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8/18/2019 DSIP LAB3 Updated
1/13
EEE40003 Digital Signal and Image Processing
SWINBURNE UNIVERSITY O TE!"NO#O$Y
EEE40003 Digital
Signal and ImageProcessingEEE40003 Digital Signal and ImageProcessing
Yew Wee Wong 10012429
LAB 3: Discrete LTI Systems
Ye% Wee Wong &000&'4'( Page 0
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EEE40003 Digital Signal and Image Processing
Table of Contents)im************************************************************************************************************************ &
Res+lt and )nal,sis************************************************************************************************'
Part B- ) Sim.le IR S,stem*******************************************************************************'
Part !- ) Sim.le IIR S,stem********************************************************************************(
!oncl+sion*********************************************************************************************************** &&
Aim• Familiarize with MATLAB
•
Examinnation of a simple FI system• Examination of a simple II system
Ye% Wee Wong &000&'4'( Page &
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EEE40003 Digital Signal and Image Processing
Result and Analysis
Part B A !im"le #$R !ystem
1)
By comparin! "oth e#$ations% the theoretical $nit p$lse response of the system is &etermine&
as "elow:
'
()*+%
'
()3+%
'
(),+%
'
()(+%
'
()-+ ===== hhhhh
Since the system shows characteristic s$ch that
-%-)+
8/18/2019 DSIP LAB3 Updated
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EEE40003 Digital Signal and Image Processing
3)
1o&e es$lt
Comment: The res$lt of the $nit p$lse response complements the theoretical response in 2art
B +() where
*%3%,%(%-%'
()+ == r r h
an& - for e0erywhere else.
Ye% Wee Wong &000&'4'( Page 3
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EEE40003 Digital Signal and Image Processing
4)
1o&e es$lt
Comment: From the res$lt o"taine&% we can see that the first ' elements of the o$tp$t si!nal
are &istorte& "eca$se the n$m"er of inp$t se#$ence is less than the win&ow/ a0era!in! len!th+ 4 '). 5hen the inp$t se#$ences are 6 '% the reconstr$ction of the o$tp$t si!nal is similar to
the inp$t similar.
Ye% Wee Wong &000&'4'( Page 4
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EEE40003 Digital Signal and Image Processing
5)
1o&e es$lt
Comment: As expecte&% the first ' elements of the o$tp$t si!nal are &istorte& &$e to the
limitation of win&ow 7 a0era!in!. The res$lt a"o0e also shows that the noise of the ori!inal
si!nal is !reatly re&$ce& "y $sin! win&ow 7 a0era!in! witho$t alterin! the shape of the
ori!inal si!nal.
Ye% Wee Wong &000&'4'( Page
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EEE40003 Digital Signal and Image Processing
6) and 7)
1o&e es$lt
Comment: The res$lt "y $sin! con0ol$tion to calc$late the $nit p$lse response of the system
is the sim$lar to the res$lt o"taine& in step 3) a"o0e. 8owe0er% there are a sli!ht &ifference in
"oth techni#$es where the res$lt "y $sin! con0ol$tion exten& $p to the 39th elements while
the res$lt o"taine& in step 3) a"o0e only reaches $p to the 3, th elements.
8)
1o&e es$lt
Comment: By $sin! con0ol$tion f$nction% the noise of the ori!inal B wa0eform is !reatly
re&$ce& which is similar to the res$lt o"taine& in step '). 8owe0er% the res$lt o"taine& "y$sin! con0ol$tion has a sli!ht &istortion at the last few elements.
Ye% Wee Wong &000&'4'( Page 1
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EEE40003 Digital Signal and Image Processing
9)
;'
8/18/2019 DSIP LAB3 Updated
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EEE40003 Digital Signal and Image Processing
10)
;9
8/18/2019 DSIP LAB3 Updated
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EEE40003 Digital Signal and Image Processing
Ye% Wee Wong &000&'4'( Page (
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EEE40003 Digital Signal and Image Processing
Part C A !im"le $$R !ystem
1)
)+)(+)(+)+ n xn yn y α α −+−=
By s$"stit$tin!>,.-=α
%
)+)>,.-(+)(+>,.-)+ n xn yn y −+−=
1omparin! the form$la with:
...),+)(+)+...),+)(+)+ ,(,(- +−+−+=+−+−+ n xbn xbn xbn yan yan ya o
Therefore%
-%>,.-%( (- =−== naaa
forotherwisen =
-%(>.-- == nbb
for otherwisen =
2)
1o&e es$lt
3)
1o&e es$lt
Ye% Wee Wong &000&'4'( Page &0
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EEE40003 Digital Signal and Image Processing
4)
Code
?ri!inal B 5a0e Filtere& B 5a0e
Question 2:
Ye% Wee Wong &000&'4'( Page &&
)+)(+)+ +−= n xn y α
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EEE40003 Digital Signal and Image Processing
Comment: The &ia!ram a"o0e pro0es that the e#$ation in step +() follows from the "loc@
&ia!ram !i0en.
Question 3: This &iscrete system shows similarity with a 1 circ$it. The characteristic of the
system shown in step +,) &emonstrates the &ischar!in! phase of the capacitors 0olta!e while
step +3) shows the char!in! phase of the capacitors 0olta!e.
Con%lusionIn a n$tshell% st$&ent s$ccessf$lly in&$l!es in more familiarization with Matla" in 2art A. In
2art B an& 1 of the la"% st$&ent s$ccessf$lly examines the characteristic of a simple FI
system an& II system an& pro0i&es rele0ant comment of their tho$!hts a"o$t their
examination.
Ye% Wee Wong &000&'4'( Page &'
)(+ −n y( n xα −
(−nα