Report DSP

DSP – REPORT

Name : Lê Văn Trình – 11DT1 Hoàng Ngọc Luân – 11DT 11DT Ngu!"n Ph#c Th$%n – 11DT Nh&m: '(

L()1(: *n+ro,uc+$on +o -(TL() an, Scr$.+/ E0erc$/e 1: diary 'TrinhLuanThien_Lab1.txt' %INSERT your name and section into these display commands disp'N!"E# disp'N!"E# Trinh Luan Thien' $ disp'SETI&N# disp'SETI&N# (!'$ (!' $ datestrcputime$ %dampedosine.m produces a plot o) a cosine *ith )re+uency 1 ,- *ith amplitude % scaled by a decayin/ exponential )i/ure x 0 2#3.31#24 y10expabsx$$.5cospi5x$4 subplot611$4 plotxy1$4 xlabel'time' xlabel 'time'$4 $4 ylabel'amplitude' ylabel 'amplitude'$4 $4 title')x$0exp7x7$cospi5x$' title')x$0exp7x7$cospi5x$' $4 subplot616$4 y60expabsx$$.5cospi5x86$4 plotxy6$4 xlabel'time' xlabel 'time'$4 $4 ylabel'amplitude' ylabel 'amplitude'$4 $4 title')x$0exp7x7$cos65pi5x$' title')x$0exp7x7$cos65pi5x$' $4 diary o))

L()1(: *n+ro,uc+$on +o -(TL() an, Scr$.+/ E0erc$/e 1: diary 'TrinhLuanThien_Lab1.txt' %INSERT your name and section into these display commands disp'N!"E# disp'N!"E# Trinh Luan Thien' $ disp'SETI&N# disp'SETI&N# (!'$ (!' $ datestrcputime$ %dampedosine.m produces a plot o) a cosine *ith )re+uency 1 ,- *ith amplitude % scaled by a decayin/ exponential )i/ure x 0 2#3.31#24 y10expabsx$$.5cospi5x$4 subplot611$4 plotxy1$4 xlabel'time' xlabel 'time'$4 $4 ylabel'amplitude' ylabel 'amplitude'$4 $4 title')x$0exp7x7$cospi5x$' title')x$0exp7x7$cospi5x$' $4 subplot616$4 y60expabsx$$.5cospi5x86$4 plotxy6$4 xlabel'time' xlabel 'time'$4 $4 ylabel'amplitude' ylabel 'amplitude'$4 $4 title')x$0exp7x7$cos65pi5x$' title')x$0exp7x7$cos65pi5x$' $4 diary o))

TrinhLuanThien_dampedCosin figure ω= 2π/T => T = 2π/ω 2π/ω Chu kì tín hiệu thứ nhất : T1= 2π/π=2s Chu kì tín hiệu thứ hai : T2=2π/(π/2) = 4 s

E0erc$/e : )unction  compexp)d$ )unction compexp)d$ %compexp.m produces a 9 plot o) a decayin/ complex exponential % *ith subplots o) ma/nitude and phase and o) real and ima/inary % components belo* it. )i/ure t 0 3#3.31#24 y05expd53.62:;5)565pi$$5t$4 subplot11$4 plottrealy$ima/y$$4 /rid xlabel't' xlabel 't'$ylabel $ylabel'Rey$' 'Rey$'$-label $-label'Imy$' 'Imy$'$4 $4 title'9 title'9 plot o) a omplex Exponential' $4 %produce ma/nitude and phase plots4 t $plottan/ley$$xlabel 't' 't'$ $ ylabel'!n/le' ylabel '!n/le'$title $title'?hase '?hase  !r/yt$$' $4 %produce real and ima/ plots4 t
Làm cho tần số dao đng gi!m mt n"a# compe$p%f&d'

compe$p%(&('#

)i!m th*ng số f đi mt n"a# compe$p%+&('#

T,ng tốc đ ph-n r. /0ng c1ch t,ng th*ng số d# compe$p%2&('#

compe$p%2&2' #

L()1): 2unc+$on/ $n -(TL() an, +he 3roo4e S+a+$on: E0erc$/e 1 3ader  )unction A y B 0 )adex le
% )adex$# this )unction )ades the audio
4emonstration# t03#3.31#1 y 0 cost .5 pi .5 62$4 subplot611$4 plotty$4 xlabel'ori/inal si/nal'$4 subplot616$4 plott )adey3.$$4 xlabel'si/nal a)ter usin/ )ade )unction *ith le
E0erc$/e  5epeater  )unction A out B 0 repeatin N yes$ % yes 01 # insert silence bet*een the repetition

)or i03 # 1# N out1 0 AinB 4 i) i003 out 0 Aout1B4 else i) yes 00 1 out0Aout 3 out1B4 else out0Aout out1B4 end end end

4emonstration# x0A1 > 6 6 B 4 %y 0A 2   ( 3B4 %x0Ax yB a03#1#>4 subplot611$4 plotax$4 xlabel'ori/inal si/nal'$4 y0repeatx63$4 % don't insert the silence bet*een the repetition b0 3#1# len/thy$14 subplot616$4 plotby$4 xlabel'si/nal a)ter repeatin/ 6 times' $4

x0A1 > 6 6 B 4 a03#1#>4 subplot611$4

plotax$4 xlabel'ori/inal si/nal'$4 y0repeatx61$4 % insert the silence bet*een the repetition b0 3#1# len/thy$14 subplot616$4 plotby$4 xlabel'si/nal a)ter repeatin/ 6 times' $4

E0erc$/e : 4e6a7 %8hift' )unction A output B 0 delay si/nal delaytime )s $ numbero)-eros 0 delaytime .5 )s r 0 -eros1numbero)-eros$4 output 0 Ar si/nalB4 end

Demon/+ra+$on: subplot611$4 plotbassdrum'$4 xlabel'bassdrum'$ y0 delaybassdrum' 18333$4 subplot616$4 ploty$4 xlabel'delayed bassdrum'$

E0erc$/e 5 9i$er  )unction A output B 0 mixer x1 x6 $ n1 0 len/thx1$4 n6 0 len/thx6$4 maxi0 maxn1 n6$4 mini 0 minn6 n1$4 di)) 0 maxi  mini4 -ero 0 -eros1di))$4 i) maxi 00 n1$ a 0 Ax6 -eroB4 output 0 x1 : a4 else b 0 Ax1 -eroB4 output 0 x6 : b4 end m 0 maxoutput$4 output 0 output8m4 end

4emonstration# a0mixerbleepbassdrum$4 subplot11$4 plotbleep$4 xlabel'bleep sound'$4 subplot16$4 plotbassdrum$4 xlabel'bassdrum sound'$4 subplot1$4 plota$4 xlabel'mixed sounds'$4

E0erc$/e 6: -a7e 8our 3roo4e

97 groo:e# x10repeatbassdrum'633$4 x60repeatbleep'633$4 )0 Ax1 x6B4 sound)$4 plot)$4 *a<*rite) 'ne*.*a<'$4

LAB2A Exercise 1:

Synthesizer 

load trumpet.mat Fs0113624 sounded1Fs$ )i/ure ploted1633#>33$$4 axis ti/ht *a<*riteed1Fs 'trumpet.*a<'$

% looGs
Dạng sóng của âm thanh trumpet ở 5 chu kỳ

Phổ tín hiệu trumpet: H 0 ))ted1 216$4 % taGe the ))t o) trumpet Hma/ 0 absH$4 % taGe the ma/ o) H ) 0 Fs 5 3#62@$82164 % /et a meanin/)ul axis plot) Hma/1#62$$4 % plot Hma/ only hal) the points are needed$ xlabel'Fre+uency ,-$'$ ylabel'"a/nitude'$ axis ti/ht

!c "#$c %& gi' tr( ")nh c*u phổ t+n s, tín hiệu trumpet: -.re/ 0 mag123-4567 0 %%610-5868 0 8969510-9;69 0 ;56%%10-%&55 0 5464710 -%885 0 546510-%58 0 8610 -%54 0 468%10-4%84 0 %%6;10-48& 0 %569410-4;7 0 %564%1< )unction AoutB0 addcosinestimeFs$ % ,am addcosines tao tin hieu am thanh si/synth1.*a< t03#18Fs#time4 )re+0A62.> 2. (@. 1322 12 12( 126 616 6(3 6@>( B4 ma/0A11. .2 @2.11 @2.11 26.2( .(( 6.1 11.@( 12.6 12.61B4 si/synth0-eros1len/tht$$4 )or i01#len/th)re+$ si/synth 0 si/synth : ma/i$5cos65pi5)re+i$5t$4 end si/synth03.(((5si/synth8maxabssi/synth$$4 *a<*ritesi/synthFs 'si/synth1.*a<'$4 out 0 si/synth4 end

Demon/+ra+$on: time28= >s2%%&45= k2a??c@sines-time0>s1= s@un?-k1=

suApB@t-40%0%1=  pB@t-e?%-4&&:7&&11= xlabel'Tin hieu trumpet' $

aCis tight suApB@t-40%041=  pB@t-k-4&&:7&&11= xlabel'Tin hieu ton/ hop G' $

aCis tight

Exercise 2:

Script phasefun: Fs03334 t03#18Fs#4 )re+0A(3.@ 2.B4 ma/0A. @2.11B4 si/10-eros1len/tht$$4 )or i01#len/th)re+$ si/1 0 si/1 : ma/i$5cos65pi5)re+i$5t$4 end

si/103.(((5si/18maxabssi/1$$4 *a<*riteFs'si/1.*a<'$4 -ero10-eros161$4 si/60A-ero1 si/1B4% Tao tin hieu si/6 delay 186 chu Gy cua si/1 Fs03334 )i/ure4 subplot611$4 plotsi/11#633$$4 xlabel'Tin hieu si/1'$4 axis ti/ht4 /rid on subplot616$4 plotsi/61#633$$4 xlabel'Tin hieu si/6'$4 axis ti/ht4 /rid on si/0si/14% tao tin hieu si/ -ero60-eros113$4 si/delay0A-ero6 si/B4% tao tin hieu delay cua tin hieu si/ si/>0Asi/ -ero6B: si/delay4% tao tin hieu si/> ban/ cach con/ si/ 1#633$$4 xlabel'Tin hieu si/>'$4 axis ti/ht4 /rid on

hi ta ?eBay tín hiệu sig4 mEt kh@*ng thFi gian AGng %H4 chu kỳ tín hiIu sig% thJ sig4 trK pha hLn s@ MNi sig% % góc %& "E6

hi ta ?Ong Bệnh s@un?sc-sig%1 M s@un?sc-sig41 thJ ta thQy tín hiệu 4 A( trK % kh@*ng thFi gian  AGng %H4 chu kỳ tín hiệu6-âm thanh sig4 nghe trK hLn16

hi ?Ong Bệnh s@un?sc-sig81 M s@un?sc-sig71 thJ ta thQy 4 tín hiệu nghe nh# nhau6

Exercise 3: R "T th( AiUn "E0 pha của Vk  )unction )ct0GG$ )ct 0 -erossi-eG$$4 )or m01#len/thG$ i) JmodGm$6$ 00 3$   )ctm$01.8;5Gm$5pi$.5cos65Gm$5pi8$cosGm$5pi8$$4 end end return4

Demon/+ra+$on: G013#134 )ct0GG$4 ma/0abs)ct$4

pha0an/le)ct$4 subplot611$4 stemGma/$4/rid on4 xlabel'G'$4 subplot616$4 stemGpha$4/rid on4 xlabel'G'$4

Coeff.tif  Wm giAAs: Wm giAAs thXc hiện tính :

RNi Y&2%= Zr@ng hm ny có s[ ?\ng hm Vk "] "#$c "(nh ngh^a ở trUn )unction Asi/synthB0/ibbsGmax$

t02#3.1#24 G0AGmax#GmaxB4 )ct0GG$4 ma/0abs)ct$4 pha0an/le)ct$4 si/synth0-eros1len/tht$$4 )or i0Gmax:1#len/thG$ si/synth 0 si/synth : 65ma/i$5cosiGmax$5t:phai$$4 end

Demon/+ra+$on: a0/ibbs2$4 t02#3.1#24 sublot11$4 plotta$4title'Gmax02'$4

ZhXc hiện t#Lng tX MNi B+n B#$t kmaC AGng %5 M 8& sau "ó M "T th( của tính hiệu sigsynth ta "#$c kIt /u*:

FourTrunc.tif 

LAB 2B

Low-pass Filtering Exercise 1: ZhiIt kI AE B!c th_ng thQp MNi t+n s, c`t a25&&4pi6

Script eC%6m C2YaMrea?-bcastanets77m6YaMb1=  2 ..t-C1= >s2&&&=  d 2 Bength-1= a 2 5&&4pi= Y 2 fdH4%:-dH41= W 2 a 6H -a  iY1= ?ap ung A@ B@c th@ng thap .igure= pB@t-Y>sHd0aAs--111=titBe-b Ph@ cua tin hieu khi chua B@cb1= .igure= pB@t-Y>sHd0aAs-W11=titBe-b Ph@ cua A@ B@c th@ng thap khi chua ?ich tan s@b 1= Wshi.t 2 ..tshi.t-W1= Dich tan thap Me trung tam .igure= pB@t-Y>sHd0aAs-Wshi.t11=titBe-b Ph@ cua A@ B@c th@ng thap khi ?ich tan s@b 1= j 2  6 Wshi.tb=  @c tin hieu  .igure= pB@t-Y>sHd0aAs-j11= titBe- b Ph@ cua tin hieu sau khi B@c th@ng thapb 1= y 2 reaB-i..t-j11= lien ?@i .@urier ngu@c s@un?-C0 >s1  @riginaB s@un? s@un?-y0 >s1  [email protected]? s@un? esult:

 dhn Ct: tín hiệu âm thanh y- tín hiệu "] "#$c B!c th_ng thQp1 nghe nho hLn s@ MNi tín hiệu C6

Exercise 2: S[ ?\ng hm: C 2 repmat-zer@s-%0 1 %0 %0 51= " tạ@ tín hiệu C-t16 Sau "ó B!c tín hiệu trUn AGng  AE B!c th_ng thQp MNi t+n s, a24&

Script eC46m C 2 repmat-zer@s-%0 1 %0 %0 51=  2 ..t-C1= >s2&&&=  d 2 Bength-1= a 2 4&4pi= Y 2 fdH4%:-dH41= W 2 a 6H -a  &65iY1= Dap ung A@ B@c th@ng thap Wshi.t 2 ..tshi.t-W1= Dich tan thap Me trung tam j 2  6 Wshi.t=  @c tin hieu  y 2 reaB-i..t-j11= lien ?@i .@urier ngu@c suApB@t-40%0%1=  pB@t-Y>sHd0 C1= titBe-bC-t1b1= yBaAeB-blien ?@b1= CBaAeB-bZan s@b1= suApB@t-40%041=

 pB@t-Y>sHd0y1= titBe-by-t1b1= yBaAeB-blien ?@b1= CBaAeB-bZan s@b1=

!igh-pass Filtering: Exercise 3: ZhiIt kI AE B!c th_ng ca@ MNi t+n s, c`t a24&&&4pi Script eC86m: C2YaMrea?-bcastanets77m6YaMb1=  2 ..t-C1= >s2&&&=  d 2 Bength-1= a 2 4&&&4pi= Y 2 fdH4%:-dH41= W 2 %f a 6H -a  iY1= ?ap ung A@ B@c th@ng thap .igure= pB@t-Y>sHd0aAs--111=titBe-b Ph@ cua tin hieu khi chua B@cb1= .igure= pB@t-Y>sHd0aAs-W11=titBe-b Ph@ cua A@ B@c th@ng ca@ khi chua ?ich tan s@b 1= Wshi.t 2 ..tshi.t-W1= Dich tan thap Me trung tam .igure= pB@t-Y>sHd0aAs-Wshi.t11=titBe-b Ph@ cua A@ B@c th@ng ca@ khi ?ich tan s@b 1= j 2  6 Wshi.tb=  @c tin hieu 

.igure= pB@t-Y>sHd0aAs-j11= titBe- b Ph@ cua tin hieu sau khi B@c th@ng ca@b 1= y 2 reaB-i..t-j11= lien ?@i .@urier ngu@c s@un?-C0 >s1  @riginaB s@un? s@un?-y0 >s1  [email protected]? s@un?

Exercise ": !c tín hiệu Aass?rum6YaM ra khoi tín hiệu miCe?6YaM  Za M phổ của tín hiệu Aass?rum tr@ng miqn t+n s,: C2YaMrea?-bAass?rum6YaMb1= 2..t-C1= >s2&&&=  d 2 Bength-C1= Y 2 fdH4% : dH4= .igure= pB@t-Y>sHd0aAs-11

Phổ của tín hiệu #ass$ru%

DXa M@ phổ của tín hiệu Aass?rum ta ch!n kh@*ng t+n s, m AiUn "E tín hiệu Aass?rum ca@ nhQt rTi thiIt kI AE B!c th_ng ?*i " B!c6 Za ch!n t+n s, c`t của AE B!c th_ng thQp B a24&&0 t+n s, c`t của AE B!c th_ng ca@ B A24&6 'p ng t+n s, của AE B!c th_ng ?*i B W2W%6W4 MNi W% B "'p ng t+n s, của AE B!c th_ng thQp0 W4 B "'p ng t+n s, của AE B!c th_ng ca@6 Z'ch tín hiệu #ass$ru%: C2YaMrea?-bmiCe?b1= 2..t-C1= >s2&&&=  d 2 Bength-C1= a 2 44&&pi=  @Y fpass: cut@.. 2 4&&  A 2 44&pi=  Wighfpass: cut@.. 2 4& Y 2 fdH4% : dH4= W% 2 a 6H -a  iY1= W4 2 % f A 6H -A  iY1= W 2 -W% 6 %& 1 6 - W4 6%& 1 =  centere? W Wshi.t 2 ..tshi.t-W1=  ncentere? W .igure= pB@t-Y>sHd0aAs-Wshi.t11 j 2 6 Wshi.tb=  >iBter 0 ncentere? j .igure= pB@t-Y>sHd0aAs-j11  uncentere? Mersi@n @. j y 2 reaB-i..t-j11=

&'p (ng #) l*c th+ng $,i

Tn hiu #ass$ru% sau /hi 0c l*c ra /hi %ixe$

La# 2: 4ntro$uction to 4%age 5rocessing Exercise 1: Edge Detection cBc= cB@se aBB= C2imrea?-b?aiBysh@Yb0bpegb1= y2rgA4gray-C1= imsh@Y-C1= suApB@t-4040%1 imsh@Y-y1= sizeC2size-C1 sizey2size-y1= h%2f% & %=f4 & 4=f% & %= h42% 4 %=& & &=f% f4 f%= v%2c@nM4-y0h%1 v42c@nM4-y0h41 suApB@t-404041= resuBt%2mat4gray-455faAs-v%11= imsh@Y-resuBt%1= suApB@t-404081= resuBt42mat4gray-455faAs-v411= imsh@Y-resuBt41= suApB@t-404071= resuBt82mat4gray-455fs/rt-v%64v46411= imsh@Y-resuBt81=

Exercise 2: Scaling cBc= cB@se aBB= s2;=  eC4 y%2w4x-s1= C2imrea?-bab0bpegb1= .igure= imsh@Y-C1= .igure= imsh@Y-y%1= hàm:

.uncti@n  y  2 w4x-s1 C2imrea?-bab0bpegb1= C2rgA4gray-C1= temp2size-C1= y2zer@s-r@un?-temp-%1Hs10r@un?-temp-41Hs11= .@r i2%:s:temp-%1 .@r  2%:s:temp-41   tempMaBue2&= .@r  u2&:%:-sf%1 .@r  M2&:%:-sf%1 i. -iu12temp-%1M2temp-41 tempMaBue 2 tempMaBue  C-iu0M1H-s41= en? en? en?   y-ceiB-iHs10ceiB-Hs112tempMaBue= en? en? y2mat4gray-y1= en?

Exercise 3: Image Flipping cBc= cB@se aBB= C2imrea?-bDaiBySh@Yb0bpegb1= y2rgA4gray-C1= y%2.BipBr-y1= y42.Bipu?-y1= y82.Bipu?-y%1= suApB@t-4040%1= imsh@Y-y1= suApB@t-404041=

imsh@Y-y%1= suApB@t-404081= imsh@Y-y41= suApB@t-404071= imsh@Y-y81=

result :

Exercise 4: Image Expanding y60EK>$4 )i/ure4 imsho*y6$ Hàm:

)unction AyB 0 EK>$ x0imread'9ailySho*'';pe/'$4 x0r/b6/rayx$4 temp10si-ex$4 y0-erostemp11$561temp16$561$4 temp60si-ey$4 )or i01#1#temp61$ )or ;01#1#temp66$ i) modi6$J03mod;6$J03   yi;$0xceili86$ceil;86$$4 else i) modi6$J03  mod;6$003

 

yi;$03.25yi;:1$:yi;1$$4 else i) modi6$003  mod;6$J03 yi;$03.25yi:1;$:yi1;$$4 else yi;$03.625yi:1;:1$:yi1;1$:yi:1;1$:yi

 

1;:1$$4 end end end end end y0mat6/rayy$4

result:

LAB 3: Assign%ent 1:

a/ x(n) = u(n-30) – u(n-50) and h1(n) = u(n-10) – u(n-20); n03#1#1334 un0nC03$4 xn0n3C03$n23C03$4 h10n13C03$n63C03$4 y0con<xnh1$4 subplot11$4 stemxn1#133$$4 xlabel 'xn$'$4 /rid subplot16$4 stemh11#133$$4 xlabel 'h1n$'$4 /rid subplot1$4 stemy1#133$$4 xlabel 'yn$'$4 /rid

b/ x(n) = u(n-30) – u(n-50) and h2(n) = (0.9)nu(n); n03#1#1334 un0nC03$4 xn0n3C03$n23C03$4

h603.($.Mn$.5un4 y0con<xnh6$4 subplot11$4 stemxn1#133$$4 xlabel 'xn$'$4 /rid subplot16$4 stemh61#133$$4 xlabel 'h6n$'$4 /rid subplot1$4 stemy1#133$$4 xlabel 'yn$'$4 /rid

c/ x(n) = u(n-30) – u(n-50) and h3(n) = δ(n) – δ(n-1); n03#1#1334 un0nC03$4 xn0n3C03$n23C03$4 h0n003$n1003$4 y0con<xnh$4 subplot11$4 stemxn1#133$$4 xlabel 'xn$'$4 /rid subplot16$4 stemh61#133$$4 xlabel 'h6n$'$4 /rid subplot1$4 stemy1#133$$4 xlabel 'yn$'$4 /rid

Assign%ent 2: x=[1 2 3 4] và h=[3 2 1]

a.  Xác

!nh "(n) = x(n)#h(n)$

CC y0con<xh$ y 0 



1>

63

11

>

b.  %&'u d&n x(n) thnh *ect+r ,x1 * "(n) thnh *ect+r x1. Xác !nh a trn 

(x,)  " = x  x 0 1 6

 > y 0   1> 63 11 > , 0  



3

3

3

 

6



3

3

 

1

6



3

 

3

1

6



 

3

3

1

6

 

3

3

3

1

c. d.

 a trn  c 4n ch6+ l các s7 &7n nhau. 8t :u t&n ch * hn :u t&n ch.

e.  Bhát

tr&'n h atlab ' thCc h&Dn ?h6? nhEn ch? tu"Fn tGnh$

)unction Ay,B0con<_tphx$ % Linear on
Exercise 3  X (z):

 X (z) 2

&645 z % −  z

%

−

+

8

−

−

&695 z

&65 z 4

−

−

7

−

+

&6&;45 z  5

&645 z

−

−

8

+

&6&;45 z  7 −

 H (z):  H (z) 2

 z  z − %H 8

−

z  z − 4

Y (z):

%645 z 8 + 465z 4 − &68%45z  Y (z) 2 8 z 9 − %& z ; + %%645z 5 − z 7 + 867895z 8 − &6895z 4 + &6%45z  −

 y (n):

>irst0 Ye s@me caBcuBat@r [email protected] t@ get the r@@ts @. the ?en@minat@r: 2{ Zhe r@@ts are 40 -&645&6788i10 -&645&6788i10 -&645 | &6 788i10 -&645 | &6 788i10 an? &688886  d@Y0 it is /uite easy t@ get j -z1 int@ .racti@n eCpansi@n &6&5:

−

 z − 4

+

%6&%84 + &6944i z − -&645 +

&6788i 1

+

&67;9 − &6489:i z − -&645 +

&6788i 1

+

%6&%84− &6944i z − -&645 −

&6788i 1

+

&67;9+ &6489:i z−

-&645 − &6788i 1

−

46&4&7 z  −

&68888

 d@Y0 Ye can get y -n1 2

&6&5-41 % u -− n − 41 +-%6&%84 + &6944i 1-&645 + &6788i 1 %u -n − %1 

−

n+

n−

-&67;9 − &6489i 1-&645 + &6788i 1 % u -n − %1  -&67;9 + &6489i 1-&645 − &6788i 1 % u -n − %1 n−

+

-%6&%84 − &6944i1-&645 − &6788 i1 n

n−

%

−

46&4&7-&688881 u -n − %1

u- n −%1 −

Y (z) by using Matlab

 get j -z1 int@ .racti@n eCpansi@n Ay using resi?ues {{ p 2 f%645 465 f&68%45 &= {{ / 2 8 f%& %%645 f 867895 f&6895 &6%45 &= {{ r0a0k 2 resi?ue -p 0 /1 r2   f&6&&5 %6&%84  &6944i &67;9& f &6489i %6&%84 f &6944i &67;9&  &6489i

n

  f46&4&7 & a2   46&&&& &645&&  &6788&i &645&&  &6788&i &645&& f &6788&i &645&& f &6788&i   &68888 & k2  D@ the c@nM@Buti@n @. C -n1 an? h-n1 using vatBaA n 2 &:%:%&&=   2 -nf416--%H416-nf4116c@s-pi-nf41H816-nf4{2&1= k 2 -%H816n6-n{2&1-416n6-fnf%{2&1= y 2 c@nM-0k1= stem -y1=

Assign%ent ":

a/ x(n) = u(n-30) – u(n-50) and h1(n) = u(n-10) – u(n-20); n03#1#1334 un0nC03$4 xn0n3C03$n23C03$4 h10n13C03$n63C03$4 K 0 ))txn$4 ,1 0 ))th1$4 H 0 ,1.5K4 y0 i))tH$4 subplot11$4 stemxn1#133$$4 xlabel 'xn$'$4 /rid subplot16$4 stemh11#133$$4 xlabel 'h1n$'$4 /rid subplot1$4 stemy1#133$$4 xlabel 'yn$'$4 /rid

b/ x(n) = u(n-30) – u(n-50) and h2(n) = (0.9)nu(n); n03#1#1334 un0nC03$4 xn0n3C03$n23C03$4 h603.($.Mn$.5un4 K 0 ))txn$4 ,6 0 ))th$4 H 0 ,6.5K4 y0 i))tH$4 subplot11$4 stemxn1#133$$4 xlabel 'xn$'$4 /rid subplot16$4 stemh61#133$$4 xlabel 'h6n$'$4 /rid subplot1$4 stemy1#133$$4 xlabel 'yn$'$4 /rid

c/ x(n) = u(n-30) – u(n-50) and h3(n) = δ(n) – δ(n-1); n03#1#1334 un0nC03$4 xn0n3C03$n23C03$4 h0n003$n1003$4 y0 i))txnh $4 subplot11$4 stemxn1#133$$4 xlabel 'xn$'$4 /rid subplot16$4 stemh1#133$$4 xlabel 'hn$'$4 /rid subplot1$4 stemy1#133$$4 xlabel 'yn$'$4 /rid