DSIP LAB3 Updated

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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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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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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

-%-)+


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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.



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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.



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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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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.



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9)

;'


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10)

;9


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Ye% Wee Wong &000&'4'( Page (


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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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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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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

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DSIP LAB3 Updated