Xử lí tính hiệu số Chap 1

7/28/2019 X l tnh hiu s Chap 1

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BAI GIANGX LY SO TN HIEU

Bien soan: PGS.TS LE TIEN THNG

Tp.HCM, 02-2005

BI GING X L S TN HIU

http://www.khvt.com (C) 2005 L Tin Thng 1


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CHNG 1: LAY MAU VA KHOI PHUC TN HIEU

1.1. Gii thieu

1.2. Mot so c ban lien quan en cac tn hieu tng t 1.3. nh ly lay mau 1.4. Lay mau cac tn hieu sine

1.5. Pho cua cac tn hieu c lay mau 1.6. Khoi phuc tn hieu tng t 1.7. Cac thanh phan c ban cua he thong DSP




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Qua trnh x ly so cac tn hieu tng t thng gom 3 bc:

- So hoa cac tn hieu tng t, tc la lay mau va lng thoa cac mau nay. Qua trnh nay c goi la bien oi A/D(Analog to Digital).

- Dung bo x ly tn hieu so e x ly cac mau va thu c. - Cac mau sau khi x ly xong se c khoi phuc lai dang

tng t bang bo khoi phuc tn hieu tng t goi la bo bienoi D/A (Digital to Analog).

1.1. Gii thieu




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Bien oi FOURIER X() cua x(t) chnh la pho tan so cua tnhieu nay:

(1.2.1)

trong o la tan so goc (rad/s). Tan so f lien he vi : = 2f (1.2.2) Bien oi Laplace c nh ngha nh sau :

(1-2-3)

1.2. Mot so c ban lien quan en cac tn hieu tng t

dtetxX tj

= )()(

dtetxsX st

= ).()(





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Xet ap ng cua mot he thong tuyen tnh (linear system)

He thong nay c ac trng bi ap ng xung h(t). aura y(t) thu c bang cach lay tch chap (convolution)trong mien thi gian:

hay phep nhan trong mien tan so:

(1.2.4) trong o H() la ap ng tan so cua he thong tren.


dttxtthty )'()'()()().()( XHY

Linear systemh(t)

x(t)input

y(t)output





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H() c nh ngha la bien oi Fourier cua ap ng xungh(t):

(1.2.5) ap ng xac lap dang sine cua he thong c nh ngha la

ap ng cua he thong khi au vao la tn hieu dang sine:

au ra la tn hieu sine tan so (), co o ln bang o ln tnhieu vao nhan cho he so H(), va pha c dch i lngarg (H()):


= dtethH tj)()(

Linear systemH()

x(t) = exp(jt)Sinusoid in

y(t) = H()exp(jt)Sinusoid out

)(arg.|)(|)()()( Hjtjtjtj eHeHtyetx





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V la chong chap tuyen tnh, neu au vao gom hai tn hieusine co cac tan so va bien o la A1, A2 tng ng:

Sau khi qua bo loc, tn hieu ra xac lap thu c:

Chu y la bo loc ch lam thay oi bien o cac thanh phan tnhieu, ch khong lam thay oi tan so.


21,

tjtj eAeAtx 21 21)(+

tjtj eHAeHAty 21 )()()( 21





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Anh hng cua bo loc cung co the c quan sat trongmien tan so bang cach dung pt (1.2.4) nh sau:

Pho tn hieu vao X() gom hai vach pho tai tan so vathu c bang cach lay bien oi Fourier cua x(t):

Pho au ra tng ng Y() thu c t pt (1.2.4):


X( )A1 A2

H( )

Y( )

A 1 H( )

A2 H( )

1 2

)(2)(2)( 2211 AAX

)()(2)()(2))(2)(2)(()()()(

222111

2211

+=+==

HAHAAAHXHY





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Xet qua trnh lay mau (c minh hoa trong H1.3.1). Tnhieu x(t) c lay mau tuan hoan theo chu ky T. Do o,thi gian c ri rac hoa theo cac n v cua T nh sau:t=nT vi n=0,1,2, Do o, se co nhieu thanh phan cao tankhong the xac nh c chen vao pho tan so tn hieu.

Chnh v the, e co the thiet ke he thong thanh cong, 2 cauhoi sau luon gi y cho ngi thiet ke: 1. Anh hng cua qua trnh lay mau len pho cua tn hieu

nh the nao? 2. Ta nen chon khoang cach lay mau ra sao?

1.3. nh ly lay mau





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Qua trnh lay mau se tao cac thanh phan cao tan, cacthanh phan nay xuat hien eu an theo quy luat, theo chu

ky tng ng vi toc o lay mau: fs=1/T

Hnh 1.3.1 Bo lay mau ly tng.

1.3. nh ly lay mau

x(t) x(nT )A nalog

signal

sampledsignal

I deal sampler

t

x(t)

0 T nT

t

x(nT )





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Cung nen lu y rang neu bat au bang viec xem xet pho(mang tnh chat lap lai) cua tn hieu a c lay mau,

khong the xac nh c tan so cua tn hieu ban au. No cothe la thanh phan nao o trong cac tan so f=f+mfs,vim=0, 1, 2, o la do bat ky tan so nao thuoc f cung euco pho giong nhau sau khi lay mau. Hien tng trung lapnay c goi la hien tng chong lan pho aliasing va cothe tranh c neu thoa man cac ieu kien cua nh ly laymau.

1.3. nh ly lay mau





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1.3. nh ly lay mau

H nh 1.3.2 Ph o b la p do la y m au.

Tanso f

f-4fs ff-3fs f-2fs f-fs f+fs f+2fs f+3fs f+4fs

G G S U




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1.3.1. nh ly lay mau Co the bieu dien chnh xac tn hieu x(t) bi cac mau x(nT),

can phai thoa man 2 ieu kien sau: - ieu kien 1: Tn hieu x(t) phai c gii han trong mot

dai, tc la pho cua tn hieu phai c gii han la ch cha

nhng thanh phan tan so nho hn mot tan so ln nhat naoo thoi (fmax) va hoan toan khong ton tai tan so nao trenvung ngoai cua fmax.

1.3. nh ly lay mau




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1.3.1. nh ly lay mau ieu kien 2: Tan so lay mau phai c chon ln hn t

nhat la hai lan fmax, tc la fs 2fmax hay bieu dien theo khoang cach thi gian lay mau:

fs=2fmax c goi la toc o Nyquist. ai lng fs/2 c goi la tan so Nyquist hay tan so gap(folding frequency)

1.3. nh ly lay mau

max21f

T




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1.3.2. Antialiasing Prefilter Viec thc hien thc te nh ly lay mau rat quan trong. Do

hau het cac tn hieu khong c gii han trong mot dai, vthe can phai a nhng tn hieu nay qua bo loc thong thap(prefilter) trc khi lay mau.

1.3. nh ly lay mau




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1.3.2. Antialiasing Prefilter1.3. nh ly lay mau

H nh 1.3 .5 B o lo c a ntialiasing p refilter.

Prefiltered spectrum

0

0-fs fsf

f-fs/2 fs/2

f

Input spectrum

prefilter

Replicatedspectrum

Bandlimited

signal

x(t)Analog siganal

Analog siganal

x(nT)x(t) Analog lowpassfilter

Sam pler and quantizer

To DSP




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So mau tren chu ky c cho bi ty so fs/f:

1.4.1. Khoi phuc tn hieu va hien tng chong lan pho(aliasing) Nhan thay rang, du cac tn hieu xm(t) th khac nhau, nhng

cac mau cua chung lai hoan toan giong nhau. Thc vay:

tap hp cac tan so:

1.4. Lay mau cac tn hieu sine

cyclesamples

cyclessamples

ffs =

sec/sec/

)()( 222)(2 nTxeeeenTx jfTnTnjmfjfTnTnmffjmss =+

,...,...,2,, sss mfffffff




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1.4.1. Khoi phuc tn hieu va hien tng chong lan pho(aliasing)


Hnh 1.4.2 Bo loc thong thap lam bo kho i phuc tn hieu ly tng

Ideal sampler Ideal reconstructor

x(t)xa(t)

Analogsignal

Analogsignal

Rate fs Lowpass filterCutoff =fs//2

-fs/2 fs/2

T x(nT)




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1.4.1. Khoi phuc tn hieu va hien tng chong lan pho Tan so nay thu c bang cach lay tan so ban au module

cho fs, fa=f mod(fs). ay chnh la tan so trong tap (1.4.2) thuc t bo khoi phuc tn hieu. V the, tn hieu sine ckhoi phuc la:

Va de dang thay rang, fa=f ch neu tan so f nam trongkhoang tan so Nyquist; tc la ch neu hay ch

khi nh ly lay mau c thoa. Con neu f nam ngoaikhoang tan so Nyquist, vi pham ieu kien cua nh ly laymau. Luc nay, tan so b chong lan fa se khac vi f; v the

tn hieu c khoi phuc xa(t) se khac vi x(t) mac duxa(nT)=x(nT).


tjf

a aetx2

)( =2/|| sff




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1.4.1. Khoi phuc tn hieu va hien tng chong lan pho Se thay ro rang hn neu xem o th fa=f mod (fs) theo tan

so f (H1.4.3). ng thang ftrue=f c be thanh nhieung thang song song neu ta dch oan thang trongkhoang [-fs/2,fs/2] tren truc tan so i cac boi so cua fs.





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1.4.1. Khoi phuc tn hieu va hien tng chong lan pho1.4. Lay mau cac tn hieu sine

Hnh 1.4.3 o th f mod (fs) theo f.

fs/2

-fs/2

fs/2 fs

2fs

-fs/2

-fs

fa=f mod ( fs)

0f

ftrue=f




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V du 1.4.1: Xem tn hieu sin tan so f=10 Hz, c lay mau vi toc o

fs=12Hz. Tn hieu c lay mau se cha tat ca cac tan soco tnh tuan hoan 10+m.12Hz, m = 0, 1, 2, hay la: , -26,-14, -2, 10, 22, 34, 46, va trong so nay ch co fa = 10

mod(12) = 10 12 = -2 Hz la nam trong khoang tan soNyquist [-6,6] Hz. Vay, tan so khoi phuc c la song sineco tan so 2 Hz thay v ung phai la 10 Hz.





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V du 1.4.2: Nam tn hieu sau c lay mau vi toc o 4Hz: (t tnh theo giay). Hay chng to rang chung se chong lan nhau do cac mau

thu c cua cac tn hieu nay eu giong nhau. Giai: Cac tan so cua 5 tn hieu nay lan lt la: -7, -3, 1, 5, 9Hz. Chung cach nhau mot lng bang boi so cua fs=4Hz.

Nam tan so nay co the c viet gon lai: fm=1+4m, m=-2, -1, 0, 1, 2. Co the bieu dien 5 tn hieu nay di dang:


t)sin(18t),sin(10t),sin(2,)6sin(),t14sin( t

2-2,-1,0,1,m)),41(2sin()2sin()( =+== ntftx mm


CHNG 1 LAY MAU VA KHOI PHUC TN HIEUBI GING X L S TN HIU


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V du 1.4.2: Thay t=nT=n/fs=n/4 giay, thu c cac mau:

Vay cac mau nay hoan toan giong nhau, va khong phuthuoc m. Hnh sau bieu dien 5 tn hieu trong khoang


)4/2sin()24/2sin(

)4/)41(2sin())41(2sin()(

nmnn

nmnTmnTxm

=+

st 10




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V du 1.4.2:





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1.4.2 Chuyen ong tron Mot cach khac trc quan hn e hieu cac tnh chat lay

mau cua cac tn hieu sine la xem tn hieu sine (di dangphc) la banh xe quay tron vi tan so f vong/giay.Giong nh at banh xe trong phong toi, dung en flash e

thay no va en flash sang fs lan trong mot giay. Tan so gocla (rad/s). Khoang thi gian gia hai lan en sangT, banh xe quay c 1 goc:

ai lng nay c goi la tan so so (digital frequency) va

co n v [radians/sample]. No co tnh chuan hoa va thuantien s dung hn tan so vat ly f.


jftetx 2)( =

f2=

sf

ffTT

22 ===




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1.4.2 Chuyen ong tron Theo , tn hieu sine c lay mau co the viet gon lai nh

sau:

Neu viet theo , tan so Nyquist f=fs/2 tr thanh = vakhoang Nyquist la [- , ]. Tap hp cac tan so f+mfs trthanh:

Do f=fs

tng ng vi = 2, tan so b chong lan c viettheo :

ai lng f/fs=fT cung c goi la tan so so va tnh bangchu ky/mau, bieu dien chuan hoa khac cho truc tan so vat

ly, vi khoang Nyquist ng vi [-0.5,0.5].


njjfTn eenTx =2)(

mmf

f

f

mff

ss

s 222)(2 +)mod(2=a


CHNG 1: LAY MAU VA KHOI PHUC TN HIEUBI GING X L S TN HIU


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1.4.2 Chuyen ong tron Neu xet banh xe quay, fT chnh la so vong quay c trong

khoang ngh gia hai lan en sang T. Neu banh xe thc sang quay vi toc o cao hn f+mfs, trong khoang thi gianT, no quay c (f+mfs) T=fT+mfsT=fT+m vong, tc la no

a hoan thanh m vong. V vay, mot ngi quan sat se hoantoan khong thay m vong nay. Toc o quay ngi quan satcam nhan c la fa=f mod(fs). Hai v du sau se giai thchnhng iem nay.





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Tn hieu c lay mau co the viet: (1.5.1)

oi vi lay mau thc te, tn hieu c lay mau la: (1.5.2)

Trong o, p(t) la xung nh ngang co o rong giay sao choCT. Qua trnh lay mau ly tng ng vi dan ve 0. Hnh1.5.1 minh hoa trng hp lay mau ly tng va thc te.

1.5. Pho cua tn hieu c lay mau

n

nTtnTxtx )()()(

nflat nTtpnTxtx )()()(




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Hnh 1.5.1 Lay mau thc te va ly tng.

0 T 2T . nT t0 T 2T . nT t

xflat(t)

)( tx)()( nTtnT

)()( nTtnT




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1.5.1. Bien oi Fourier ri rac thi gian Pho cua tn hieu c lay mau chnh la khai trien

Fourier: (1.5.3) Thay pt (1.5.1) vao pt (1.5.3)va hoan oi phep tnh tch

phan va tong vi nhau, thu c: (1.5.4)

ay la cach th nhat bieu dien .


)(tx

dtetxfX jft2)()(

haynT)e-(tx(nT)

)()()(

-n-

jft2-

2

dt

dtenTtnTxfX jft

n

=

)( fX




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1.5.1. Bien oi Fourier ri rac thi gian Co nhieu van e can quan tam nh sau: 1. DTFT: Ham tnh theo cong thc (1.5.4) c goi

la bien oi Fourier ri rac trong mien thi gian DTFT. ch tnh c khi biet trcx(nT). 2. Tnh tuan hoan: la ham tuan hoan theo chu ky fs:

ieu nay la do he so tuan hoan theof. Khoang[-fs/2,fs/2] gii han trong mot chu ky, goi la dai Nyquist.


)( fX

)( fX

)( fX

( ) )( fXffX s =+jfTne 2




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1.5.1. Bien oi Fourier ri rac thi gian 3. Chuoi Fourier: xet ve phng dien toan hoc, phng

trnh (1.5.4) xem nh la khai trien Fourier cua ham tuanhoan , trong o x(nT) la cac he so tng ng cuachuoi. Do o x(nT) co the c tnh theo bang congthc Fourier ngc:

(1.5.5)


)( fX)(fX

==2/

2/

2

2)()(

1)(

s

s

f

f

nejfTn deXdfefXf

nTX




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1.5.1. Bien oi Fourier ri rac thi gian 4. Xap x toan hoc: da vao nh ngha cua phep tch phan,

pho tan so cua tn hieu x(t) co the c tnh xap x bangphng trnh (1.5.6):

hoac: (1.5.6) Xap x nay ung khi T tien en 0: (1.5.7)

Ket qua nay chng to rang co the dung bien oi Fourierri rac e tnh pho thc cua tn hieu tng t.


+

+

=

=n

jfnTjft TenTxdtetxfX 22 )()()(

)()( fXTfX

)(lim)(0

fXTfXT

=




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1.5.1. Bien oi Fourier ri rac thi gian 5. Xap x thc te: khi tnh toan pho thc cua tn hieu,

can phai thc hien trc hai phep xap x sau: (a) Ch dung mot so lng hu han cac mau x(nT) vi

chieu dai L (n = 0, 1, 2, ,L-1), va phng trnh (1.5.4)

c tnh gan ung theo: (1.5.8)

Xap x nay dan en y tng phan tch tn hieu theo tngca so thi gian. ieu nay se c trnh bay cu the chng 9.


=

=1

0

2)()()(L

n

jfTnL enTxfXfX




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1.5.1. Bien oi Fourier ri rac thi gian (b) Ta ch can tnh tai mot so gia tr f nao o c

chon trc. Viec chon la thch hp mot tap hp cac giatrf nay se tao thanh cac thuat giai hieu qua e tm bienoi Fourier ri rac DFT, chang han nh thuat giai FFT

se c e cap chng 9. 6. Bien oi z: phng trnh (1.5.4) dan en bien oi z sau:

vi


)( fX

=

=n

nznTxzX )()(

jfTej eez 2==




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C NG : U V O UC N U

1.5.2. Bo antialiasing prefilter thc te: Hnh 1.5.5 minh hoa mot bo loc prefilter tng t ly

tng. No hoat ong giong nh mot bo loc thong thap lytng ch cho cac thanh phan tan so thap hn tan soNyquistfs/2 i qua.


0 -fs/2 0 fs/2 -fs 0 fs

Xin(f) bo tien loc X(f) bo lay mau X (f)ly tng H(f) ly tng T

Tn hieu pho gi i pho lay mau

tng t hanHnh 1.5.5 Bo antialiasing prefilter ly tng.




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1.5.2. Bo antialiasing prefilter thc te:1.5. Pho cua tn hieu c lay mau

|H(f)| bo loc ly tng

vungchuyen tiep

Astop

fs/2 fs/2-fstop -fpass 0 fpass fstop f

bang chan bang thong bang chan

Hnh 1.5.6 Bo loc antialiasing prefilter thc tehttp://www.khvt.com (C) 2005 L Tin Thng 38



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1.5.2. Bo antialiasing prefilter thc te: Bo antialiasing prefilter dung trong thc te la khong ly

tng, khong loai bo c het cac thanh phan tan sonam ngoai dai Nyquist. V vay hien tng chong pho vanxay ra. Tuy nhien viec thiet ke mot bo loc thch hp se

lam cho s chong pho suy giam en mc chap nhanc. Mot bo loc prefilter thc te c trnh bay hnh1.5.6. Dai thong [-fpass, fpass] c goi la quang tan so huch, can phai nho hn dai Nyquist.





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phan 1.4.1, viec khoi phuc tn hieu c thc hien bangcac bo loc thong thap ly tng vi tan so cat la tan so

Nyquist. Trong phan nay, se e cap en cac bo khoi phucthc te.

Hnh 1.6.1 Bo khoi phuc bac thang.

Hnh 1.6.2 Bo khoi phuc tng t nh mot bo loc thong thap.

1.6. Khoi phuc tn hieu tng t

y (t) ya(t) y (t) B o kh oi ph uc y a(t)

ba c thangA /Dt

tn h ie u la y m a u tn h ie u kho i phu c

y(t) Bo khoi phuc ya(t)tng t

tn hieu h(t) tn hieulay mau khoi phuc




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Ta can xac nh ap ng cua bo khoi phuc h(t) ca trong haitrng hp ly tng va thc te. Quan he gia tn hieu khoi

phuc ngo ra vi tn hieu lay mau au vao y(nT) c tmnh sau:

thay vao

ta co (1.6.1)


+

=

=n

nTtnTyty )()()(

+

=

=n

a nTthnTyty )()()(

+

=

=na

nTthnTyty )()()(




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Bieu thc tren cho thay viec lap khoang trong c thchien bang cach bat au t mau tn hieu hien taiy(nT) va

noi suy theo hamh(t) cho en khi gap mau mi. Noi cachkhac, mot ban sao cuah(t) c ghep vao sau moi mau tnhieu y(nT), va tat ca tao thanh tn hieu tng t ckhoi phuc. Trong mien tan so, bieu thc (1.6.1) tr thanh:

(1.6.2)

vi Y(f) la pho lap cho bi (1.5.11):


)(1)(

=

=m

smffYT

fY

)()()( fYfHfYa =




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1.6.1. Bo khoi phuc ly tngMot bo khoi phuc la ly tng neu tao ra c Ya(f) giong

nh pho tn hieu goc Y(f). Neu pho Y(f) gii han trong motbang thong va cac pho lap khong chong lan len nhau,TY(f) coi nh giong vi Y(f) trong dai Nyquist theo

(1.5.15): vi (1.6.3)

Bo loc khoi phuc H(f) la mot bo loc LP ly tng vi tan socat la tan so Nyquist:

)(1

)( fYT

fY =


22

ss ff

f

H(f) T

-fs/2 0 fs/2http://www.khvt.com (C) 2005 L Tin Thng 43



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1.6.1. Bo khoi phuc ly tng

Gia tr o li Tcua bo loc se c tnh di ay.Tren hnh 1.6.3, bo loc loai bo tat ca cac pho lap,gi lai thanh phan ben trong dai Nyquist. Cong

thc (1.6.3):

o li Tcua bo loc lam cho triet tieu he so 1/Tcuapho tn hieu lay mau.


)()(1

.)()()( fYfYT

TfYfHfYa ===




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Hnh 1.6.3 Bo khoi phuc ly tng tren mien tan so.


)( fYT

bo khoi phuc ly tng

Y(f+2fs) Y(f+fs) Y(f) Y(f-fs) Y(f-2fs)

-2fs -fs -fmax 0 fmax fs 2fs f




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1.6.1. Bo khoi phuc ly tngBen ngoai dai Nyquist cac thanh phan pho eu b triet tieu.Do o Ya(f) = Y(f) vi moi f, ngha la tn hieu ya(t) c khoiphuc giong het nh tn hieu goc ban au y(t). Ket hp vi(1.6.1), co c nh ly lay mau Shannon [35-39]:

ap ng xung cua bo khoi phuc ly tng co the c tm

bang bien oi ngc Fourier:

hoac:


+

=

=n

nTthnTyty )()()(

+

==

2/

2/

22)()(s

s

f

f

jfTjft dfTedfefHth

ftf

TTtth s

)sin(/

)/sin()( ==http://www.khvt.com (C) 2005 L Tin Thng 46



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Hnh ve 1.6.4 la o th cua bo khoi phuc ly tng. Tuy

nhien tren thc te mot bo khoi phuc nh vay khong baogi ton tai bi v ap ng xung cua no la phi nhan qua vavo han. V vay tren thc te ngi ta thay the bang cac bo

khoi phuc khac, chang han nh bo gi bac thang.


h(t)

bo khoi phuc bo khoi phucly tng bac thang

-3T -2T -T 0 T 2T 3T t

Hnh 1.6.4 ap ng xung cua bo loc ly tng.http://www.khvt.com (C) 2005 L Tin Thng 47



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1.6.1. Bo khoi phuc ly tngTuy nhien co the tao ra bo khoi phuc gan vi ly tng bangcach cat bt ap ng xung cua no e tr nen hu han, dungthiet ke bo loc so noi suy FIR cho ky thuat oversampling vacac ng dung chuyen oi tan so lay mau. Bo khoi phuc bac

thang.





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1.6.1. Bo khoi phuc ly tngBo khoi phuc bac thang hnh 1.6.1 la bo khoi phuc tnhieu n gian nhat va thng dung trong thc te. No tao ratn hieu hnh bac thang xap x vi tn hieu goc. Lu y rangno khong giong nh qua trnh lay mau ma o xung lay

mau p(t) co o rong rat hep t


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1.6.1. Bo khoi phuc ly tngBien oi Laplace cua h(t) la:ap ng tan so bo khoi phuc bac thang c so sanh vi bokhoi phuc ly tng tren hnh 1.6.5. Lu y rang ap ng naytriet tieu cac v tr tan so la so nguyen lan cua tan so lay

mau. Cac thanh phan tan so cao c e cap ay la phanpho nam ngoai dai Nyquist.

Hnh 1.6.5 ap ng tan so cua bo khoi phuc bac thang.


sTe

ss

sH =11

)(

|H(f)|bo khoi phuc T

ly tng 4 dB

-2fs -fs -fs/2 0 fs/2 fs 2fs f




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1.6.1. Bo khoi phuc ly tngCo the thay ro bo khoi phuc bac thang khong loai bo hetc cac thanh pho lap giong nh bo khoi phuc ly tng.Hnh 1.6.6 cho ta so sanh gia pho cua tn hieu lay mau vapho cua tn hieu khoi phuc bang bo khoi phuc bac thang.

Hnh 1.6.6. ap ng tan so cua bo khoi phuc bac thang.


bo khoi phuc bo khoi phuc

ly tng bac thang

-2fs -fs -fs/2 0 fs/2 fs 2fs fpho chnh Cac pho lap con d b suy hao





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1.6.1. Bo khoi phuc ly tngBien oi Laplace cua h(t) la:ap ng tan so bo khoi phuc bac thang c so sanh vi bokhoi phuc ly tng tren hnh 1.6.5. Lu y rang ap ng naytriet tieu cac v tr tan so la so nguyen lan cua tan so lay

mau. Cac thanh phan tan so cao c e cap ay la phanpho nam ngoai dai Nyquist.

Hnh 1.6.5 ap ng tan so cua bo khoi phuc bac thang.


sTe

ss

sH =11

)(

|H(f)|bo khoi phuc T

ly tng 4 dB





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1.6.2. Bo loc thong thap anti-image postfilter Cac thanh phan pho lap con lai co the c loai bo bang

mot bo loc thong thap khac goi la bo loc anti-imagepostfilter, vi tan so cat cua bo loc la tan so Nyquist.Hoat ong cua no c the hien tren hnh 1.6.7.


t t tBo khoi phuc anti-image

tn hieu bac thang tn hieu postfilter tn hieu

so tng t tng ttan so catfs/2

Bo khoi phuc ly tng

Hnh 1.6.7 Bo loc anti-image postfilter.http://www.khvt.com (C) 2005 L Tin Thng 53



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1.6.2. Bo loc thong thap anti-image postfilter Tren mien thi gian, tac dung cua bo postfilter the hien

cho cac goc gia cac bac thang c nan lai cho phang.Tren mien tan so, bo postfilter ket hp vi bo khoi phucbac thang lam cho hau het cac thanh phan pho lap c

loai bo, nh o co ap ng giong nh la mot bo khoiphuc ly tng. Cac thong so cua bo loc postfilter cung giong nh cua bo

loc antialiasing prefilter, bao gom bang thong phang vitan so cat bang vi tan so Nyquist. Cac ng dung DSPchat lng cao, chang han nh thong tin vo tuyen kythuat so, oi hoi thong so cua cac bo loc prefilter va

postfilter phai co o chnh xac nghiem ngat.






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1.6.2. Bo loc thong thap anti-image postfilter1.6. Khoi phuc tn hieu tng t

anti-image suy hao

postfilter bang chan

Apost


Hnh 1.6.8 Pho tn hieu sau bo postfilter.

y(nT) Bo loc yEQ(nT) Bo khoi ya(t) Bo loc yPOST(t)tn hieu can bang tn hieu phuc tn hieu postfilter tn hieu

so HEQ(f) so H(f) tng t HPOST(f) tng t

Hnh 1.6.9 Bo loc so can bang cho bien oi D/A.http://www.khvt.com (C) 2005 L Tin Thng 55



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1.6.2. Bo loc thong thap anti-image postfilter1.6. Khoi phuc tn hieu tng t

|HEQ(f)|

4 dB

|H(f)| /T

-fs -fs/2 0 fs/2 fs f

Hnh 1.6.10 ap ng tan so cua bo can bang DAC.




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1.6.2. Bo loc thong thap anti-image postfilter Bo loc can bang bien oi chuoi y(nT) thanh chuoi can

bang yEQ(nT) va a vao bo bien oi ADC va bo locpostfilter. Pho cua yEQ(nT) la YEQ(f) = HEQ(f)Y(f). Phocua ngo ra bo DAC la Ya(f) =H(f)YEQ(f). Cuoi cung phocua tn hieu khoi phuc sau cung se la: YPOST(f) =HPOST(f)Ya(f) =HPOST(f)H(f)HEQ(f)Y(f)

Ben trong dai Nyquist, ket hp (1.6.7) va (1.5.15) va dungbo loc postfilter co bang thong phangH

POST(f) = 1, ta co:

YPOST(f) =HPOST(f)H(f)HEQ(f)Y(f) = 1 . T. 1/T.Y(f) = Y(f) Ben ngoai dai Nyquist, coi nhHPOST(f) = 0, ta co YPOST(f)

= 0. Viec ket hp bo can bang, bo bien oi DAC va boloc postfilter se tao thanh mot bo khoi phuc ly tng.





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Nh a trnh bay cac phan 1.5 va 1.6, cac thanh phan toithieu cua mot he thong x ly so tn hieu bao gom:

1. Mot bo loc thong thap antialiasing prefilter e giihan pho tn hieu trong mot bang thong thuoc dai Nyquist.2. Mot bo bien oi A/D (lay mau va lng t hoa).

3. Mot bo x ly so tn hieu.4. Mot bo bien oi D/A (bo khoi phuc bac thang), co the ikem vi mot bo loc so can bang.

5. Mot bo loc thong thap anti-image postfilter co tac dungloai bo het cac thanh phan pho anh con sot lai do qua trnhlay mau.

1.7. Cac thanh phan c ban cua he thong DSP




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1.7. Cac thanh phan c ban cua he thong DSPxa(t) Bo loc x(t) Bo lay x(t) y(t) Bo khoi y(t) Bo loc ya(t)

prefilter mau & DSP phuc D/A postfilter HPRE(f) A/D HDSP(f) HDAC(f) HPOST(f)Tn hieu Tn hieu

tng t tng tngo vao xung clock ngo ra

Hnh 1.7.1 Cac thanh phan cua he thong DSP.




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Bo loc antialiasing prefilter HPRE(f) co tac dung gii hanpho tn hieu vao trong mot bang thong tren dai Nyquist [-f

s/2, f

s/2]. Ngo ra x(t) c a vao bo lay mau vi toc o f

smau trong mot giay. Theo ung thiet ke th cac pho lap doqua trnh lay mau sinh ra se khong b chong lan len nhau.

Chat lng cua bo loc prefilter anh hng rat ln en ca he

thong, mc o chong lan cua cac pho lap hoan toan phuthuoc vao ac tuyen ap ng tan so cua bo loc nay.

Tn hieu sau khi c lay mau (va lng t hoa) c a

vao bo x ly so tn hieu DSP co tac dung chnh sa lai dangpho tn hieu vi ham truyen at la HDSP(f), do o ta co: Y(f) =HDSP(f)X(f)





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Ngo ra y(t) hay y(nT) c a vao khoi phuc DAC taothanh tn hieu bac thang y(t). Cuoi cung y(t) c lam trnqua bo postfilter tao ra tn hieu tng t ngo ra cua hethong. T (1.5.11) ta co:

[X(f) + pho lap]

Da vao ham truyen at cua cac tang ta tm c pho tnhieu ngo ra cuoi cung nh sau:Y

a

(f) = HPOST

(f)Y(f) = HPOST

(f)HDAC

(f)Y(f)= HPOST(f)HDAC(f)HDSP(f)X(f)=HPOST(f)HDAC(f)HDSP(f)(1/T)[X(f) + pho lap ]

=HPOST(f)HDAC(f)HDSP(f)(1/T)[HPRE(f)X(f) + pho lap]

TmffX

TfX

ms

1)(

1)( ==

=




1 7 C th h h b h th DSP



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Tac dung cua bo loc prefilter a am bao cho cac pho lapkhong chong lan len nhau. Cuoi cung v bo loc prefilter coinh la bo loc thong thap gan ly tng nen o li trong bang

thong coi nh bang 1. Ket qua cuoi cung tn hieu ngo ra copho hau nh nam gon trong dai Nyquist.

HPOST(f)HDAC(f) T; Pho lap 0;HPRE(f) 1Vi cac xap x tren thoa man nham nang cao chat lng hethong, ta co ket qua:

hoac la

vi (1.7.1)Nh vay, cach sap xep cac tang nh tren tao thanh mot bo

loc tuyen tnh cho tn hieu tng t ngo vao, vi hamtruyen HDSP(f) tao bi bo x ly DSP.

[ ]0)(11

)()( += fXT

fHTfY aDSPa

)()()( fXfHfY aDSPa = 2sff



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