8/8/2019 LAB NO.3 DISCRETE TIME SYSTEMS IN TIME DOMAIN IMPULSE RESPONSE OF LTI SYSTEM

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LAB NO.3

DISCRETE TIME SYSTEMS IN TIME DOMAIN

IMPULSE RESPONSE OF LTI SYSTEM

Source Code:

clf;

N=40;

Num=[2.2403 2.4908 2.2403];

Den=[1 -0.4 0.75];

Y=impz (Num,Den,N);

stem(Y);

xlabel('time index n');

ylabel('amplitude');

title('Impulse Response');

grid;

Output:

8/8/2019 LAB NO.3 DISCRETE TIME SYSTEMS IN TIME DOMAIN IMPULSE RESPONSE OF LTI SYSTEM

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CONVOLUTION PROCESS

Source Code:

%generate the input sequence

n=0:40;

a=2;b=-3;

x1=cos(2*pi*0.1*n);

x2=cos(2*pi*0.4*n);

x=(a*x1)+(b*x2);

num=[2.2403 2.4908 2.2403];

den=[1 -0.4 0.75];

ic=[0 0]; %set zero initial conditions

y1=filter(num,den,x1,ic); %compute the output y1(n)

y2=filter(num,den,x2,ic); %compute the output y2(n);

y=filter(num,den,x,ic); %compute the output y(n);

yt=(a*y1)+(b*y2);

d=y-yt; %compute the difference output d[n]

%plot the outputs and difference signal

subplot(3,1,1);stem(n,y);

ylabel('amplitude');

title('output due to weighed input');

subplot(3,1,2);stem(n,yt);

ylabel('Amplitude');title('weighed output');

subplot(3,1,3);stem(n,d);

xlabel('time index n');title('difference signal');

Output:

8/8/2019 LAB NO.3 DISCRETE TIME SYSTEMS IN TIME DOMAIN IMPULSE RESPONSE OF LTI SYSTEM

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CHECKING OF LINEAR OR NON-LINEAR SYSTEM

Source Code:

%generate the input sequence

n=0:40;D=10;a=3.0;b=-2;

x=a*cos(2*pi*0.1*n)+b*cos(2*pi*0.4*n);

xd=[zeros(1,D) x];

num=[2.2403 2.4908 2.2403];den=[1 -0.4 0.75];

ic=[0 0];

% compute the output y(n)

y=filter(num,den,x,ic);

%compute the output yd(n)

yd=filter(num,den,xd,ic);

%compute the difference output d[n]

d=y-yd(1+D:41+D);

%plot the outputs

subplot(3,1,1);stem(n,y);

ylabel('Amplitude');title('output y[n]');grid;

subplot(3,1,2);stem(n,yd(1:41));

ylabel('Amplitude');title('output due to delayed input');grid;

subplot(3,1,3);stem(n,d);

xlabel('time index n');ylabel('amplitude');

title('Difference signal');grid;

0 5 10 15 20 25 30 35 40-40

-20

0

20

amplitude

output due to weighed input

0 5 10 15 20 25 30 35 40-50

0

50

Amplitude

weighed output

0 5 10 15 20 25 30 35 40

-5

0

5x 10

-15

time index n

difference signal

8/8/2019 LAB NO.3 DISCRETE TIME SYSTEMS IN TIME DOMAIN IMPULSE RESPONSE OF LTI SYSTEM

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Output:

GENERATION OF DISCRETE TIME SIGNALS AND TO FIND THEIR DIFFERENCE

clf;n=0:40;a=2;b=-3;

x1=cos (2*pi*0.1*n);x2=cos (2*pi*0.4*n);x=(a*x1) + (b*x2);

num=[2.2403 2.4908 2.2403];den=[1 -0.4 0.75];ic=[0 0];

y1=filter (num,den,x1,ic);y2=filter (num,den,x2,ic);

y=filter (num,den,x,ic);

y3=(a*y1)+(b*y2);d=y-y3;

subplot(3,1,1);stem(n,y);

xlabel ('time domain representation');ylabel ('Amplitude');

title ('output due to weighed input');grid;

subplot (3,1,2);stem (n,y3);

xlabel ('Time Index n');ylabel ('amplitude');title ('weighed output');grid;

subplot (3,1,3);stem(n,d);

xlabel ( 'time index n');

ylabel ('amplitude');title ('Difference signal');grid;

0 5 10 15 20 25 30 35 40-40

-20

0

20

Am

plitude

output y[n]

0 5 10 15 20 25 30 35 40-50

0

50

Amplitude

output due to delayed input

0 5 10 15 20 25 30 35 40-1

0

1

time index n

am

plitude

Difference signal

8/8/2019 LAB NO.3 DISCRETE TIME SYSTEMS IN TIME DOMAIN IMPULSE RESPONSE OF LTI SYSTEM

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Output:

0 5 10 15 20 25 30 35 40-50

0

50

time domain representation

Amplitude

output due to weighed input

0 5 10 15 20 25 30 35 40-50

0

50

Time Index n

amplitude

weighed output

0 5 10 15 20 25 30 35 40-5

0

5x 10

-15

time index n

amplitude

Difference signal