q1 � N �� �� � � � �0J�

6H HVFUHYHPRV INJ H IQOJ FRPR YHWRUHV OLQKD N H Q� WHPRV

: >H[S��M�

0N7Q�@�

'HVVD IRUPD� WHPRV

;7 [7 >H[S��M�

0Q7N�@� ������

$ I�RUPXOD ���� SRGH VHU LPSOHPHQWDGD QR 0$7/$%�&RPR H[HPSOR� FRQVLGHUHPRV D VHT¦XAHQFLD [>Q@ ����� H[S�M� ���Q � � � Q � ��� 9DPRV

FDOFXODU ;�HM�� H LQYHVWLJDU VXD SHULRGLFLGDGH� 3DUD LQYHVWLJDUPRV D SHULRGLFLGDGH� YDPRV FDO�FXODU H PRVWUDU RV JU�D�FRV UHSUHVHQWDWLYRV GH ;�HM�� HP ��� IUHT¦XAHQFLDV QR LQWHUYDOR >���� ��@�2V JU�D�FRV GH PDJQLWXGH � IDVH� SDUWH UHDO H SDUWH LPDJLQ�DULD GH ;�HM�� HVWaDR PRVWUDGRV QD�JXUD ����

��� $PRVWUDJHP GH VLQDLV FRQW��QXRV

����� ,QWURGX�FaDR

1RUPDOPHQWH R SURFHVVDPHQWR GH VLQDLV FRQW��QXRV �H LPSOHPHQWDGR DWUDY�HV GH XP SURFHVVR GHDPRVWUDJHP GR VLQDO� VHJXLGR GR SURFHVVDPHQWR GR VLQDO GLVFUHWR REWLGR� LVWR �H� VXD WUDQVIRU�PD�FaDR HP XP RXWUR VLQDO GLVFUHWR TXH GHSRLV �H WUDQVIRUPDGR SRU VXD YH] QXP VLQDO FRQW��QXR�

����� $PRVWUDJHP SHUL�RGLFD

2 P�HWRGR XVXDO GH REWHUPRV XP VLQDO GLVFUHWR D SDUWLU GH XP VLQDO FRQW��QXR �H DWUDY�HV GDDPRVWUDJHP SHUL�RGLFD � GLJDPRV GH SHU��RGR 7 � GR VLQDO FRQW��QXR REWHQGR� DVVLP� XPD VHT¦XAHQFLDGH DPRVWUDV [>Q@ D SDUWLU GR VLQDO FRQW��QXR [F�W� DWUDY�HV GD UHOD�FaDR

[>Q@ [F>Q7 @ � Q � ==� ������

7 �H R SHU��RGR GH DPRVWUDJHP H IV �7�H D IUHT¦XAHQFLD GH DPRVWUDJHP�

1RV UHIHULPRV DR VLVWHPD TXH LPSOHPHQWD D RSHUD�FaDR GDGD SHOD HTXD�FaDR ���� FRPR XPFRQYHUVRU LGHDO FRQW��QXR�GLVFUHWR�&�'� H D UHSUHVHQWD�FaDR HP GLDJUDPD GH EORFRV �H GDGD QD�JXUD ���� 1D SU�DWLFD� D RSHUD�FaDR GH DPRVWUDJHP �H LPSOHPHQWDGD SRU XP FRQYHUVRU DQDO�RJLFR�GLJLWDO �$�'� TXH VHU�D HVWXGDGR PDLV WDUGH�

��

Page 33: Analise de Sinais

)LJXUD ���� �D�0DJQLWXGH��E�)DVH��F�3DUWH UHDO��G�3DUWH ,PDJLQ�DULD�

$ RSHUD�FaDR GH DPRVWUDJHP� JHUDOPHQWH� QaDR �H LQYHUV��YHO� LVWR �H� GDGD D VD��GD [>Q@ QaDR �HSRVV��YHO� GH PRGR JHUDO� UHFRQVWUXLU [F�W��2 GLDJUDPD GH EORFRV GD RSHUD�FaDR TXH UHSUHVHQWD D REWHQ�FaDR GH [>Q@ D SDUWLU GH [F�W� �H

GDGD QD �JXUD ���2 SURFHVVR GH DPRVWUDJHP �H IHLWR HP GRLV HVW�DJLRV� 1R SULPHLUR HVW�DJLR R VLQDO [F�W� �H

PXOWLSOLFDGR SRU XP WUHP GH LPSXOVRV V�W� H QR VHJXQGR HVW�DJLR R WUHP GH LPSXOVRV REWLGR�[V�W�� �H FRQYHUWLGR SDUD XPD VHT¦XAHQFLD [>Q@�(VTXHPDWLFDPHQWH WHPRV D UHSUHVHQWD�FaDR QD �JXUD ����

����� 5HSUHVHQWD�FaDR GDV DPRVWUDV QR GRP��QLR GD IUHT¦XAHQFLD

3DUD REWHUPRV D UHOD�FaDR QR GRP��QLR GD IUHT¦XAHQFLD HQWUH D HQWUDGD H D VD��GD GH XP FRQYHUVRU&�'� YDPRV FRQVLGHUDU D FRQYHUVaDR GH [F�W� SDUD [V�W��6HMD V�W� XP WUHP GH LPSXOVRV SHUL�RGLFRV� $VVLP�

V�W�

��;Q ��

��W� Q7 � ������

��

Page 34: Analise de Sinais

)LJXUD ���� 'LDJUDPD GH EORFR GH UHSUHVHQWD�FaDR GH XP FRQYHUVRU LGHDO FRQW��QXR�GLVFUHWR �&�'�

)LJXUD ���� 'LDJUDPD GH EORFRV UHSUHVHQWDQGR D RSHUD�FaDR GH DPRVWUDJHP�

RQGH � �H R LPSXOVR XQLW�DULR�'D���

[V�W� [F�W�V�W� [F�W�

��;Q ��

��W� Q7 � ������

RX

[V�W�

��;Q ��

[F�Q7 ���W� Q7 �� ������

'HVHMDPRV REWHU D WUDQVIRUPDGD GH )RXULHU GH [V�W�� 3RGHPRV PRVWUDU TXH

V�W�� 6�M�� ��

7

��;N ��

���� N�V�� ������

RQGH �V ��

7�H D IUHT¦XAHQFLD GH DPRVWUDJHP HP UDG�V�

0DV

;V�M�� �

��;F�M�� � 6�M��� ������

/RJR

;V�M�� �

7

��;N ��

;F�M�� NM�V�� ������

��

Page 35: Analise de Sinais

)LJXUD ���� 5HSUHVHQWD�FaDR HVTXHP�DWLFD GD DPRVWUDJHP�

2EVHUYDPRV TXH ;V�M�� FRQVLVWH GH F�RSLDV UHSHWLGDV GD WUDQVIRUPDGD GH )RXULHU GH [F�W��$ �JXUD ��� PRVWUD R SURFHVVR GH DPRVWUDJHP QR GRP��QLR GD IUHT¦XAHQFLD�2EVHUYDPRV TXH TXDQGR

�6 � �1 � �1 RX �6 � ��1 ������

DV U�HSOLFDV GH ;F�M�� QaDR VH VREUHSaRHP� $VVLP� [F�W� SRGH VHU UHFXSHUDGR� D SDUWLU GH [V�W��XVDQGR XP �OWUR LGHDO SDVVD�EDL[D FRQYHQLHQWH�FRP IUHT¦XAHQFLD GH FRUWH �F� �1 � �F � �V��1 �$ �JXUD ���� PRVWUD R HVTXHPD GH UHFXSHUD�FaDR GH [F�W��

3RU�HP� VH

�6 � ��1 ������

HQWaDR DV F�RSLDV GH ;F�M�� VH VREUHSaRHP �REVHUYDGR QD �JXUD ���� H ;F�M�� QaDR �H UHFXSHU�DYHOSRU XP �OWUR SDVVD�EDL[D� $ GLVWRU�FaDR RFRUULGD QR VLQDO GH VD��GD� QHVWH FDVR� GHQRPLQD�VHPDVFDUDPHQWR �RX DOLDVLQJ� SRLV XP VLQDO �H VXEVWLWX��GR SRU RXWUR� $ GLVFXVVaDR DFLPD �H D EDVHSDUD XP WHRUHPD FRQKHFLGR FRPR 7HRUHPD GD $PRVWUDJHP �

����� 7HRUHPD GD DPRVWUDJHP

7HRUHPD �

8P VLQDO OLPLWDGR HP IDL[D� L�H�� TXH QaDR WHP QHQKXPD FRPSRQHQWH HVSHFWUDO DFLPD GD IUHT¦XAHQFLD�1 UDG V� �H GHWHUPLQDGR XQLYRFDPHQWH SRU VXDV DPRVWUDV � [>Q@ [FIQ7J � Q ����� � � �WRPDGDV D LQWHUYDORV XQLIRUPHV PHQRUHV GR TXH �

�1VHJXQGRV � ,VWR �H� R SHU��RGR GH DPRVWUDJHP

GHYH VDWLVID]HU 7 � ��1� $ IUHT¦XAHQFLD GH DPRVWUDJHP � ��

7GHYH� HQWaDR� VDWLVID]HU � ! ��1 �

&KDPDPRV R Q�XPHUR ��1 GH IUHT¦XAHQFLD GH 1\TXLVW�(VVH WHRUHPD �H FRQKHFLGR FRPR 7HRUHPD GD $PRVWUDJHP 8QLIRUPH�'LVFXWLUHPRV XP SRXFR PDLV VREUH R 7HRUHPD GD $PRVWUDJHP H R SUREOHPD GH PDVFDUDPHQWR�

��

Page 36: Analise de Sinais

)LJXUD ���� �D� 7UDQVIRUPDGD GH )RXULHU OLPLWDGD FRP IUHT� P�D[� �1 �E� 7UHP GH LPSXOVRVSHUL�RGLFRV 6�M�� �F� *U�D�FR GH ;6�M�� FRP �V ! ��1 �G� *U�D�FR GH ;6�M�� FRP �V � ��1

&RQVLGHUHPRV XP VLQDO GDGR SRU

[F�W� FRV��RW��

$ WUDQVIRUPDGD GH )RXULHU GHVVH VLQDO �H PRVWUDGD QD �JXUD �����)D]HPRV D DPRVWUDJHP GR VLQDO� REWHQGR �

[V�W�

��;Q ��

[F�Q7 ���W� Q7 ��

3ULPHLUR� XVDPRV XPD IUHT¦XAHQFLD GH DPRVWUDJHP �V ! ��R� LVWR �H� XVDPRV 7 � ��R� $

WUDQVIRUPDGD GH )RXULHU GH [V�W� SDUD HVVH FDVR �H PRVWUDGD QD �JXUD �����$JRUD� XVDPRV XPD IUHT¦XAHQFLD GH DPRVWUDJHP �V � ��R� LVWR �H� XVDPRV 7 ! �

�R� $

WUDQVIRUPDGD GH )RXULHU GH [V�W� SDUD HVVH FDVR �H PRVWUDGD QD �JXUD �����$ �JXUD ���� �D� PRVWUD D WUDQVIRUPDGD GH )RXULHU DS�RV D SDVVDJHP SHOR �OWUR SDVVD�EDL[D�

SDUD R FDVR HP TXH �R � �V �� LVWR �H� VHP RFRUUAHQFLD GH PDVFDUDPHQWR� $ IUHT¦XAHQFLD GH FRUWHGR �OWUR �H �F �V ��

��

Page 37: Analise de Sinais

)LJXUD ����� �D� 'LDJUDPD GH EORFRV GD UHFXSHUD�FaDR GR VLQDO� �E���F���G� H �H� UHFRQVWUX�FaDR GH[F�W��

$ �JXUD ���� �E� PRVWUD D WUDQVIRUPDGD GH )RXULHU DS�RV D SDVVDJHP SHOR �OWUR SDVVD�EDL[D�SDUD R FDVR HP TXH �R ! �V �� LVWR �H� FRP RFRUUAHQFLD GH PDVFDUDPHQWR� $ IUHT¦XAHQFLD GH FRUWHGR �OWUR �H D PHVPD GR FDVR DQWHULRU�6HP D SUHVHQ�FD GH PDVFDUDPHQWR� D VD��GD UHFRQWUX��GD [U�W� �H

[U�W� FRV��RW�

H FRP D SUHVHQ�FD GH PDVFDUDPHQWR� D VD��GD UHFRQWUX��GD VHU�D

[U�W� FRV��V ��R�W�

2EVHUYDPRV TXH R VLQDO FRV��RW� WURFRX GH LGHQWLGDGH �DOLDV� H IRL PDVFDUDGR SHOR VLQDO GHIUHT¦XAHQFLD PDLV EDL[D FRV��V � �R�W�'HVHMDPRV� DJRUD� HQFRQWUDU XPD UHOD�FaDR HQWUH ;�HM��� D WUDQVIRUPDGD GH )RXULHU GLVFUHWD

GH [>Q@ H DV WUDQVIRUPDGDV GH )RXULHU ;V�M�� H ;F�M�� GH [V�W� H [F�W�� UHVSHFWLYDPHQWH�6DEHPRV TXH

[V�W�

��;Q ��

[F�Q7 ���W� Q7 ��

��

Page 38: Analise de Sinais

)LJXUD ����� 7UDQVIRUPDGD GH )RXULHU GH [F�W��

)LJXUD ����� 7UDQVIRUPDGD GH )RXULHU GH [V�W�� FRP 7 � ��R�

$SOLFDQGR D WUDQVIRUPDGD GH )RXULHU D HVVD HTXD�FaDR� WHPRV

;V�M��

�;Q ��

[F�Q7 �H�M�7Q�

&RPR [>Q@ [F�Q7 � H

;�HM��

��;Q ��

[>Q@H�M�Q

WHPRV�

;V�M�� ;�HM�� M� �7 ;�HM�7 ��

3RU RXWUR ODGR� VDEHPRV TXH

;V�M�� �

7

��;N ��

;F�M�� NM�V��

$VVLP�

;�HM�7 � ;�HM�� �

7

��;N ��

;F�M�

7� M

��N

7�� ������

��

Page 39: Analise de Sinais

)LJXUD ����� 7UDQVIRUPDGD GH )RXULHU GH [V�W�� FRP 7 ! ��R�

)LJXUD ����� �D� 6HP RFRUUAHQFLD GH PDVFDUDPHQWR��E� &RP RFRUUAHQFLD GH PDVFDUDPHQWR�

2EVHUYDPRV TXH ;�HM�� �H XPD YHUVaDR GH;F�M��� WUDQVODGDGD H FRP XPD PXGDQ�FD GH HVFDODWDQWR HP DPSOLWXGH FRPR HP IUHT¦XAHQFLD�3DUD HQWHQGHUPRV R TXH IRL GLWR DW�H DTXL� FRQVLGHUHPRV R VLQDO

[F�W� H�����MWM�

8VDQGR D DSUR[LPD�FaDR H�� �� QRWDPRV TXH [F�W� SRGH VHU DSUR[LPDGR SRU XP VLQDO GHGXUD�FaDR �QLWD QR LQWHUYDOR ������ � W � ������ 0RVWUDPRV HVVH VLQDO QD �JXUD ���� �D��'HVHMDPRV DQDOLVDU HVVH VLQDO QR GRP��QLR GD IUHT¦XAHQFLD�6XD WUDQVIRUPDGD GH )RXULHU SRGH VHU FDOFXODGD GD VHJXLQWH IRUPD �

;F�M��

= ��

��

[F�W�H�M�WGW

= �

��

H����WH�M�WGW�

= ��

H�����WH�M�WGW

�����

� � � �

�������

8VDQGR WDPE�HP D DSUR[LPD�FaDR H�� ��WHPRV TXH ;F�M�� � SDUD � � ��������� 2JU�D�FR GH ;F�M�� �QHVVH FDVR VHU�D UHDO�� �H PRVWUDGR QD �JXUD ���� �E��$PRVWUHPRV� HQWaDR� [F�W� FRP IUHT¦XAHQFLD GH DPRVWUDJHP GH �V ����+]� REWHQGR D

VHT¦XAHQFLD [�>Q@� 2 JU�D�FR GH [�>Q@ DVVLP FRPR R JU�D�FR GH VXD WUDQVIRUPDGD GH )RXULHUGLVFUHWD ;��H

M�� VaDR PRVWUDGRV QD �JXUD ����� 0RVWUDPRV PDLV GH XP SHU��RGR GH ;��HM���

&RP HVVD IUHT¦XAHQFLD GH DPRVWUDJHP QaDR REVHUYDPRV D SUHVHQ�FD GH PDVFDUDPHQWR�

��

Page 40: Analise de Sinais

)LJXUD ����� �D�*U�D�FR GH [F�W���E�*U�D�FR GH ;F�M���

$PRVWUDPRV� DJRUD� [F�W� FRP IUHT¦XAHQFLD GH DPRVWUDJHP �V ����+] H REWHPRV [�>Q@�0RVWUDPRV R JU�D�FR GH [�>Q@ DVVLP FRPR GH VXD WUDQVIRUPDGD ;��H

M�� QD �JXUD �����2EVHUYDPRV� DVVLP� D SUHVHQ�FD GH PDVFDUDPHQWR� &RPR HUD GH VH HVSHUDU SRLV D IUHT¦XAHQFLD

GH ���� +] �H PHQRU TXH D IUHT¦XAHQFLD GH 1\TXLVW � QR QRVVR FDVR ���� +]��

����� 5HFRQVWUX�FaDR GH XP VLQDO OLPLWDGR HP IDL[D D SDUWLU GH VXDVDPRVWUDV

9LPRV TXH VH DV FRQGL�FaRHV GR WHRUHPD GD DPRVWUDJHP VaDR VDWLVIHLWDV H VH R WUHP GH LPSXOVRV�[V�W�� �H �OWUDGR SRU XP �OWUR SDVVD�EDL[D DSURSULDGR HQWaDR D WUDQVIRUPDGD GH )RXULHU GD VD��GDGR �OWUR VHU�D LGAHQWLFD �D WUDQVIRUPDGD GH )RXULHU GR VLQDO RULJLQDO [F�W�� 6H XPD VHT¦XAHQFLD GHDPRVWUDV [>Q@ IRU FRQKHFLGD� SRGHPRV IRUPDU XP WUHP GH LPSXOVRV [V�W� GHVFULWR PDWHPDWLFD�PHQWH SRU

[V�W�

��;Q ��

[>Q@��W� Q7 � ������

RQGH 7 �H R SHU��RGR GH DPRVWUDJHP DVVRFLDGR D [>Q@�$ UHSUHVHQWD�FaDR GR SURFHVVR GH UHFRQVWUX�FaDR �H PRVWUDGD QD �JXUD �����

����� 3URFHVVDPHQWR GLVFUHWR GH VLQDO FRQW��QXR

8PD GDV DSOLFD�FaRHV GH VLVWHPDV GLVFUHWRV �H QR SURFHVVDPHQWR GH VLQDLV FRQW��QXRV� (VWH SUR�FHVVDPHQWR �H UHDOL]DGR SRU XP VLVWHPD FXMD IRUPD JHUDO �H GDGR QD �JXUD ����� 1HVVH HVTXHPDFRQVLGHUDPRV R PHVPR SHU��RGR GH DPRVWUDJHP SDUD RV FRQYHUVRUHV &�' H '�&� PDV LVVR QaDR�H HVVHQFLDO�8P VLQDO FRQW��QXR [F�W� HQWUD QR FRQYHUVRU &�' JHUDQGR XPD VHT¦XAHQFLD [>Q@� (VVD VHT¦XAHQFLD

�H D HQWUDGD SDUD XP VLVWHPD GLVFUHWR FXMD VD��GD� DS�RV D WUDQVIRUPD�FaDR LPSRVWD SHOR VLVWHPDGLVFUHWR �H \>Q@� $ VHT¦XAHQFLD \>Q@ �H HQWaDR FRQYHUWLGD HP XP VLQDO DQDO�RJLFR \U�W��

��

Page 41: Analise de Sinais

)LJXUD ����� *U�D�FRV GH [�>Q@ H GH ;��HM���

6H R VLVWHPD GLVFUHWR IRU OLQHDU H LQYDULDQWH QR WHPSR�HQWaDR

< �HM�� +�HM��;�HM�� ������

VHQGR +�HM�� D UHVSRVWD HP IUHT¦XAHQFLD GR VLVWHPD� ;�HM�� H < �HM�� VaDR DV WUDQVIRUPDGDV GH)RXULHU GH [>Q@ H \>Q@�$S�RV FHUWRV F�DOFXORV SRGHPRV REWHU

<U�M�� +HII �M��;F�M�� RQGH � �

7������

H

+HII �M��

�+�HM�7 �� M � M� � 7�� M � M� � 7

������

�H D FKDPDGD UHVSRVWD HP IUHT¦XAHQFLD HIHWLYD� LVWR �H� R VLVWHPD WRWDO �H HTXLYDOHQWH D XP VLVWHPDOLQHDU LQYDULDQWH QR WHPSR FRP UHVSRVWD HP IUHT¦XAHQFLD +HII �M���

��� &RQVLGHUD�FaRHV SU�DWLFDV

����� ,QWURGX�FaDR

1D SU�DWLFD VLQDLV FRQW��QXRV QaDR VaDR OLPLWDGRV HP IDL[D� �OWURV LGHDLV QaDR VaDR UHDOL]�DYHLV HFRQYHUVRUHV LGHDLV &�' H '�& QaDR H[LVWHP� 2 GLDJUDPD GH EORFRV GD �JXUD ���� PRVWUD XPPRGHOR PDLV UHDOLVWD SDUD SURFHVVDPHQWR GLJLWDO GH VLQDLV FRQW��QXRV �DQDO�RJLFRV��

��

Page 42: Analise de Sinais

)LJXUD ����� *U�D�FRV GH [�>Q@ H GH ;��HM���

����� 3U�H��OWUDJHP SDUD HYLWDU PDVFDUDPHQWR

6H D HQWUDGD QaDR IRU OLPLWDGD HP IDL[D RX VH D IUHT¦XAHQFLD GH 1\TXLVW GD HQWUDGD IRU PXLWRDOWD� D SU�H��OWUDJHP �H IUHT¦XHQWHPHQWH XVDGD� ,VVR SRGH VHU REWLGR SHOD �OWUDJHP� DWUDY�HV GHXP �OWUR SDVVD�EDL[D� GR VLQDO FRQW��QXR DQWHV GH HQWUDU QR FRQYHUVRU &�'� 2 �OWUR SDVVD�EDL[DTXH SUHFHGH R FRQYHUVRU &�' �H FKDPDGR GH �OWUR DQWL�PDVFDUDPHQWR� ,GHDOPHQWH� D UHVSRVWDHP IUHT¦XAHQFLD GR �OWUR DQWL�PDVFDUDPHQWR GHYH VHU

+DD�M��

��� M � M� �F � � 7�� M � M! �F�

������

1D SU�DWLFD +DD�M�� GHYH VHU SHTXHQR SDUD M � M!�7�

����� &RQYHUVaDR DQDO�RJLFD�GLJLWDO

8P FRQYHUVRU LGHDO &�' FRQYHUWH XP VLQDO FRQW��QXR QXP VLQDO GLVFUHWR HP PDWHP�DWLFD UHDO�LVWR �H� FDGD DPRVWUD �H FRQKHFLGD FRP SUHFLVaDR LQ�QLWD� 1D SU�DWLFD LVWR QaDR �H SRVV��YHO H DVVLPR VLVWHPD GD �JXUD ���� FRQYHUWH XP VLQDO DQDO�RJLFR [D�W� QXP VLQDO GLJLWDO A[%>Q@ � LVWR �H�XPD VHT¦XAHQFLD GH SUHFLVaDR �QLWD GH DPRVWUDV TXDQWL]DGDV� 4XDQWL]D�FaDR DSDUHFH VHPSUH TXH VHWUDEDOKD FRP PDWHP�DWLFD �QLWD�2 FRQYHUVRU $�' �H XP GLVSRVLWLYR TXH FRQYHUWH DPSOLWXGH GH WHQVaDR RX FRUUHQWH GD VXD

HQWUDGD QXP F�RGLJR ELQ�DULR UHSUHVHQWDWLYR GR YDORU GH DPSOLWXGH TXDQWL]DGD PDLV SU�R[LPDGD DPSOLWXGH GH HQWUDGD� 6RE R FRQWUROH GH XP UHO�RJLR H[WHUQR� R FRQYHUVRU $�' FRPH�FD HFRPSOHWD XPD FRQYHUVaDR $�' D FDGD 7 VHJXQGRV� 3RU�HP� D FRQYHUVaDR QaDR �H LQVWDQWADQHD H SRUHVVD UD]aDR LQFOXL�VH R EORFR FRP R W��WXOR C$PRVWUD H 6HJXUD �

��

Page 43: Analise de Sinais

)LJXUD ����� 'LDJUDPD GH EORFRV UHSUHVHQWDWLYR GD UHFRQVWUX�FaDR�

)LJXUD ����� 3URFHVVDPHQWR GLVFUHWR GH VLQDO FRQW��QXR�

2 VLVWHPD LGHDO C$PRVWUD H 6HJXUD �H R VLVWHPD FXMD VD��GD �H

[R�W�

��;Q ��

[>Q@KR�W� Q7 � ������

RQGH [>Q@ [D�Q7 � VaDR DV DPRVWUDV GH [D�W� H KR�W� �H D UHVSRVWD DR LPSXOVR GR VLVWHPD� LVWR �H�

KR�W�

��� � � W � 7�� FDVR FRQWU�DULR �

������

(VSHFL�FDPHQWH D VD��GD GHVVH VLVWHPD �H XPD RQGD FRP D IRUPD GH HVFDGD RQGH RV YDORUHVGH DPRVWUDJHP VaDR PDQWLGRV FRQVWDQWHV GXUDQWH R SHU��RGR GH DPRVWUDJHP GH 7 VHJXQGRV�FRQIRUPH PRVWUD D �JXUD �����$ UHSUHVHQWD�FaDR SRU GLDJUDPD GH EORFRV� GR FRQYHUVRU $�'� QXPD IRUPD PDLV FRPSOHWD �H

GDGD QD �JXUD ����

��

Page 44: Analise de Sinais

)LJXUD ����� 0RGHOR PDLV UHDOLVWD GH SURFHVVDPHQWR GLJLWDO GH VLQDO DQDO�RJLFR

)LJXUD ����� &RQ�JXUD�FaDR GR FRQYHUVRU DQDO�RJLFR�GLJLWDO

2 TXDQWL]DGRU �H XP VLVWHPD QaDR�OLQHDU FXMR REMHWLYR �H WUDQVIRUPDU D VHT¦XAHQFLD GH HQWUDGD[>Q@ QXP FRQMXQWR �QLWR GH YDORUHV SUHVFULWRV� 5HSUHVHQWDPRV HVWD RSHUD�FaDR FRPR

A[>Q@ 4�[>Q@� ������

H FKDPDPRV A[>Q@ GH DPRVWUD TXDQWL]DGD� $S�RV D TXDQWL]D�FaDR� RV Q��YHLV VHUaDR URWXODGRV SRUXP F�RGLJR TXH GH PRGR JHUDO �H XP F�RGLJR ELQ�DULR � �%�� Q��YHLV SRGHP VHU FRGL�FDGRV FRP XPF�RGLJR ELQ�DULR GH �%��� ELWV ��$V DPRVWUDV TXDQWL]DGDV A[>Q@ VaDR� HP JHUDO� GLIHUHQWHV GDV YHUGDGHLUDV [>Q@� $ GLIHUHQ�FD

HQWUH HODV �H FKDPDGD GH HUUR GH TXDQWL]D�FaDR� GH�QLGD SRU

H>Q@ A[>Q@� [>Q@� ������

*HUDOPHQWH H>Q@ QaDR �H FRQKHFLGR H XP PRGHOR HVWDW��VWLFR GHYH VHU XVDGR�$ UHSUHVHQWD�FaDR HVWDW��VWLFD GH HUURV GH TXDQWL]D�FaDR �H EDVHDGD QDV VHJXLQWHV FRQVLGHUD�FaRHV �

�L� $ VHT¦XAHQFLD H>Q@ �H XPD VHT¦XAHQFLD GH DPRVWUDV GH XP SURFHVVR DOHDW�RULR HVWDFLRQ�DULR��LL� $ VHT¦XAHQFLD GH HUUR H>Q@ QaDR �H FRUUHODWD FRP D VHT¦XAHQFLD [>Q@ ��LLL� $V YDUL�DYHLV DOHDW�RULDV GR SURFHVVR GH HUUR QaDR VaDR FRUUHODWDV� LVWR �H� R HUUR �H XP SURFHVVRGH UX��GR EUDQFR��LY� $ GLVWULEXL�FaDR GH SUREDELOLGDGH GR SURFHVVR GH HUUR �H XQLIRUPH�

����� &RQYHUVaDR GLJLWDO�DQDO�RJLFD

2 VLVWHPD TXH WRPD D VHT¦XAHQFLD \>Q@ FRPR HQWUDGD H SURGX] \U�W� FRPR VD��GD �H FKDPDGRFRQYHUVRU LGHDO '�&� 8P GLVSRVLWLYR �VLFDPHQWH UHDOL]�DYHO SU�R[LPR GR FRQYHUVRU LGHDO '�& �HXP FRQYHUVRU GLJLWDO�DQDO�RJLFR �'�$� DFRPSDQKDGR SRU XP �OWUR SDVVD�EDL[D�

��

Page 45: Analise de Sinais

)LJXUD ����� 5HSUHVHQWD�FaDR GH XPD VLVWHPD $PRVWUD H 6HJXUD LGHDO�

)LJXUD ����� 6LQDLV W��SLFRV GH HQWUDGD H VD��GD SDUD R VLVWHPD $PRVWUD H 6HJXUD�

8P FRQYHUVRU '�$ WRPD XPD VHT¦XAHQFLD GH SDODYUDV F�RGLJR ELQ�DULDV A\% >Q@ FRPR HQWUDGD HSURGX] XPD VD��GD FRQW��QXD GD IRUPD

\'$�W�

��;Q ��

<PA\% >Q@KR�W� Q7 �

��;Q ��

A\>Q@KR�W� Q7 � ������

RQGH <P �H XP SDUADPHWUR UHODFLRQDGR FRP R TXDQWL]DGRU� A\%>Q@ �H D VHT¦XAHQFLD GH SDODYUDV F�RGLJR�A\>Q@ �H D VHT¦XAHQFLD TXDQWL]DGD UHSUHVHQWDWLYD GR VLQDO GLJLWDO H KR�W� �H D UHVSRVWD DR LPSXOVR GHXP VLVWHPD C$PRVWUD H 6HJXUD � 2 GLDJUDPD GH EORFRV GH XP FRQYHUVRU '�$ �H PRVWUDGR QD�JXUD �����6H XVDUPRV R PRGHOR GH UX��GR DGLWLYR SDUD UHSUHVHQWDU RV HIHLWRV GH TXDQWL]D�FaDR SRGHPRV

HVFUHYHU

\'$�W�

��;Q ��

\>Q@KR�W� Q7 � �

��;Q ��

H>Q@KR�W� Q7 �� ������

'H�QLQGR

\R�W�

��;Q ��

\>Q@KR�W� Q7 � ������

��

Page 46: Analise de Sinais

)LJXUD ����� 5HSUHVHQWD�FaDR PDWHP�DWLFD GR FRQYHUVRU $�'�

)LJXUD ����� 'LDJUDPD GH EORFRV GH XP FRQYHUVRU '�$

H

HR�W�

��;Q ��

H>Q@KR�W� Q7 � � ������

WHPRV�

\'$�W� \R�W� � HR�W�� ������

$ FRPSRQHQWH \R�W� HVW�D UHODFLRQDGD FRP R VLQDO GHVHMDGR \D�W� H R UX��GR HR�W� GHSHQGH GDTXDQWL]D�FaDR�3RGHPRV PRVWUDU� DS�RV DOJXQV F�DOFXORV� TXH GH�QLQGR XP �OWUR FRP UHVSRVWD HP IUHT¦XAHQFLD

a+U�M��

��7 �

VHQ��7 ��HM�7 �� M � M� � 7

�� M � M! � 7������

SRGHPRV REWHU D VD��GD \D�W� VH D HQWUDGD GR �OWUR IRU \R�W��3RU�HP� D HQWUDGD GR �OWUR �H \'$�W� \R�W� � HR�W� H D VD��GD VHU�D

A\U�W� \D�W� � HD�W� ������

RQGH HD�W� VHU�D XP UX��GR EUDQFR OLPLWDGR HP IDL[D�'H PRGR JHUDO WHUHPRV

<D�M�� a+U�M��+R�M��+�HM�7 �+DD�M��;F�M�� ������

RQGH +DD�M�� � +R�M�� H a+U�M�� VaDR DV UHVSRVWDV HP IUHT¦XAHQFLD GR �OWUR DQWL�PDVFDUDPHQWR�CDPRVWUD H VHJXUD H GR �OWUR SDVVD�EDL[D GH UHFRQVWUX�FaDR� UHVSHFWLYDPHQWH� +�HM�7 � �H D UH�VSRVWD HP IUHT¦XAHQFLD GR VLVWHPD GLVFUHWR�

��

Page 47: Analise de Sinais

��� $ 7UDQVIRUPDGD 'LVFUHWD GH )RXULHU �7')�

����� ,QWURGX�FaDR

1�RV M�D GLVFXWLPRV D UHSUHVHQWD�FaDR GH VHT¦XAHQFLDV H VLVWHPDV OLQHDUHV LQYDULDQWHV QR WHPSR HPWHUPRV GD WUDQVIRUPDGD GH )RXULHU� 3DUD VHT¦XAHQFLDV GH GXUD�FaDR �QLWD �H SRVV��YHO GHVHQYROYHUXPD UHSUHVHQWD�FaDR GH )RXULHU DOWHUQDWLYD� UHIHULGD FRPR 7UDQVIRUPDGD 'LVFUHWD GH )RXULHU�7')�� $ 7') �H XPD VHT¦XAHQFLD H QaDR XPD IXQ�FaDR GH YDUL�DYHO FRQW��QXD H FRUUHVSRQGH DVDPRVWUDV� LJXDOPHQWH HVSD�FDGDV HP IUHT¦XAHQFLD� GD WUDQVIRUPDGD GH )RXULHU GR VLQDO� $ 7')WHP XP SDSHO LPSRUWDQWH QD LPSOHPHQWD�FaDR GH DOJRULWPRV GH SURFHVVDPHQWR GH VLQDLV GLJLWDLV�

����� $ V�HULH GLVFUHWD GH )RXULHU

&RQVLGHUH XPD VHT¦XAHQFLD a[>Q@ SHUL�RGLFD GH SHU��RGR 1 WDO TXH a[>Q@ a[>Q � U1 @ SDUD TXDOTXHULQWHLUR U� &RPR QR FDVR GH VLQDLV FRQW��QXRV� WDO VHT¦XAHQFLD SRGH VHU UHSUHVHQWDGD SRU XPD VRPDGH VHT¦XAHQFLDV H[SRQHQFLDLV FRPSOH[DV KDUPRQLFDPHQWH UHODFLRQDGDV� $ UHSUHVHQWD�FaDR HP V�HULHGH )RXULHU GH a[>Q@ WHP D IRUPD

a[>Q@ �

1

1��;R

a;>N@HM��� 1�NQ ������

RQGH

a;>N@

1��;Q �

a[>Q@H�M��� 1�NQ� ������

1RWH TXH a;>N@ �H SHUL�RGLFD GH SHU��RGR 1�1RUPDOPHQWH GH�QLPRV :1 H�M��� 1� H HVFUHYHPRV ���� H ���� FRPR

a[>Q@ �

1

1��;N �

a;>N@:�NQ1 ������

H

a;>N@

1��;Q �

a[>Q@:�NQ1 � ������

&RQVLGHUHPRV� FRPR H[HPSOR� TXH D VHT¦XAHQFLD a[>Q@ �H GDGD SHOD �JXUD �����$VVLP�

a;>N@

�;Q �

a[>Q@H�M������NQ

�;Q �

H�M��� ���NQ H�M��N� ���VHQ�N� ��

VHQ�N� ���� ������

��

Page 48: Analise de Sinais

)LJXUD ����� 6HT¦XAHQFLD SHUL�RGLFD FRP SHU��RGR 1 ��

)LJXUD ����� 0DJQLWXGH GH a;>N@�

2 JU�D�FR GD PDJQLWXGH GH a;>N@ �H GDGR QD �JXUD ���� �$ VHT¦XAHQFLD SHUL�RGLFD QD HTXD�FaDR ���� SRGH VHU LQWHUSUHWDGD FRPR DPRVWUDV LJXDOPHQWH

HVSD�FDGDV GD WUDQVIRUPDGD GH )RXULHU GLVFUHWD GH XP SHU��RGR GH a[>Q@�

&RQVLGHUHPRV

[>Q@

�a[>Q@� � � Q � 1 � ��� FDVR FRQWU�DULR�

������

$VVLP�

;�HM��

1��;Q �

[>Q@H�M�Q

1��;Q �

a[>Q@H�M�Q� ������

&RPSDUDQGR ���� FRP ���� REVHUYDPRV TXH

a;>N@ ;�HM�� SDUD � �N� 1 ������

TXH FRUUHVSRQGH �D WUDQVIRUPDGD GH )RXULHU GLVFUHWD SDUD 1 IUHT¦XAHQFLDV LJXDOPHQWH HVSD�FDGDVHQWUH � � H � �� FRP R HVSD�FR HQWUH IUHT¦XAHQFLDV GH �� 1 �9HQGR TXH D VHT¦XAHQFLD GDGD SHOD �JXUD ���� �H SHUL�RGLFD� WRPHPRV DSHQDV XP SHU��RGR�

$VVLP�

[>Q@

��� � � Q � ��� � � Q � ��

������

��

Page 49: Analise de Sinais

$ WUDQVIRUPDGD GH )RXULHU GLVFUHWD GH [>Q@ �H

;�HM��

�;�

H�M�Q H�M��VHQ��� ��

VHQ�� ��� ������

2 JU�D�FR GD PDJQLWXGH GH ;�HM�� �H GDGR SHOD �JXUD ���� �

)LJXUD ����� 0DJQLWXGH GH ;�HM���

8QLQGR DV �JXUDV ���� H ���� QXP �XQLFR JU�D�FR REVHUYDPRV R JU�D�FR GD �JXUD �����

����� $ WUDQVIRUPDGD GLVFUHWD GH )RXULHU �7')�

2EVHUYDPRV DQWHULRUPHQWH TXH GDGD XPD VHT¦XAHQFLD SHUL�RGLFD a[>Q@� RV FRH�FLHQWHV GD V�HULHGLVFUHWD GH )RXULHU GH a[>Q@ VaDR DV DPRVWUDV GD WUDQVIRUPDGD GH )RXULHU GLVFUHWD GH XP SHU��RGRGH a[>Q@� 'DGD XPD VHT¦XAHQFLD GH FRPSULPHQWR �QLWR [>Q@ Q�RV SRGHPRV IRUPDU XPD VHT¦XAHQFLDSHUL�RGLFD a[>Q@ GDGD SRU

a[>Q@ [>Q@ �

��;U ��

��Q � U1�

��;U ��

[>Q � U1 @ ������

)LJXUD ����� 8QLaDR GRV JU�D�FRV GH M a;>N@ M H M ;�HM�� M�

��

Page 50: Analise de Sinais

TXH SRGH VHU UHSUHVHQWDGD SRU XPD V�HULH GH )RXULHU� $OWHUQDWLYDPHQWH� GDGD D VHT¦XAHQFLD GHFRH�FLHQWHV GH )RXULHU a;>N@� SRGHPRV DFKDU a[>Q@ H XVDU D UHOD�FaDR

[>Q@

�a[>Q@� � � Q � 1 � ��� FDVR FRQWU�DULR

������

SDUD REWHU [>Q@�3RGHPRV HQWaDR XVDU D V�HULH GLVFUHWD GH )RXULHU SDUD UHSUHVHQWDU VHT¦XAHQFLDV GH FRPSULPHQWR

�QLWR H FKDPDPRV GH 7UDQVIRUPDGD 'LVFUHWD GH )RXULHU �7')��&RQVLGHUHPRV XPD VHT¦XAHQFLD [>Q@ GH FRPSULPHQWR 1 ��QLWR� WDO TXH [>Q@ � IRUD GR

LQWHUYDOR � � Q � 1 � �� $VVRFLHPRV XPD VHT¦XAHQFLD SHUL�RGLFD a[>Q@ GDGD SRU

a[>Q@

��;U ��

[>Q � U1 @� ������

$ VHT¦XAHQFLD [>Q@ SRGH VHU UHFXSHUDGD GH a[>Q@ SRU

[>Q@

�a[>Q@� � � Q � 1 � ��� FDVR FRQWU�DULR�

������

2V FRH�FLHQWHV GD V�HULH GLVFUHWD GH )RXULHU a;>N@ GD VHT¦XAHQFLD SHUL�RGLFD a[>Q@ �H XPD VHT¦XAHQFLDSHUL�RGLFD GH SHU��RGR 1� (VFROKHPRV XPD VHT¦XAHQFLD IRUPDGD SRU HOHPHQWRV FRPSUHHQGLGRV HPXP SHU��RGR GH a;>N@� (VWD VHT¦XAHQFLD GH GXUD�FaDR �QLWD� ;>N@� �H UHIHULGD FRPR D WUDQVIRUPDGDGLVFUHWD GH )RXULHU �7')� GH [>Q@� $VVLP� VH [>Q@ �H XPD VHT¦XAHQFLD GH FRPSULPHQWR �QLWR H VXDWUDQVIRUPDGD GLVFUHWD GH )RXULHU �H ;>N@ HQWaDR

;>N@

1��;Q �

[>Q@: NQ1 ������

H

[>Q@ �

1

1��;N �

;>N@:�NQ1 � ������

&RPR H[HPSOR� FRQVLGHUHPRV D VHT¦XAHQFLD GH GXUD�FaDR �QLWD [>Q@ PRVWUDGD QD �JXUD ���� �D��FRP 1 ��� &RQVWUX��PRV D VHT¦XAHQFLD SHUL�RGLFD a[>Q@ D SDUWLU GH [>Q@� PRVWUDGD QD �JXUD �����E�� 2V FRH�FLHQWHV GD V�HULH GLVFUHWD GH )RXULHU VaDR PRVWUDGRV QD �JXUD ���� �F�� DVVLP FRPR DPDJQLWXGH GD 7UDQVIRUPDGD GH )RXULHU GLVFUHWD� M ;�HM�� M � GH [>Q@� &ODUDPHQWH� a;>N@ �H XPDVHT¦XAHQFLD GH DPRVWUDV GH ;�HM�� QDV IUHT¦XAHQFLDV �N �N� 1 � $ 7') GH �� SRQWRV GH [>Q@FRUUHVSRQGH �D VHT¦XAHQFLD GH FRPSULPHQWR �QLWR REWLGD DR H[WUDLUPRV XP SHU��RGR GH a;>N@� $PDJQLWXGH GD 7') GH �� SRQWRV GH [>Q@ �H PRVWUDGD QD �JXUD ���� �G��

��

Page 51: Analise de Sinais

)LJXUD ����� ([HPSOR GH 7')�

����� $ WUDQVIRUPDGD U�DSLGD GH )RXULHU

$ 7') �H D �XQLFD WUDQVIRUPDGD TXH �H GLVFUHWD QR WHPSR H QD IUHT¦XAHQFLD H �H GH�QLGD SDUDVHT¦XAHQFLDV GH GXUD�FaDR �QLWD� (PERUD HOD SRVVD VHU FDOFXODGD QXPHULFDPHQWH� D LPSOHPHQWD�FaDRGLUHWD GD HTXD�FaDR ���� �H LQH�FLHQWH� HVSHFLDOPHQWH TXDQGR R FRPSULPHQWR 1 GD VHT¦XAHQFLD IRUJUDQGH� 9�DULRV DOJRULWPRV H�FLHQWHV IRUDP GHVHQYROYLGRV H HVVHV DOJRULWPRV VaDR FRQKHFLGRVFROHWLYDPHQWH FRPR WUDQVIRUPDGD U�DSLGD GH )RXULHU �))7��&RQVLGHUH XPD VHT¦XAHQFLD GH 1 SRQWRV [>Q@� 6XD 7') GH 1 SRQWRV �H GDGD SHOD HTXD�FaDR ����

H UHSURGX]LGD D VHJXLU

;>N@

1��;Q �

[>Q@: NQ1 � � � N � 1 � � ������

��

Page 52: Analise de Sinais

RQGH :1 H�M�� 1 � 3DUD REWHUPRV XPD DPRVWUD GH ;>N@ Q�RV SUHFLVDPRV GH 1 PXOWLSOL�FD�FaRHV FRPSOH[DV H �1 � �� DGL�FaRHV FRPSOH[DV� 'D��� SDUD REWHUPRV XP FRQMXQWR FRPSOHWR GRVFRH�FLHQWHV GD 7')� Q�RV SUHFLVDPRV GH 1� PXOWLSOLFD�FaRHV FRPSOH[DV H 1�1 ��� � 1� DGL�FaRHVFRPSOH[DV� &ODUDPHQWH� R Q�XPHUR GH F�DOFXORV SDUD DFKDU D 7') GH XPD VHT¦XAHQFLD GH 1 SRQWRVGHSHQGH TXDGUDWLFDPHQWH GH 1� TXH VHU�D GHQRWDGR SRU

&1 R�1 ���

3DUD 1 JUDQGH� R�1�� �H LQDFHLW�DYHO QD SU�DWLFD� *HUDOPHQWH� R WHPSR GH SURFHVVDPHQWRSDUD XPD DGL�FaDR �H PXLWR PHQRU TXH SDUD XPD PXOWLSOLFD�FaDR� 3RU LVVR� D SDUWLU GH DJRUDQRV FRQFHQWUDUHPRV DSHQDV QR Q�XPHUR GH PXOWLSOLFD�FaRHV FRPSOH[DV� RQGH FDGD PXOWLSOLFD�FaDRUHTXHU TXDWUR PXOWLSOLFD�FaRHV UHDLV H GXDV DGL�FaRHV UHDLV� $ GHSHQGAHQFLD TXDGU�DWLFD SRGH VHUUHGX]LGD VH REVHUYDUPRV TXH PXLWRV F�DOFXORV SRGHPV VHU HOLPLQDGRV XVDQGR DV SURSULHGDGHV GHSHULRGLFLGDGH

: NQ1 :

N�Q�1�1 :

�N�1�Q1

H GH VLPHWULD

:NQ�1 �1 �: NQ

1

GR IDWRU I: NQ1 J�

&RPH�FDUHPRV FRP XP H[HPSOR SDUD LOXVWUDU DV YDQWDJHQV GDV SURSULHGDGHV GH VLPHWULD HSHULRGLFLGDGH SDUD UHGX]LU R Q�XPHUR GH F�DOFXORV�2 0$7/$% SRVVXL XPD IXQ�FaDR FKDPDGD �W SDUD FDOFXODU D 7') GH XP YHWRU [� $ VLQWD[H

�H ; IIW�[�1� TXH FDOFXOD D 7') GH 1 SRQWRV� 6H R FRPSULPHQWR GH [ �H PHQRU TXH 1�HQWaDR [ �H FRPSOHWDGR FRP ]HURV� 6H R DUJXPHQWR 1 �H RPLWLGR HQWaDR R FRPSULPHQWR GD 7') �H RFRPSULPHQWR GH [� 6H 1 IRU XPD SRWAHQFLD GH � HQWaDR XP DOJRULWPR ))7 GH UDLR � �H XWLOL]DGR�6H 1 QaDR IRU XPD SRWAHQFLD GH �� HQWaDR 1 �H GHFRPSRVWR HP IDWRUHV SULPRV H XP DOJRULWPR))7 GH UDLR PLVWR �H XWLOL]DGR� )LQDOPHQWH� VH 1 IRU SULPR� HQWaDR D IXQ�FaDR �W FDOFXOD D 7')GLUHWDPHQWH SHOD I�RUPXOD� $ 7') LQYHUVD �H FDOFXODGD XVDQGR D IXQ�FaDR L�W� TXH WHP DV PHVPDVFDUDFWHU��VWLFDV GD �W�$SUHVHQWDPRV� QD �JXUD ����� XP UHVXPR GDV UHOD�FaRHV HQWUH R GRP��QLR GR WHPSR H GD

IUHT¦XAHQFLD DWUDY�HV GD WUDQVIRUPDGD GH )RXULHU� DQDO�RJLFD H GLJLWDO�0RVWUDPRV QD �JXUD ���� XP UHVXPR PRVWUDQGR D GXDOLGDGH HQWUH RV GLIHUHQWHV WLSRV GH

WUDQVIRUPDGDV�

��

Page 53: Analise de Sinais

� �

)LJXUD ����� 5HVXPR GDV UHOD�FaRHV HQWUH RV GRP��QLRV GR WHPSR H GD IUHT¦XAHQFLD� DWUDY�HV GDVWUDQVIRUPDGDV GH )RXULHU�

��

Page 54: Analise de Sinais

� �

)LJXUD ����� 'XDOLGDGH HQWUH RV GLIHUHQWHV WLSRV GH WUDQVIRUPDGDV�

��

Page 55: Analise de Sinais

)LJXUD ����� *U�D�FRV GH �D� [F H GH ;F�M����E�[>Q@ H GH M ;>N@ M�

����� ([HPSORV

�� &RQVLGHUHPRV R VLQDO FRQW��QXR [F GDGR SRU

[F�W� � � � � W � ��

7RPHPRV RLWR DPRVWUDV GHVVH VLQDO QHVVH LQWHUYDOR� FRQVWUXLQGR D VHT¦XAHQFLD

[>Q@ I�� �� �� �� ���� �� �J�

0RVWUDPRV RV JU�D�FRV GH [F H GH M ;F�M�� M QD �JXUD ���� �D��1D �JXUD ���� �E� PRVWUDPRV RV JU�D�FRV GH [>Q@ H GD DPSOLWXGH GD ))7 GH [>Q@� LVWR �H�

M ;>N@ M� SDUD � � N � ��&RQVLGHUHPRV� DJRUD� R VLQDO [F GDGR SRU �

[F�W�

��� � � W � ��� � � W � ���

7RPHPRV �� DPRVWUDV GHVVH VLQDO� FRQVWUXLQGR D VHT¦XAHQFLD

[>Q@ I�� �� �� �� �� �� �� �� ���� �� �� ���� �� �J�

��

Page 56: Analise de Sinais

)LJXUD ����� *U�D�FRV GH �D� [F H GH ;F�M�� �E� GH [>Q@ H GH M ; M ;>N@ M�

0RVWUDPRV RV JU�D�FRV GH [F H GH M ;F�M�� M QD �JXUD ���� �D�� 1D �JXUD ���� �E� PRVWUDPRVRV JU�D�FRV GH [>Q@ H GD DPSOLWXGH GD 7') GH [>Q@� LVWR �H� M ;>N@ M SDUD � � N � ���2EVHUYDPRV TXH M ;>N@ M� QD �JXUD ���� �E� QaDR UHSUHVHQWD VLJQL�FDWLYDPHQWH M ;F�M�� M�

3RU�HP� QD �JXUD ���� D UHSUHVHQWD�FaDR �H VLJQL�FDWLYD� (VVH SUREOHPD VHU�D GLVFXWLGR PDLV DGLDQWH�/HPEUDPRV TXH D 7') GH XPD VHT¦XAHQFLD [>Q@ GH 1 WHUPRV UHSUHVHQWD DPRVWUDV LJXDOPHQWH

HVSD�FDGDV GH ;F�M�� SDUD � �N�1FRP � � N � 1 � �� 0RVWUDPRV QDV �JXUDV ���� H ����� RV

JU�D�FRV GD DPSOLWXGH GD 7') FRORFDQGR QR HL[R KRUL]RQWDO RV YDORUHV GH Q� 6H GHVHM�DVVHPRVPRVWUDU� QR HL[R KRUL]RQWDO� RV YDORUHV GD IUHT¦XAHQFLD �� EDVWD TXH ID�FDPRV XPD PXGDQ�FD GHHVFDOD� 7HU��DPRV DVVLP RV JU�D�FRV PRVWUDGRV QD �JXUD �������&RQVLGHUHPRV R VLQDO FRQW��QXR [F GDGR SRU

[F�W� VHQ���W� �� � W � ��

'HVHMDPRV REWHU �� DPRVWUDV� LJXDOPHQWH HVSD�FDGDV� GHVVH VLQDO� 'HVVD IRUPD� IRUPDPRV DVHT¦XAHQFLD �

[>Q@ VHQ���1

��� SDUD 1 �� �� � � � � ���

0RVWUDPRV D UHSUHVHQWD�FaDR JU�D�FD GHVVD VHT¦XAHQFLD QD �JXUD �����

��

Page 57: Analise de Sinais

)LJXUD ����� *U�D�FRV GH M ;>N@ M�

)LJXUD ����� 5HSUHVHQWD�FaDR JU�D�FD GH XPD VHT¦XAHQFLD�

&DOFXODPRV D 7') GHVVD VHT¦XAHQFLD� XVDQGR R 0$7/$% H PRVWUDPRV R JU�D�FR GH VXDDPSOLWXGH QD �JXUD �����2 JU�D�FR PRVWUDGR QD �JXUD ���� �H IRUPDGR SRU DPRVWUDV LJXDOPHQWH HVSD�FDGDV GH XP

SHU��RGR GD WUDQVIRUPDGD GH )RXULHU 'LVFUHWD� ;�HM��� GH [>Q@� 'HYHPRV LQWHUSUHW�D�OR GDVHJXLQWH IRUPD � RV WHUPRV GD VHT¦XAHQFLD FRUUHVSRQGHQWHV DRV YDORUHV GH 1 HQWUH � H �� FRUUH�VSRQGHP �DV DPRVWUDV GH ;�HM�� HQWUH � H � H SDUD RV YDORUHV GH 1 HQWUH �� H �� FRUUHVSRQGHP�DV DPRVWUDV GH ;�HM�� HQWUH �� H ��&RQVLGHUHPRV R VLQDO [F GDGR SRU

[F�W�

�VHQ���W�� � � W � ��� � � W � �

7RPHPRV ��� DPRVWUDV GHVVH VLQDO� &DOFXODPRV D 7') H PRVWUDPRV RV JU�D�FRV GD VHT¦XAHQFLDREWLGD HP ���� �D� H GD PDJQLWXGH GD 7') HP ���� �E��2EVHUYDPRV GLIHUHQ�FDV HQWUH RV JU�D�FRV GDV DPSOLWXGHV GD 7') � GD PHVPD IRUPD TXH QR

H[HPSOR ��

��

Page 58: Analise de Sinais

)LJXUD ����� 0DJQLWXGH GD 7') GH [>Q@�

�� &RQVLGHUHPRV R VLQDO [F GDGR SRU

[F�W�

�W� � � W � ��� � � W � ��

7RPHPRV �� DPRVWUDV GHVVH VLQDO H FDOFXOHPRV D 7')� 0RVWUDPRV RV JU�D�FRV GD VHT¦XAHQFLDREWLGD DVVLP FRPR GD PDJQLWXGH GD 7') QD �JXUD �����'HVWD YH] QaDR REVHUYDPRV TXDVH D WRWDOLGDGH GDV DPRVWUDV� HP M ;>N@ M � QXODV FRPR QRV

FDVRV DQWHULRUHV H QaDR SUHFLVDPRV DFUHVFHQWDU ]HURV QR �QDO GD VHT¦XAHQFLD�$ DSDUAHQFLD GDV 7')V REWLGDV QDV �JXUDV ���� H ���� �H XPD LOXVaDR UHVXOWDQWH GD DPRVWUDJHP

HVSHFWUDO� $ UD]aDR GLVWR �H TXH D WUDQVIRUPDGD GLVFUHWD GH )RXULHU �H H[DWDPHQWH ]HUR QDVIUHT¦XAHQFLDV TXH VaDR DPRVWUDGDV� H[FHWR SDUD DOJXQV SRXFRV YDORUHV GH N� 'HVVD IRUPD� �H UH�FRPHQG�DYHO TXH DFUHVFHQWHPRV ]HURV QR �QDO GD VHT¦XAHQFLD GH IRUPD D REWHUPRV XPD DPRVWUDJHPPDLV UH�QDGD GR HVSHFWUR�

��� $Q�DOLVH GH VLQDLV XVDQGR 7')

����� ,QWURGX�FaDR

8PD GDV DSOLFD�FaRHV GH 7') �H QD DQ�DOLVH HP IUHT¦XAHQFLD GH VLQDLV FRQW��QXRV� 2V SDVVRV E�DVLFRVSDUD D DSOLFD�FaDR GD 7') D VLQDLV FRQW��QXRV VaDR LQGLFDGRV QD �JXUD �����2 �OWUR DQWL�PDVFDUDPHQWR �H XVDGR SDUD HOLPLQDU RX PLQLPL]DU R PDVFDUDPHQWR� $ QHFHV�

VLGDGH GD PXOWLSOLFD�FaDR GH [>Q@ SRU XPD VHT¦XAHQFLD �QLWD FKDPDGD Z>Q@ �WDPE�HP FKDPDGD GHMDQHOD� �H XPD FRQVHT¦XAHQFLD GD QHFHVVLGDGH GD VHT¦XAHQFLD VHU GH FRPSULPHQWR �QLWR SDUD TXHSRVVDPRV DSOLFDU D 7')�1�RV GHVHQYROYHPRV D WUDQVIRUPDGD GLVFUHWD GH )RXULHU �7')� FRPR XPD UHSUHVHQWD�FaDR GH

VLQDLV GH FRPSULPHQWR �QLWR� 'LVFXWLPRV� WDPE�HP� XPD IRUPD GH FDOFXO�D�OD QXPHULFDPHQWHXVDQGR RV DOJRULWPRV FKDPDGRV FRQMXQWDPHQWH GH 7')� 3DUD VLQDLV GH FRPSULPHQWR �QLWR� D7') FRQVLVWH GH DPRVWUDV QR GRP��QLR GD IUHT¦XAHQFLD LJXDOPHQWH HVSD�FDGDV GD WUDQVIRUPDGD GH)RXULHU GLVFUHWD �7)'� H DV LPSOLFD�FaRHV GHVVD DPRVWUDJHP GHYHP VHU FODUDPHQWH HQWHQGLGDV�

��

Page 59: Analise de Sinais

)LJXUD ����� *U�D�FRV GH [>Q@ H GH M ;>N@ M�

&RPH�FDPRV FRP XP VLQDO FRQW��QXR [F�W� TXH DS�RV D SDVVDJHP SHOR �OWUR DQWL�PDVFDUDPHQWR�VH WUDQVIRUPD QR VLQDO [�W�� 2 VLQDO [�W� �H HQWaDR FRQYHUWLGR HP XPD VHT¦XAHQFLD [>Q@� 1R GRP��QLRGD IUHT¦XAHQFLD� D FRQYHUVaDR GH [�W� SDUD D VHT¦XAHQFLD [>Q@ �H UHSUHVHQWDGD SRU U�HSOLFDV SHUL�RGLFDVGD WUDQIRUPDGD GH )RXULHU GH [�W��;�M��� H QRUPDOL]D�FaDR GD IUHT¦XAHQFLD� LVWR �H�

;�HM�� �

7

��;N ��

;F�M�

7� M

�N�

7��

/HPEUDPRV TXH QD SU�DWLFD R �OWUR DQWL�PDVFDUDPHQWR QaDR WHP DWHQXD�FaDR LQ�QLWD QD EDQGDGH SDVVDJHP H DVVLP DOJXPD SUHVHQ�FD GH PDVFDUDPHQWR SRGH RFRUUHU� SRU�HP R HUUR FRPHWLGRVHU�D PXLWR SHTXHQR� 7DPE�HP� VH [>Q@ IRU XP VLQDO GLJLWDO� XP HUUR GH TXDQWL]D�FaDR SRGH VHULQWURGX]LGR �$ VHT¦XAHQFLD [>Q@ �H HQWaDR PXOWLSOLFDGD SRU XPD VHT¦XAHQFLD GH FRPSULPHQWR �QLWR Z>Q@ �MDQHOD�

SRLV D HQWUDGD GD ')7 GHYH VHU GH GXUD�FaDR �QLWD� 6H Z>Q@ IRU FRQVWDQWH SDUD WRGRV RV YDORUHVGH Q FRQVLGHUDGRV� FKDPDPRV GH MDQHOD UHWDQJXODU WHPSRUDO� 3RU�HP� H[LVWHP RXWURV WLSRV GHMDQHODV TXH VHUaDR GLVFXWLGRV PDLV WDUGH� $ RSHUD�FaDR �QDO �H D 7') GD VHT¦XAHQFLD Y>Q@ H �H GDGDSRU

��

Page 60: Analise de Sinais

)LJXUD ����� *U�D�FRV GH [>Q@ H GH M ;>N@ M�

9 >N@

1��;Q �

Y>Q@H�M��� 1�NQ � N �� �� � � � � 1 � ��

9 >N@ FRUUHVSRQGH D DPRVWUDV LJXODPHQWH HVSD�FDGDV GD WUDQVIRUPDGD GH )RXULHU GLVFUHWD GHY>Q@� LVWR �H�

9 >N@ 9 �HM�� M� �N� 1 �

&RQKHFHPRV D UHOD�FaDR � �7 H DVVLP DV IUHT¦XAHQFLDV REWLGDV QD 7') FRUUHVSRQGHP �DVIUHT¦XAHQFLDV �N GDGDV SRU �

�N �N�

17�

0XLWRV DQDOLVDGRUHV GH HVSHFWUR FRPHUFLDLV VaDR EDVHDGRV QR TXH IRL GLVFXWLGR DTXL� 3RU�HP�GHYHPRV HVWDU FLHQWHV TXH PXLWRV IDWRUHV DIHWDP D LQWHUSUHWD�FaDR GD WUDQVIRUPDGD GH )RXULHU GDHQWUDGD HP WHUPRV GD 7') GH XPD VHT¦XAHQFLD IRUPDGD GDV DPRVWUDV GR VLQDO� 'HVHMDPRV HVWXGDUSRVWHULRUPHQWH DV FRQVHT¦XAHQFLDV GD PXOWLSOLFD�FaDR GD VHT¦XAHQFLD SRU XPD MDQHOD H GDV DPRVWUDVQR GRP��QLR GD IUHT¦XAHQFLD H SDUD LVVR FRQVLGHUDPRV GHVSUH]��YHLV RV SUREOHPDV GH PDVFDUDPHQWRH R HUUR GH TXDQWL]D�FaDR LQWURGX]LGR QD FRQYHUVaDR $�'�

��

Page 61: Analise de Sinais

)LJXUD ����� 'LDJUDPD GH EORFRV GRV SDVVRV E�DVLFRV SDUD D DSOLFD�FaDR GD 7')�

����� -DQHODV � 2 YD]DPHQWR

,QWURGX�FaDR

(P PXLWDV DSOLFD�FaRHV RV VLQDLV QaDR WAHP FRPSULPHQWR �QLWR� 'HVHMDQGR DQDOLVDU DSHQDV GHWHU�PLQDGR LQWHUYDOR GH WHPSR� WUXQFDPRV R VLQDO HP XP GHWHUPLQDGR LQWHUYDOR� (VVD RSHUD�FaDRHTXLYDOH D PXOWLSOLFDU R VLQDO SRU XPD MDQHOD UHWDQJXODU WHPSRUDO� 3RU�HP� HVVD PXOWLSOLFD�FaDRSRGH OHYDU D UHVXOWDGRV LQGHVHM�DYHLV TXH SRGHP VHU REVHUYDGRV QR GRP��QLR GD IUHT¦XAHQFLD� 2E�VHUYDPRV DVVLP R IHQARPHQR FRQKHFLGR FRPR YD]DPHQWR� RX OHDNDJH� TXH VHU�D HVWXGDGR DGLDQWH�&RQVLGHUH R VLQDO VHQRLGDO GDGR SRU

I�W� FRV���W��

6DEHPRV TXH D WUDQVIRUPDGD GH )RXULHU GHVVH VLQDO �H GDGD SRU

) ��� �

�>��� � ��� � ��� � ���@

RX VHMD� GRLV LPSXOVRV ORFDOL]DGRV HP ��� H ����&RQVLGHUHPRV� DJRUD� D PXOWLSOLFD�FaDR GH I�W� SRU XPD MDQHOD UHWDQJXODU WHPSRUDO GDGD SRU

�7 �W�

��� �7 � W � 7�� FDVR FRQWU�DULR�

2EWHPRV� DVVLP� XPD QRYD IXQ�FaDR

J�W� FRV���W��7 �W�

FXMD WUDQVIRUPDGD GH )RXULHU �H GDGD SRU

*��� VHQ�� � ���7

� � ���

VHQ�� � ���7

� � ���

*��� HVW�D UHSUHVHQWDGD QD �JXUD ���� �'HYLGR �D WUXQFDJHP GR VLQDO RFRUUHX XP �HVSDOKDPHQWR� SDUD IUHT¦XAHQFLDV GLIHUHQWHV GH ���

2 HVSDOKDPHQWR �H PDLRU VH 7 IRU PHQRU�

��

Page 62: Analise de Sinais

)LJXUD ����� *U�D�FR GH *����

����� &RQVHTXAHQFLD GD DSOLFD�FaDR GH MDQHODV

&RQVLGHUHPRV XP VLQDO FRQW��QXR FRQVLVWLQGR GD VRPD GH GXDV FRPSRQHQWHV VHQRLGDLV� LVWR �H�

[F�W� $RFRV��RW� �R� �$�FRV���W� ��� � �� � W ��� ������

&RQVLGHUDQGR DPRVWUDJHP LGHDO VHP D SUHVHQ�FD GH PDVFDUDPHQWR H QHQKXP HUUR GH TXDQ�WL]D�FaDR� REWHPRV R VLQDO GLVFUHWR

[>Q@ $RFRV��RQ� �R� �$�FRV���Q� ��� � �� � Q � ��� ������

RQGH �R �R7 H �� ��7 � $S�RV D DSOLFD�FaDR GD MDQHOD Z>Q@ HP [>Q@ REWHPRV

Y>Q@ $RZ>Q@FRV��RQ� �R� �$�Z>Q@FRV���Q � ���� ������

$ WUDQVIRUPDGD GH )RXULHU GLVFUHWD GH Y>Q@ VHU�D

9 �HM�� $R

�HM�R: �HM����R�� �

$R

�H�M�R: �HM����R��

�$��HM��: �HM������� �

$��H�M��: �HM������� � ������

RQGH: �HM�� �H D WUDQVIRUPDGD GH )RXULHU GLVFUHWD GH Z>Q@� $VVLP� D WUDQVIRUPDGD GH )RXULHUGLVFUHWD GH Y>Q@ FRQVLVWH GH U�HSOLFDV GD WUDQVIRUPDGD GH )RXULHU GH Z>Q@ FRP GLIHUHQWH HVFDODGH DPSOLWXGH�

��

Page 63: Analise de Sinais

([HPSOR

&RQVLGHUHPRV R VLQDO GDGR SRU ���� H REWHPRV D VHT¦XAHQFLD GDGD SRU ���� FRP IUHT¦XAHQFLD GHDPRVWUDJHP GH � 7 ��N+]� &RQVLGHUHPRV XPD MDQHOD UHWDQJXODU Z>Q@ GH FRPSULPHQWR LJXDOD ��� &RQVLGHUHPRV� DLQGD� $R �� $� ���� H SRU FRQYHQLAHQFLD �R �� �� &DOFXOHPRV9 �HM�� SDUD Y�DULRV YDORUHV GH �R H ��� 0RVWUDUHPRV DSHQDV RV JU�D�FRV UHODWLYRV �DV PDJQLWXGHVGD WUDQVIRUPDGD GH )RXULHU GLVFUHWD �1D �JXUD ���� �D� PRVWUDPRV R JU�D�FR GH M : �HM�� M H QDV �JXUDV ���� �E� � ���� �D���E�

H ���� PRVWUDPRV R JU�D�FR GH M 9 �HM�� M SDUD Y�DULRV YDORUHV GH �R H �� RX HTXLYDOHQWHPHQWH �R

H ���

)LJXUD ����� �D�M : �HM�� M��E� M 9 �HM�� M SDUD �R ���� � H �� ��� ���

$ HTXD�FaDR ���� PRVWUD TXH VH QaDR KRXYHU VXSHUSRVL�FaDR HQWUH DV U�HSOLFDV GH : �HM�� HP �R H��� KDYHU�D XP SLFR GH DPSOLWXGH ��$R HP �R H XP SLFR GH DPSOLWXGH ��$� HP ��� SRLV : �H

M��WHP XP SLFR GH DPSOLWXGH ��� 1D �JXUD ���� �E� RV GRLV SLFRV HVWaDR� DSUR[LPDGDPHQWH� HP�R �� � H �� �� � H DV DPSOLWXGHV GRV SLFRV HVWaDR DSUR[LPDGDPHQWH QD UD]aDR �

�����1D

�JXUD ���� �D� K�D VXSHUSRVL�FaDR HQWUH DV U�HSOLFDV GH : �HM�� HP �R H ��� 2EVHUYDPRV GRLV SLFRVGLVWLQWRV� SRU�HP D DPSOLWXGH GR HVSHFWUR HP �R �H DIHWDGR SHOD DPSOLWXGH GR VLQDO VHQRLGDO QDIUHT¦XAHQFLD �� H YLFH�YHUVD� (VWD LQWHUD�FaDR �H FKDPDGD GH YD]DPHQWR� D FRPSRQHQWH HP XPDIUHT¦XAHQFLD �YD]D� QD YL]LQKDQ�FD GH RXWUD FRPSRQHQWH GHYLGR DR �HVSDOKDPHQWR� HVSHFWUDOLQWURGX]LGR SHOD MDQHOD� $ �JXUD ���� �E� PRVWUD R FDVR RQGH R YD]DPHQWR �H PDLRU� 2EVHUYHFRPR DV DPSOLWXGHV GRV SLFRV VaDR UHGX]LGDV� 1D �JXUD ���� D VXSHUSRVL�FaDR HQWUH DV U�HSOLFDV

��

Page 64: Analise de Sinais

)LJXUD ����� �D� M 9 �HM�� M SDUD �R ��� ��� H �� ��� �����E� M 9 �HM�� M SDUD �R ��� ���

H �� ��� ����

GH : �HM�� �H WaDR VLJQL�FDQWH TXH QaDR VaDR PDLV YLV��YHLV GRLV SLFRV PDV DSHQDV XP� (P RXWUDVSDODYUDV� FRP HVWD MDQHOD DV GXDV IUHT¦XAHQFLDV FRUUHVSRQGHQWHV QaDR VaDR GLIHUHQFLDGDV QR HVSHFWUR�5HVROX�FaDR UHGX]LGD H YD]DPHQWR VaDR GRLV HIHLWRV TXH RFRUUHP FRPR UHVXOWDGR GD DSOLFD�FaDR

GH MDQHODV DR VLQDO� $ UHVROX�FaDR �H LQ�XHQFLDGD SHOR ODUJXUD GR ORER SULQFLSDO �GLVWADQFLD HQWUH DVGXDV SULPHLUDV IUHT¦XAHQFLDV VLP�HWULFDV� GH : �HM��� HQTXDQWR R JUDX GH YD]DPHQWR GHSHQGH GRTXRFLHQWH HQWUH D DPSOLWXGH P�D[LPD GR ORER SULQFLSDO H D DPSOLWXGH P�D[LPD GR SULPHLUR ORERVHFXQG�DULR GH : �HM�� � &KDPDUHPRV HVVH YDORU GH $V� *HUDOPHQWH HVWH YDORU �H GDGR HP G%�GHFLEHO�� LVWR �H� FDOFXODPRV ��ORJ M $V M� $ ODUJXUD GR ORER SULQFLSDO GHSHQGH GR FRPSULPHQWRGD MDQHOD �TXDQWR PDLRU R FRPSULPHQWR GD MDQHOD� PHQRU D ODUJXUD GR ORER SULQFLSDO� H D DP�SOLWXGH UHODWLYD GR ORER SULQFLSDO H GRV ORERV VHFXQG�DULRV GHSHQGH GR IRUPDWR GD MDQHOD �TXDQWRPDLV �EUXVFDPHQWH� D MDQHOD YDL GH XP D ]HUR RX GH ]HUR D XP� PDLRU R YDORU GH $V��+�D Y�DULDVMDQHODV FRQKHFLGDV H HODV HVWaDR GLVSRQ��YHLV QR 0$7/$% �WRROER[ �VLJQDO SURFHVVLQJ��� 6aDR HODV�MDQHOD UHWDQJXODU� MDQHOD GH %DUWOHWW� MDQHOD GH +DQQLQJ� MDQHOD GH +DPPLQJ� MDQHOD GH %ODFN�PDQ H MDQHOD GH .DLVHU� 2V QRPHV IRUDP GDGRV HP KRPHQDJHP D VHXV DXWRUHV� 'LVFXWLUHPRVXP SRXFR VREUH FDGD XPD GHODV�

��

Page 65: Analise de Sinais

)LJXUD ����� M 9 �HM�� M SDUD �R ��� ��� H �� ��� ����

����� 7LSRV GH MDQHODV

-DQHOD UHWDQJXODU

$ MDQHOD UHWDQJXODU �H GH�QLGD SRU

Z>Q@

��� � � Q �0 � ��� FDVR FRQWU�DULR

$ ODUJXUD GR ORER SULQFLSDO SDUD HVWD MDQHOD �H LJXDO D ��0� 2 YDORU GH $V �H LJXDO D �� G%�

3DUD XP FRPSULPHQWR GDGR� HVWD MDQHOD SRVVXL D PHQRU ODUJXUD GH ORER SULQFLSDO� PDV R PDLRUYDORU GH $V FRPSDUDQGR FRP DV RXWUDV MDQHOD FRQKHFLGDV�0RVWUDPRV RV JU�D�FRV GH Z>Q@ H GH M: �HM�� M �HP G%�� QD �JXUD ����� SDUD 0 ���

)LJXUD ����� -DQHOD UHWDQJXODU�0 ��

-DQHOD GH %DUWOHWW

%DUWOHWW VXJHULX XPD MDQHOD TXH SRVVXL XPD WUDQVL�FaDR PDLV JUDGXDO GR TXH D MDQHOD UHWDQJXODU�WUDQVL�FaDR HQWUH � H ��� (VVD MDQHOD �H GH�QLGD SRU

��

Page 66: Analise de Sinais

Z>Q@

���

�Q0��

� � � Q � 0���

� � �Q0��

� 0���� Q �0 � �

�� FDVR FRQWU�DULR�

������

$ ODUJXUD GR ORER SULQFLSDO QHVWH FDVR �H DSUR[LPDGDPHQWH LJXDO D ��0H R YDORU GH $V �H LJXDO

D �� G%� 0RVWUDPRV RV JU�D�FRV GH Z>Q@ H GH M: �HM�� M� QD �JXUD �����

)LJXUD ����� -DQHOD GH %DUWOHWW� 0 ���

-DQHOD GH +DQQLQJ

(VWD MDQHOD �H GH�QLGD SRU

Z>Q@

����>� � FRV� ��Q

0���@� � � Q �0 � �

�� FDVR FRQWU�DULR�������

1HVWH FDVR� R FRPSULPHQWR GR ORER SULQFLSDO �H DSUR[LPDGDPHQWH LJXDO D ��0H $V ��G%�

0RVWUDPRV RV JU�D�FRV GH Z>Q@ H GH M: �HM�� M QD �JXUD �����

-DQHOD GH +DPPLQJ

(VWD MDQHOD �H GH�QLGD SRU

Z>Q@

����� � ����FRV� ��Q

0���� � � Q �0 � �

�� FDVR FRQWU�DULR�������

1HVWH FDVR� R FRPSULPHQWR GR ORER SULQFLSDO �H DSUR[LPDGDPHQWH LJXDO D ��0H $V ��G%�

0RVWUDPRV RV JU�D�FRV GH Z>Q@ H GH M: �HM�� M QD �JXUD �����

��

Page 67: Analise de Sinais

)LJXUD ����� -DQHOD GH +DQQLQJ� 0 ��

)LJXUD ����� -DQHOD GH +DPPLQJ� 0 ���

-DQHOD GH %ODFNPDQ

(VWD MDQHOD �H GH�QLGD SRU

Z>Q@

������ ���FRV� ��Q

0��� � ����FRV� ��Q

0���� � � Q �0 � �

�� FDVR FRQWU�DULR�������

1HVWH FDVR� R FRPSULPHQWR GR ORER SULQFLSDO �H DSUR[LPDGDPHQWH LJXDO D ��0H $V ��G%�

0RVWUDPRV RV JU�D�FRV GH Z>Q@ H GH M: �HM�� M QD �JXUD �����

-DQHOD GH .DLVHU

(VWD MDQHOD �H GH�QLGD SRU

Z>Q@

�,R >����>�Q��� �@��� �

,R���� � � Q �0

�� FDVR FRQWU�DULR������

��

Page 68: Analise de Sinais

)LJXUD ����� -DQHOD GH %ODFNPDQ� 0 ���

RQGH � 0�H ,R UHSUHVHQWD D IXQ�FaDR GH %HVVHO PRGL�FDGD GH RUGHP ]HUR GH SULPHLUR WLSR�

$ MDQHOD GH .DLVHU WHP GRLV SDUADPHWURV� R FRPSULPHQWR �0��� H XP SDUADPHWUR GH IRUPD ����0RVWUDPRV QD �JXUD ���� RV JU�D�FRV GH Z>Q@ H GH M : �HM�� SDUD R FDVR HP TXH 0 �� H� ������ 1HVVH FDVR� R FRPSULPHQWR GR ORER SULQFLSDO �H LJXDO D ���

0H $V �� G%�

)LJXUD ����� -DQHOD GH .DLVHU� 0 ��� � �����

'HYHPRV UHVVDOWDU TXH FDGD XPD GHVVDV MDQHODV WHP XPD GHWHUPLQDGD DSOLFD�FaDR�

([HPSOR

&RQVLGHUHPRV D VHT¦XAHQFLD GR H[HPSOR DQWHULRU� WRPDQGR DV IUHT¦XAHQFLD ZR �� �� H Z� �� ��)DUHPRV XPD FRPSDUD�FaDR HQWUH RV JU�D�FRV GH M 9 �HM�� M XWLOL]DQGR DV MDQHODV UHWDQJXODU� GH%ODFNPDQ H GH +DQQLQJ�8WLOL]DPRV D VHT¦XAHQFLD�

Y>Q@ Z>Q@FRV���

��Q� � Z>Q@����FRV�

��

�Q�

SDUD Q HQWUH � H ���

��

Page 69: Analise de Sinais

0RVWUDPRV QD �JXUD ���� �D� R JU�D�FR GH M 9 �HM�� M XWLOL]DQGR D MDQHOD UHWDQJXODU� QD�JXUD ���� �E�� XWLOL]DQGR D MDQHOD GH +DQQLQJ H QD �JXUD ���� �F�� XWLOL]DQGR D MDQHOD GH%ODFNPDQ�2EVHUYDPRV TXH R TXRFLHQWH HQWUH RV GRLV SLFRV GH DPSOLWXGH GHYHULD VHU LJXDO D �

���� ������

&RP D MDQHOD UHWDQJXODU REWLYHPRV ������ � FRP D MDQHOD GH +DQQLQJ REWLYHPRV ������ HFRP D MDQHOD GH %ODFNPDQ REWLYHPRV �������� $VVLP� DV MDQHODV GH %ODFNPDQ H GH +DQQLQJUHGX]LUDP R SUREOHPD GH /HDNDJH� FRPR HUD HVSHUDGR� &RP MDQHOD GH +DQQLQJ REWLYHPRV RPHOKRU UHVXOWDGR�

)LJXUD ����� �D� 8WLOL]D�FaDR GD MDQHOD UHWDQJXODU� �E� 8WLOL]D�FaDR GD MDQHOD GH +DQQLQJ��F� 8WLOL]D�FaDR GD MDQHOD GH %ODFNPDQ�

��

Page 70: Analise de Sinais

&DS��WXOR �

'XDV DSOLFD�FaRHV

��� 0XOWLSOH[D�FaDR

����� &RQFHLWR

6H XP FLUFXLWR XWLOL]DQGR XP SDU GH FRQGXWRUHV SHUPLWH TXH GXDV SHVVRDV SRVVDP HVWDEHOHFHUXP GL�DORJR VHP SUREOHPDV� SRGHPRV SHUFHEHU TXH� VH TXDWUR DVVLQDQWHV WLUDVVHP R WHOHIRQH GRJDQFKR DR PHVPR WHPSR� WRGRV RXYLULDP D FRQYHUVD GRV RXWURV� 4XDQWR PDLRU R Q�XPHUR GHDVVLQDQWHV� PDLRU VHULD R SUREOHPD� $VVLP� K�D D QHFHVVLGDGH GD XWLOL]D�FaDR GH XPD W�HFQLFD TXHSRVVLELOLWH D FRPXQLFD�FaDR� VHP LQWHUIHUAHQFLD HQWUH RV FLUFXLWRV� SRU�HP XWLOL]DQGR R PHVPR PHLRGH WUDQVPLVVaDR� $ PXOWLSOH[D�FaDR �H HVVD W�HFQLFD� (OD XWLOL]D FLUFXLWRV D TXDWUR �RV FRP FDQDLVGH LGD �GRLV �RV� H FDQDLV GH YROWD �GRLV �RV�� $ �JXUD ��� PRVWUD HVTXHPDWLFDPHQWH D OLJD�FaDRXWLOL]DQGR D W�HFQLFD GH PXOWLSOH[D�FaDR�2 PHLR GH WUDQVPLVVaDR GHVFULWR SRGH VHU XP SDU GH �RV� R DU �UDGLRHQODFH�� �EUD �RWLFD� HWF�

)LJXUD ���� /LJD�FaDR WHOHIARQLFD DWUDY�HV GD PXOWLSOH[D�FaDR�

��

Page 71: Analise de Sinais

����� 7LSRV GH PXOWLSOH[D�FaDR

$WXDOPHQWH VaDR XWLOL]DGRV GLYHUVRV WLSRV GH PXOWLSOH[D�FaDR� GLYLGLGRV HP GRLV JUXSRV� GH DFRUGRFRP D W�HFQLFD XWLOL]DGD�

� 7�HFQLFD GLJLWDO � $ PXOWLSOH[D�FaDR TXH XWLOL]D HVWD W�HFQLFD �H D FKDPDGD PXOWLSOH[D�FaDR SRUGLYLVaDR GH WHPSR�

� 7�HFQLFD DQDO�RJLFD � $ PXOWLSOH[D�FaDR TXH XWLOL]D HVVD W�HFQLFD �H D FKDPDGD PXOWLSOH[D�FaDRSRU GLYLVaDR HP IUHT¦XAHQFLD

$ HVFROKD GR PHLR GH WUDQVPLVVaDR D VHU XWLOL]DGR QXP VLVWHPD PXOWLSOH[ �H SULPRUGLDOPHQWHEDVHDGR QR Q�XPHUR GH FDQDLV D VHUHP WUDQVPLWLGRV� SRU�HP D GLVWADQFLD HQWUH RV SRQWRV TXHGHVHMDP VH FRPXQLFDU� DV GL�FXOGDGHV JHRJU�D�FDV HQWUH RV PHVPRV� EHP FRPR D FRQ�DELOLGDGHH TXDOLGDGH GHVHMDGDV SDUD R VLVWHPD WDPE�HP LUaDR GLWDU TXDO R SURFHVVR PDLV HFRQARPLFR D VHUXWLOL]DGR�2V PHLRV GH WUDQVPLVVaDR EDVLFDPHQWH QaDR DOWHUDP R HTXLSDPHQWR PXOWLSOH[� VHQGR GLYLGLGRV

HP GRLV JUXSRV� FRQIRUPH D SURSDJD�FaDR GR VLQDO VHMD QR HVSD�FR RX QXP PHLR I��VLFR� VLVWHPDVGH WUDQVPLVVaDR YLD U�DGLR H VLVWHPDV GH WUDQVPLVVaDR YLD OLQKD I��VLFD�$ FRQ�JXUD�FaDR JHUDO SDUD D OLJD�FaDR YLD U�DGLR �H PRVWUDGD QD �JXUD ����

)LJXUD ���� /LJD�FaDR YLD U�DGLR�

2 VLQDO TXH UHSUHVHQWD D LQIRUPD�FaDR H TXH YDULDU�D XPD FDUDFWHU��VWLFD GH XPD RQGD� FKDPDGDGH RQGD SRUWDGRUD� FKDPD�VHD RQGD PRGXODGRUD� $R SURFHVVR GH YDULD�FaDR GH XPD FDUDFWHU��VWLFDGD RQGD SRUWDGRUD GH DFRUGR FRP R VLQDO GD LQIRUPD�FaDR� FKDPDPRV GH PRGXOD�FaDR� $ FDUDFWH�U��VWLFD TXH VRIUH YDULD�FaDR SRGH VHU D DPSOLWXGH H FKDPDPRV GH PRGXOD�FaDR HP DPSOLWXGH �$0��RX D FDUDFWHULVWLFD �H D IUHT¦XAHQFLD H FKDPDPRV GH PRGXOD�FaDR HP IUHT¦XAHQFLD �)0��

��

Page 72: Analise de Sinais

(PERUD R PXOWLSOH[ WHOHIARQLFR VH GHVWLQH SULPRUGLDOPHQWH �D WUDQVPLVVaDR GH VLQDLV GH YR]�HOH WDPE�HP �H XWLOL]DGR SDUD R HQYLR GH LQIRUPD�FaRHV VRE RXWUDV IRUPDV GH VLQDLV� WDLV FRPR�VLQDLV WHOHJU�D�FRV� VLQDLV GH ID[� VLQDLV GH GDGRV� HWF�$VVLP� R PXOWLSOH[ WHOHIARQLFR �H HPSUHJDGR SRU TXDVH WRGRV RV VHUYL�FRV GH WHOHFRPXQLFD�FaRHV�

RQGH WHP D IXQ�FaDR GH FRQFHQWUDGRU D �P GH XWLOL]DU GH PDQHLUD PDLV UDFLRQDO XP PHLR GHWUDQVPLVVaDR GH DOWD FDSDFLGDGH�$ �JXUD ��� PRVWUD XP HVTXHPD GH XP VLVWHPD GH WHOHFRPXQLFD�FaRHV RQGH Y�DULRV VHUYL�FRV

SRGHP VHU SUHVWDGRV�

)LJXUD ���� 6HUYL�FRV GH WHOHFRPXQLFD�FaRHV�

&RPR D XWLOL]D�FaDR SULPRUGLDO GR PXOWLSOH[ �H SDUD FRPXQLFD�FaRHV WHOHIARQLFDV� R FDQDO XWLOL]DGRQHVWH VLVWHPD �H FKDPDGR GH FDQDO PXOWLSOH[ WHOHIARQLFR RX FDQDO GH YR] H R FLUFXLWR VHU�D FKDPDGRGH FLUFXLWR PXOWLSOH[ WHOHIARQLFR RX FLUFXLWR GH YR]�+�D Y�DULRV WLSRV GH FDQDLV GLVSRQ��YHLV GHSHQGHQGR GD DSOLFD�FaDR� 3RU H[HPSOR XP FDQDO

GH � .K] GH IDL[D WHP HPSUHJR HP VLVWHPDV GH SHTXHQD FDSDFLGDGH� RQGH R EDL[R SUH�FR GRHTXLSDPHQWR �H PDLV LPSRUWDQWH TXH R DSURYHLWDPHQWR GR PHLR SDUD WUDQVPLVVaDR GH XP PDLRUQ�XPHUR GH FDQDLV�

��

Page 73: Analise de Sinais

��� 7UDQVOD�FaDR GH IUHT¦XAHQFLDV

&KDPDPRV GH WUDQVOD�FaDR �RX FRQYHUVaDR GH IUHT¦XAHQFLDV� D WUDQVIHUAHQFLD GH VLQDLV TXH RFXSDPXPD GHWHUPLQDGD IDL[D QR HVSHFWUR GH IUHT¦XAHQFLDV SDUD XPD RXWUD SRVL�FaDR GHVWH HVSHFWUR� GHWDO PDQHLUD TXH VHMD PDQWLGD D SRVL�FaDR UHODWLYD GDV IUHT¦XAHQFLDV GHQWUR GD IDL[D� $ WUDQVOD�FaDR�H D RSHUD�FaDR E�DVLFD GD PXOWLSOH[D�FaDR� VHQGR UHDOL]DGD SRU SURFHVVRV GH PRGXOD�FaDR� TXH SRGHVHU HP DPSOLWXGH�$0�� IUHT¦XAHQFLD�)0� RX IDVH �30��$ �JXUD ��� PRVWUD HVTXHPDWLFDPHQWH D WUDQVOD�FaDR GH IUHT¦XAHQFLDV�

)LJXUD ���� 7UDQVOD�FaDR GH IUHT¦XAHQFLDV�

��� 0RGXOD�FaDR H GHPRGXOD�FaDR

$ PRGXOD�FaDR �H XP SURFHVVR RQGH GXDV IUHT¦XAHQFLDV RX VLQDLV VaDR FRPELQDGRV� GH WDO PDQHLUDTXH VaDR FULDGDV QRYDV IUHT¦XAHQFLDV�$ �JXUD "" PRVWUD HVVH SURFHVVR HVTXHPDWLFDPHQWH�

)LJXUD ���� (VTXHPD GD PRGXOD�FaDR�

1D PRGXOD�FaDR XP GRV VLQDLV TXH VHU�D FRPELQDGR �H FKDPDGR GH RQGD SRUWDGRUD H R RXWUR�VLQDO PRGXODQWH� $R SURGXWR GD PRGXOD�FaDR GDPRV R QRPH GH VLQDO PRGXODGR� $R SURFHVVR GHUHVWDXUD�FaDR GR VLQDO PRGXODQWH� D SDUWLU GR VLQDO PRGXODGR H GD RQGD SRUWDGRUD� FKDPDPRVGH GHPRGXOD�FaDR�

��

Page 74: Analise de Sinais

����� 7LSRV GH PRGXOD�FaDR

+�D Y�DULDV IRUPDV GH VH PRGXODU XP VLQDO H� JHUDOPHQWH� D RQGD SRUWDGRUD �H XPD RQGD VHQRLGDOTXH SRGH VHU GDGD SRU

D3 $3 FRV���I3 W� ���

$ PRGXOD�FaDR HP DPSOLWXGH �H REWLGD VRPHQWH SHOD YDULD�FaDR GD DPSOLWXGH $3 � GH IRUPD TXHR GHVYLR UHVXOWDQWH� HP UHOD�FaDR �D DPSOLWXGH� VHMD GLUHWDPHQWH SURSRUFLRQDO DR YDORU LQVWDQWADQHRGR VLQDO PRGXODQWH� SRU�HP LQGHSHQGHQWH GD VXD IUHT¦XAHQFLD�$ PRGXOD�FaDR HP ADQJXOR� TXH SRGH VHU SRU DPSOLWXGH RX SRU IUHT¦XAHQFLD� �H REWLGD TXDQGR

ID]�VH YDULDU R ADQJXOR ��I3 W� ��

����� 0RGXOD�FaDR HP DPSOLWXGH

1D PRGXOD�FaDR HP DPSOLWXGH� R YDORU P�D[LPR GD RQGD SRUWDGRUD �H YDULDGR SHOD LQWHQVLGDGH GRVLQDO PRGXODQWH� TXH �H D TXDQWLGDGH PRGXODGRUD�&RQVLGHUHPRV D RQGD RQGD SRUWDGRUD UHSUHVHQWDGD SRU

D3 $3 FRV���I3 W�

H D RQGD PRGXODQWH SRU

DP $PFRV���IPW��

'HVHMDPRV REWHU D RQGD PRGXODGD HP DPSOLWXGH� $ YDULD�FaDR GH DPSOLWXGH HP WRUQR GH (3

VHU�D VHQRLGDO� GH IRUPD TXH D DPSOLWXGH HP IXQ�FaDR GR WHPSR �H GDGD SRU

$3 �$0FRV���IPW�

VHQGR R YDORU P�D[LPR GD DPSOLWXGH LJXDO D $3 � $P H R YDORU P��QLPR LJXDO D $3 � $P� $RQGD PRGXODGD VHU�D GDGD SRU

$ >$3 �$PFRV���IPW�@FRV���I3 W��

&KDPDQGR D UD]aDR $P

$3GH P� WHPRV �

$ $3 >� �PFRV���IPW�@FRV���I3 W��

([SDQGLQGR D H[SUHVVaDR DFLPD WHPRV

$

RQGD SRUWDGRUD] `_ ^$3 FRV���I3 W� �

IUHT¦XAHQFLD ODWHUDO LQIHULRU] `_ ^P$3

�FRV���I3 � IP�W �

IUHT¦XAHQFLD ODWHUDO VXSHULRU] `_ ^P$3

�FRV���I3 � IP�W �

(VVD HTXD�FaDR LQGLFD D H[LVWAHQFLD GH WUAHV IUHT¦XAHQFLDV GLVWLQWDV QD RQGD PRGXODGD� D VDEHU� DIUHT¦XAHQFLD GD RQGD SRUWDGRUD� XPD IUHT¦XAHQFLD VXSHULRU $3 �$P H XPD LQIHULRU $3 �$P�

��

Page 75: Analise de Sinais

)LJXUD ���� �D�'RP��QLR GR WHPSR� �E� 'RP��QLR GD IUHT¦XAHQFLD�

&RPR H[HPSOR GHVVH SURFHVVR FRQVLGHUHPRV D RQGD RQGD SRUWDGRUD GDGD SRU DS �FRV����W�H R VLQDO PRGXODQWH GDGR SRU DP FRV���W�� 5HSUHVHQWDPRV QD �JXUD ��� R VLQDO PRGXODQWH�D RQGD SRUWDGRUD H R VLQDO PRGXODGR� QR GRP��QLR GR WHPSR H GD IUHT¦XAHQFLD�1HVWH FDVR R VLQDO PRGXODQWH IRL FRQVLGHUDGR FRPR XP VLQDO VHQRLGDO� 1R HQWDQWR� QRV FDVRV

UHDLV� R VLQDO YDULD FRQWLQXDPHQWH QXPD IDL[D FRQVLGHU�DYHO� ID]HQGR FRP TXH DV IUHT¦XAHQFLDVODWHUDLV TXH HQFRQWUDPRV VHMDP VXEVWLWX��GDV SRU IDL[DV GH IUHT¦XAHQFLDV� GHQRPLQDGDV EDQGDODWHUDO LQIHULRU H EDQGD ODWHUDO VXSHULRU� FXMD ODUJXUD �H LJXDO �D GLIHUHQ�FD HQWUH R YDORU P�D[LPR HRYDORU P��QLPR GDV IUHT¦XAHQFLDV GR VLQDO PRGXODQWH�&RQVLGHUHPRV� FRPR H[HPSOR� TXH R VLQDO [�W� FRQW�HP D LQIRUPD�FaDR TXH GHVHMDPRV WUDQVPL�

WLU� &RQVLGHUHPRV R VLQDO GD RQGD SRUWDGRUD GDGR SRU [3 �W� $3 FRV���I3 W�� $VVLP� R VLQDOPRGXODGR VHU�D GDGR SRU

[P�W� $3 FRV���I3 W� �P[�W�$3 FRV���I3 W� $3 >� �P[�W�@FRV���I3 W��

P �H GHQRPLQDGR ��QGLFH GH PRGXOD�FaDR H �H GDGR SRU P $P

$3�

��

Page 76: Analise de Sinais

1R GRP��QLR GD IUHT¦XAHQFLD� D WUDQVIRUPDGD GH )RXULHU GR VLQDO [P �H GDGR SRU

;3 �I � $3

�>��I � I3 � � ��I � I3 �@ �

P$3

�>;�I � I3 � �;�I � I3 �@�

$VVLP� R HVSHFWUR GH XP VLQDO PRGXODGR $0 �H R HVSHFWUR GD PHQVDJHP GHVORFDGR� PDLV XPSDU GH LPSXOVRV� HP �I3 � TXH UHSUHVHQWDP D RQGD SRUWDGRUD GR VLQDO�3RU H[HPSOR� TXDQGR XPD RQGD SRUWDGRUD GH ���� .+] �H PRGXODGD SRU XP VLQDO GH �DXGLR

TXH YDULD GH ��� +] D ���� +]� D IUHT¦XAHQFLD P�D[LPD GD IDL[D VXSHULRU VHU�D GH ���� .K] H DIUHT¦XAHQFLD P��QLPD GD IDL[D LQIHULRU VHU�D GH ��� .+]� FRPR LOXVWUDPRV QD �JXUD ����

)LJXUD ���� 0RGXOD�FaDR HP DPSOLWXGH GH XP FDQDO GH YR]�

+�D Y�DULRV SURFHVVRV GH PRGXOD�FaDR $0 XWLOL]DGRV SHOD W�HFQLFD SHOR P�HWRGR GD GLYLVaDR HPIUHT¦XAHQFLD� 6aDR HOHV �

� $0�'6% � 0RGXOD�FaDR HP DPSOLWXGH FRP IDL[D ODWHUDO GXSOD

� $0�'6%�6& � 0RGXOD�FaDR HP DPSOLWXGH FRP IDL[D ODWHUDO GXSOD H RQGD RQGD SRUWDGRUDVXSULPLGD

� $0�66% � 0RGXOD�FaDR HP DPSOLWXGH FRP IDL[D ODWHUDO �XQLFD

� $0�66%�6& � 0RGXOD�FaDR HP DPSOLWXGH FRP IDL[D ODWHUDO �XQLFD H RQGD SRUWDGRUD VXSULP�LGD�

'H WRGRV HVVHV SURFHVVRV R PDLV HPSUHJDGR �H R $0�66%�6&� (VVH �H R PDLV XWLOL]DGR SRLVD WUDQVPLVVaDR GD RQGD SRUWDGRUD �H GHVQHFHVV�DULD SRLV QaDR FRQW�HP LQIRUPD�FaDR H DO�HP GLVVRJDVWDU��DPRV HQHUJLD SDUD D VXD WUDQVPLVVaDR� 9HUL�FDPRV WDPE�HP TXH DV GXDV EDQGDV ODWHUDLVSRVVXHP D PHVPD LQIRUPD�FaDR H SRU LVVR V�R VH ID] QHFHVV�DULD D WUDQVPLVVaDR GH XPD GHODV R TXHWUD] GXDV YDQWDJHQV � HFRQRPLD GH SRWAHQFLD H GH IDL[D GH IUHT¦XAHQFLD �RFXSD�VH XPD IDL[D PHQRU��$ RQGD RQGD SRUWDGRUD V�R VHU�D QHFHVV�DULD SDUD D GHPRGXOD�FaDR� SRGHQGR VHU JHUDGD QRYDPHQWHDS�RV D UHFHS�FaDR QR RXWUR H[WUHPR� $ VXSUHVVaDR GD RQGD SRUWDGRUD �H UHDOL]DGD SRU PRGXODGRUHVFKDPDGRV GHPRGXODGRUHV EDODQFHDGRV� $ VHOH�FaDR GD EDQGD ODWHUDO D VHU WUDQVPLWLGD �H H[HFXWDGDSRU GLVSRVLWLYRV FKDPDGRV GH �OWURV SDVVD�IDL[D�

��

Page 77: Analise de Sinais

%DQGD GH IUHT¦XAHQFLD )UHT¦XAHQFLD GH RQGD SRUWDGRUD /DUJXUD GH IDL[D

2QGDV ORQJDV GH U�DGLR ��� N+] � N+]2QGDV FXUWDV GH U�DGLR � 0+] ��� N+]

9+) ��� 0+] � 0+]0LFURRQGDV � *+] ��� 0+]

2QGDV PLOLP�HWULFDV ��� *+] � *+])DL[D �RWLFD �� ����+] ���� +]

7DEHOD ���� )UHT¦XAHQFLD GH RQGD SRUWDGRUDV H ODUJXUDV GH IDL[D VHOHFLRQDGDV�

$ �JXUD ��� DSUHVHQWD R GLDJUDPD HP EORFRV GH XPD PRGXOD�FaDR HP DPSOLWXGH FRP RQ�GD SRUWDGRUD VXSULPLGD H WUDQVPLVVaDR GH XPD V�R EDQGD ODWHUDO� EHP FRPR D LQGLFD�FaDR GDVRSHUD�FaRHV QR GRP��QLR GD IUHT¦XAHQFLD�$ W��WXOR GH FXULRVLGDGH� D WDEHOD ��� PRVWUD DV IUHT¦XAHQFLDV GH RQGD SRUWDGRUDV H DV ODUJXUDV

GH IDL[D SDUD GHWHUPLQDGRV WLSRV GH VLQDLV�

��� 'HPRGXOD�FaDR

$R SURFHVVR GH UHVWDXUD�FaDR GR VLQDO PRGXODQWH RX LQIRUPD�FaDR� D SDUWLU GR VLQDO PRGXODGR H GDRQGD SRUWDGRUD� FKDPDPRV GH GHPRGXOD�FaDR�8WLOL]DUHPRV� FRPR LOXVWUD�FaDR� D IRUPD VHQRLGDO SDUD D GHPRGXOD�FaDR WDO FRPR �]HPRV SDUD

D PRGXOD�FaDR�7RPHPRV FRPR H[HPSOR XP VLQDO PRGXODGR D IUHT¦XAHQFLD ODWHUDO LQIHULRU� FXMD H[SUHVVaDR D

VHJXLU UHSUHVHQWD XP VLQDO VHQRLGDO GH IUHT¦XAHQFLD �I3 � IP��

D%/, P$3

�FRV>���I3 � IP�W@�

$ RQGD RQGD SRUWDGRUD� LGAHQWLFD HP IUHT¦XAHQFLD �D PRGXOD�FaDR� �H UHSUHVHQWDGD SHOD H[SUHVVaDR�

D3 $3 FRV���I3 W��

$VVLP� R VLQDO GHPRGXODGR VHU�D GDGR SRU

D >$3 �P$3

�FRV>���I3 � IP�W@FRV���I3 W��

$S�RV DOJXPDV PDQLSXOD�FaRHV DOJ�HEULFDV FKHJDPRV D �

D

RQGD SRUWDGRUD] `_ ^$3 FRV���I3 W� �

IUHT¦XHQFLD ODWHUDO LQIHULRU] `_ ^$P

�FRV���IPW� �

IUHT¦XAHQFLD ODWHUDO VXSHULRU] `_ ^$P

�FRV����I3 � IP�W �

3RGHPRV REVHUYDU TXH D GHPRGXOD�FaDR �H D PRGXOD�FaDR QD GLUH�FaDR LQYHUVD� QD TXDO REWHPRVXPD IUHT¦XAHQFLD ODWHUDO LQIHULRU LGAHQWLFD �D LQIRUPD�FaDR RULJLQDO� SRU�HP FRP XPD DPSOLWXGH PHQRU�

��

Page 78: Analise de Sinais

'HYHPRV REVHUYDU TXH QaDR FRQVLGHUDPRV QHVWD DQ�DOLVH D YDULD�FaDR GH IDVH HQWUH DV RQGDSRUWDGRUDV QD WUDQVPLVVaDR H QD UHFHS�FaDR� VRPHQWH OHYDQGR HP FRQWD D LJXDOGDGH GH IUHT¦XAHQFLD�3RU�HP� VH HVWLYHUPRV WUDQVPLWLQGR XP WLSR GH LQIRUPD�FaDR TXH WHQKD QHFHVVLGDGH GR UHFRQKH�FLPHQWR GH VXD IRUPD GH RQGD QD UHFHSD�FaDR� XPD GHIDVDJHP HQWUH DV RQGD SRUWDGRUDV SRGHGHIRUPDU R VLQDO� D SRQWR GH WRUQ�D�OR LUUHFRQKHF��YHO�0RVWUDPRV QD �JXUD ��� XP HVTXHPD GR SURFHVVR GH PXOWLSOH[D�FaDR H GH GHPXOWLSOH[D�FaDR�

��� $SOLFD�FaDR �D (QJHQKDULD 0HFADQLFD� SURFHVVDPHQWR

GH VLQDLV SURYHQLHQWHV GH DFHOHUARPHWURV H WUDQVGX�

WRUHV GH IRU�FD

3DUD HVWXGDUPRV D DSOLFD�FaDR GH DQ�DOLVH H SURFHVVDPHQWR GH VLQDLV QD (QJHQKDULD 0HFADQLFD�GLVFXWLUHPRV XPD H[SHULAHQFLD UHDOL]DGD SDUD GHWHUPLQDU IUHT¦XAHQFLDV QDWXUDLV H PRGRV GH YL�EUD�FaDR GH XPD YLJD HP EDODQ�FR� $ FRQ�JXUD�FaDR XWLOL]DGD �H D GD �JXUD ���� $ YLJD �H H[FLWDGDDWUDY�HV GH XP YLEUDGRU� XWLOL]DQGR� SDUD LVVR� XP VLQDO DOHDW�RULR� 2V VLQDLV GD H[FLWD�FaDR� FDS�WDGR SRU XP WUDQVGXWRU GH IRU�FD� H GD UHVSRVWD� FDSWDGD SRU XP DFHOHUARPHWUR� VaDR DQDOLVDGRV HSURFHVVDGRV SRU XP DQDOLVDGRU GH VLQDLV� (VFROKHPRV QR DQDOLVDGRU D RS�FaDR GH IXQ�FaDR UHVSRVWDHP IUHT¦XAHQFLD� 1HVVH FDVR� RV VLQDLV SURYHQLHQWHV GR DFHOHUARPHWUR H GR WUDQVGXWRU GH IRU�FDVaDR WUDQVIRUPDGRV SDUD R GRP��QLR GD IUHT¦XAHQFLD H GLYLGLGRV XP SHOR R RXWUR �GHWHUPLQD�FaDRGD IXQ�FaDR UHVSRVWD HP IUHT¦XAHQFLD � VD��GD GLYLGLGD SHOD HQWUDGD�� &RPR H[HPSOR� SRGHPRVREVHUYDU R JU�D�FR GD PDJQLWXGH GD IXQ�FaDR UHVSRVWD HP IUHT¦XAHQFLD� PRVWUDGD QD �JXUD �����$ SDUWLU GRV ?SLFRV� GHVVH JU�D�FR SRGHPRV GHWHUPLQDU DV IUHT¦XAHQFLDV QDWXUDLV GD HVWUXWXUD�3DUD GHWHUPLQDU RV PRGRV GH YLEUD�FaDR� H[FLWDPRV D HVWUXWXUD HP FDGD XPD GDV IUHT¦XAHQFLDVQDWXUDLV� XVDQGR XP VLQDO VHQRLGDO� 2V PRGRV GH YLEUD�FaRHV SRGHP VHU YLVXDOL]DGRV XVDQGRPDVFDUDPHQWR FRP XP HVWURVERVF�RSLR�3RU�HP� DV SULQFLSDLV DSOLFD�FaRHV VaDR QD �DUHD GH FRQWUROH GH 6LVWHPDV 'LQADPLFRV� PDV �FD

SDUD XPD RXWUD YH] ���(VWDV 1RWDV� IHLWDV FRPR XP URWHLUR SDUD R QRVVR PLQL�FXUVR� QaDR VaDR DXWR�VX�FLHQWHV�

5HFRPHQGDPRV TXH RV LQWHUHVVDGRV FRQVXOWHP RV OLYURV GH 2SSHQKHLP H R PDQXDO GR 7RROER[0$7/$% GH 3URFHVVDPHQWR GH 6LQDLV� 2 XVR GHVVH 7RROER[ VHUD FREHUWR QDV DSUHVHQWD�FaRHV GRPLQLFXUVR�&RQYLGDPRV YRFHV D YLVLWDUHP R /DERUDW�RULR GH 'LQADPLFD GD 38&�5LR SDUD YHUHP FR�

PR DV LG�HLDV DSUHVHQWDGDV DTXL VaDR XVDGDV SDUD FDUDFWHUL]DU� PRQLWRUDU H FRQWURODU 6LVWHPDV'LQADPLFRV�

(VSHUDPRV YRFHV QD 38&�5LR

��

Page 79: Analise de Sinais

)LJXUD ���� (VTXHPD GH PXOWLSOH[D�FaDR H GHPXOWLSOH[D�FaDR GH WUAHV FDQDLV GH YR]�

��

Page 80: Analise de Sinais

)LJXUD ���� 'HVFUL�FaDR GD H[SHULAHQFLD

)LJXUD ����� $PSOLWXGH GD IXQ�FaDR UHVSRVWD HP IUHT¦XAHQFLD�

��