Part C only thx with the matlab 2. Analysing a Discrete-Time System: In this exe

Question

Part C only thx with the matlab

2. Analysing a Discrete-Time System: In this exercise we will introduce discrete convolution and use this, along with frequency analysis, to analyse a discrete-time system a) Generate the following discrete signals fIn] (1.4.2,5,6) and gln]- (1.3,-1.2) Note that the arrows indicate the position at which n0 i. Calculate y-fg using the conv command and plot y[n] with labelled axes Note either use conv(f,g) or conv(f,g,'full') to do this calculation ii. How many elements are in y[n]? How does this number relate to the length of f lli. Now re-compute the convolution sum using conv(f,g,'same'). How do the values iv. Finally, re-compute the convolution sum using conv(f,g,'valid'). How do the v. Repeat part i) with gIn] -[01.3,-1,2) and g? you obtain relate to the values obtained in i)? values you obtain relate to the values obtained in i)? b) The following equation defines 1 period of a periodic discrete signal: 2 n for 0sns 25 25 f [n] n-4 for 25

Explanation / Answer

c (i). Calculate the values of h[n] using the given relation and substituting with the requireed values.

Editor:

n=0:299
h=1/3.*(n<=2)
x= -2*n/25.*(0<=n<=25)
x= (2*n/25-4).*(25<n<=75)
x= (-2*n/25)+8.*(75<n<=99)
y=conv(x,h)

Command Window Output:

y =

Columns 1 through 12

2.6667 5.3067 7.9200 7.8400 7.7600 7.6800 7.6000 7.5200 7.4400 7.3600 7.2800 7.2000

Columns 13 through 24

7.1200 7.0400 6.9600 6.8800 6.8000 6.7200 6.6400 6.5600 6.4800 6.4000 6.3200 6.2400

Columns 25 through 36

6.1600 6.0800 6.0000 5.9200 5.8400 5.7600 5.6800 5.6000 5.5200 5.4400 5.3600 5.2800

Columns 37 through 48

5.2000 5.1200 5.0400 4.9600 4.8800 4.8000 4.7200 4.6400 4.5600 4.4800 4.4000 4.3200

Columns 49 through 60

4.2400 4.1600 4.0800 4.0000 3.9200 3.8400 3.7600 3.6800 3.6000 3.5200 3.4400 3.3600

Columns 61 through 72

3.2800 3.2000 3.1200 3.0400 2.9600 2.8800 2.8000 2.7200 2.6400 2.5600 2.4800 2.4000

Columns 73 through 84

2.3200 2.2400 2.1600 2.0800 2.0000 1.9200 1.8400 1.7600 1.6800 1.6000 1.5200 1.4400

Columns 85 through 96

1.3600 1.2800 1.2000 1.1200 1.0400 0.9600 0.8800 0.8000 0.7200 0.6400 0.5600 0.4800

Columns 97 through 108

0.4000 0.3200 0.2400 0.1600 0.0800 -0.0000 -0.0800 -0.1600 -0.2400 -0.3200 -0.4000 -0.4800

Columns 109 through 120

-0.5600 -0.6400 -0.7200 -0.8000 -0.8800 -0.9600 -1.0400 -1.1200 -1.2000 -1.2800 -1.3600 -1.4400

Columns 121 through 132

-1.5200 -1.6000 -1.6800 -1.7600 -1.8400 -1.9200 -2.0000 -2.0800 -2.1600 -2.2400 -2.3200 -2.4000

Columns 133 through 144

-2.4800 -2.5600 -2.6400 -2.7200 -2.8000 -2.8800 -2.9600 -3.0400 -3.1200 -3.2000 -3.2800 -3.3600

Columns 145 through 156

-3.4400 -3.5200 -3.6000 -3.6800 -3.7600 -3.8400 -3.9200 -4.0000 -4.0800 -4.1600 -4.2400 -4.3200

Columns 157 through 168

-4.4000 -4.4800 -4.5600 -4.6400 -4.7200 -4.8000 -4.8800 -4.9600 -5.0400 -5.1200 -5.2000 -5.2800

Columns 169 through 180

-5.3600 -5.4400 -5.5200 -5.6000 -5.6800 -5.7600 -5.8400 -5.9200 -6.0000 -6.0800 -6.1600 -6.2400

Columns 181 through 192

-6.3200 -6.4000 -6.4800 -6.5600 -6.6400 -6.7200 -6.8000 -6.8800 -6.9600 -7.0400 -7.1200 -7.2000

Columns 193 through 204

-7.2800 -7.3600 -7.4400 -7.5200 -7.6000 -7.6800 -7.7600 -7.8400 -7.9200 -8.0000 -8.0800 -8.1600

Columns 205 through 216

-8.2400 -8.3200 -8.4000 -8.4800 -8.5600 -8.6400 -8.7200 -8.8000 -8.8800 -8.9600 -9.0400 -9.1200

Columns 217 through 228

-9.2000 -9.2800 -9.3600 -9.4400 -9.5200 -9.6000 -9.6800 -9.7600 -9.8400 -9.9200 -10.0000 -10.0800

Columns 229 through 240

-10.1600 -10.2400 -10.3200 -10.4000 -10.4800 -10.5600 -10.6400 -10.7200 -10.8000 -10.8800 -10.9600 -11.0400

Columns 241 through 252

-11.1200 -11.2000 -11.2800 -11.3600 -11.4400 -11.5200 -11.6000 -11.6800 -11.7600 -11.8400 -11.9200 -12.0000

Columns 253 through 264

-12.0800 -12.1600 -12.2400 -12.3200 -12.4000 -12.4800 -12.5600 -12.6400 -12.7200 -12.8000 -12.8800 -12.9600

Columns 265 through 276

-13.0400 -13.1200 -13.2000 -13.2800 -13.3600 -13.4400 -13.5200 -13.6000 -13.6800 -13.7600 -13.8400 -13.9200

Columns 277 through 288

-14.0000 -14.0800 -14.1600 -14.2400 -14.3200 -14.4000 -14.4800 -14.5600 -14.6400 -14.7200 -14.8000 -14.8800

Columns 289 through 300

-14.9600 -15.0400 -15.1200 -15.2000 -15.2800 -15.3600 -15.4400 -15.5200 -15.6000 -15.6800 -15.7600 -15.8400

Columns 301 through 312

-10.5867 -5.3067 0 0 0 0 0 0 0 0 0 0

Columns 313 through 324

0 0 0 0 0 0 0 0 0 0 0 0

Columns 325 through 336

0 0 0 0 0 0 0 0 0 0 0 0

Columns 337 through 348

0 0 0 0 0 0 0 0 0 0 0 0

Columns 349 through 360

0 0 0 0 0 0 0 0 0 0 0 0

Columns 361 through 372

0 0 0 0 0 0 0 0 0 0 0 0

Columns 373 through 384

0 0 0 0 0 0 0 0 0 0 0 0

Columns 385 through 396

0 0 0 0 0 0 0 0 0 0 0 0

Columns 397 through 408

0 0 0 0 0 0 0 0 0 0 0 0

Columns 409 through 420

0 0 0 0 0 0 0 0 0 0 0 0

Columns 421 through 432

0 0 0 0 0 0 0 0 0 0 0 0

Columns 433 through 444

0 0 0 0 0 0 0 0 0 0 0 0

Columns 445 through 456

0 0 0 0 0 0 0 0 0 0 0 0

Columns 457 through 468

0 0 0 0 0 0 0 0 0 0 0 0

Columns 469 through 480

0 0 0 0 0 0 0 0 0 0 0 0

Columns 481 through 492

0 0 0 0 0 0 0 0 0 0 0 0

Columns 493 through 504

0 0 0 0 0 0 0 0 0 0 0 0

Columns 505 through 516

0 0 0 0 0 0 0 0 0 0 0 0

Columns 517 through 528

0 0 0 0 0 0 0 0 0 0 0 0

Columns 529 through 540

0 0 0 0 0 0 0 0 0 0 0 0

Columns 541 through 552

0 0 0 0 0 0 0 0 0 0 0 0

Columns 553 through 564

0 0 0 0 0 0 0 0 0 0 0 0

Columns 565 through 576

0 0 0 0 0 0 0 0 0 0 0 0

Columns 577 through 588

0 0 0 0 0 0 0 0 0 0 0 0

Columns 589 through 599

0 0 0 0 0 0 0 0 0 0 0

(ii) & (iii). Use the commands below to obtain the results of part (ii) & (iii). For part (iii), replace x and y with X and Y.

n=0:1:299
h=1/3.*(0<=n<=2)
h=0.*(2<n<=299)
x= -2*n/25.*(0<=n<=25)
x= (2*n/25-4).*(25<n<=75)
x= (-2*n/25)+8.*(75<n<=99)
y=0.*(99<n<=299)
y=conv(x,h)
axis([0 299 0 15])
Y=fft(y)
X=fft(x)
hold on
plot(n,y)
hold on
plot(n,x)

(iv). Obtain the values of h[n] as done in part (i) just replace h by that given below and follow the commands in previous parts.

h=1/10.*(0<=n<=9)
h=0.*(9<n<=299)

Hope this was helpful. Feel free to share your feedbacks.

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