find the stability of the following systems and responce using matlab

1.       Write the program to find the stability of the following systems:

a.       H(z) = (1 – 0.8 z^-1)/(1 – 1.5z^-1  - 0.9z^-2 )

Plot all the responses.

Programme :

clc;

clear all;

close all;

b=input('Enter the coefficeint of input(numerator) : ');

a=input('Enter the coefficeint of output(denominator) :');

n = [-100:1000];

h = impz(b,a,n);

subplot(1,1,1);

stem(n,h);

title('Impulse Response Q1');

xlabel('n');

ylabel('h(n)');

OUTPUT:

Ø  Here, IR (impulse response)  of system goes to infinity,

Ø  So We can say that SYSTEM IS  NOT STABLE.

2.       Write the program to find the stability of the following systems:

b.      y(n) = x(n) – 4 x(n - 1) + 3 x(n - 2) + 1.7 x(n - 3) + 1.7 y(n - 1) –y(n - 2)

Plot all the responses.

Programme :

clc;

clear all;

close all;

b=input('Enter the coefficeint of input(numerator) : ');

a=input('Enter the coefficeint of output(denominator) :');

n = [-100:1000];

h = impz(b,a,n);

subplot(1,1,1);

stem(n,h);

title('Impulse Response Q1');

xlabel('n');

ylabel('h(n)');

OUTPUT:

Ø  Here, IR (impulse response)  of system DOES NOT goes to infinity,

Ø  So we can say that SYSTEM IS STABLE.

1.       Write the program to find the stability of the following systems:

c.       y(n) = x(n – 1) + y(n - 1) +y(n - 2)

Plot all the responses.

Programme :

clc;

clear all;

close all;

b=input('Enter the coefficeint of input(numerator) : ');

a=input('Enter the coefficeint of output(denominator) :');

n = [-100:1000];

h = impz(b,a,n);

subplot(1,1,1);

stem(n,h);

title('Impulse Response Q1');

xlabel('n');

ylabel('h(n)');

OUTPUT:

Ø  Here, IR (impulse response)  of system goes to infinity,

Ø  So We can say that SYSTEM IS  NOT STABLE.

1.       Write the program to find the stability of the following systems:

d.      y(n) = 2 x(n) – x(n – 2) +0.7 y(n – 1) – 1.1 y(n – 2)

Plot all the responses.

Programme :

clc;

clear all;

close all;

b=input('Enter the coefficeint of input(numerator) : ');

a=input('Enter the coefficeint of output(denominator) :');

n = [-100:1000];

h = impz(b,a,n);

subplot(1,1,1);

stem(n,h);

title('Impulse Response Que-1.d');

xlabel('n');

ylabel('h(n)');

OUTPUT:

Ø  Here, IR (impulse response)  of system goes to infinity,

Ø  So We can say that SYSTEM IS  NOT STABLE.

1.       Write the program to find the stability of the following systems:

e.      y(n) = x( n) + 0.6 y(n – 1) – 0.08y(n – 2)

Plot all the responses.

Programme :

clc;

clear all;

close all;

b=input('Enter the coefficeint of input(numerator) : ');

a=input('Enter the coefficeint of output(denominator) :');

n = [-100:1000];

h = impz(b,a,n);

subplot(1,1,1);

stem(n,h);

title('Impulse Response Que-1.e');

xlabel('n');

ylabel('h(n)');

OUTPUT:

Ø  Here, IR (impulse response)  of system DOES NOT  goes to infinity,

Ø  So We can say that SYSTEM IS  STABLE.

2.       Consider the following two discrete time systems characterized by the difference equation for 200 samples:

a.       y(n) = 0.5 x(n) + 0.27x(n - 1) + 0.77 x(n - 2)

b.      y(n) = 0.45x(n) + 0.5 x(n - 1) + 0.45x(n - 2) + 0.53 y(n - 1) – 0.46 y(n - 2)

Compute the output of the above two systems for an input

X(n) = cos(20πn/256) + cos(200πn/256), with 0≤ n ≤ 299.

 Plot all the responses. Also plot the time shifted responses by selecting appropriate time delay.

Program:

% Generate the input sequence

clc;

close all;

clear all;

n = 0:299;

x1 = cos(2*pi*10*(n)/256);

x2 = cos(2*pi*100*(n)/256);

x = x1+x2;

x3 = cos(2*pi*10*(n-5)/256);  %input sequence Delayed by 5 samples/time

x4 = cos(2*pi*100*(n-5)/256); %input sequence Delayed by 5 samples/time

x5 = x3+x4;

% Compute the output sequences

%den1 = [0 1 0 0];

num1 = [0.5 0.27 0.77];

y1 = filter(num1,1,x); % Output of System No. 1

y5 = filter(num1,1,x5); % Delayed Output of System No. 1

den2 = [1 -0.53 0.46];

num2 = [0.45 0.5 0.45];

y2 = filter(num2,den2,x); % Output of System No. 2

y6 = filter(num2,den2,x5); % Delayed Output of System No. 1

% Plot the output sequences

subplot(2,2,1);

plot(n,y1);axis([0 300 -2 2]);

ylabel('Amplitude');

title('Output of System No. 1');grid;

subplot(2,2,2);

plot(n,y2);axis([0 300 -2 2]);

xlabel('Time index n');

ylabel('Amplitude');

title('Output of System No. 2');grid;

subplot(2,2,3);

plot(n,y5);axis([0 300 -2 2]);

ylabel('Amplitude');

title('delayed Output of System No. 1');grid;

subplot(2,2,4);

plot(n,y6);axis([0 300 -2 2]);

xlabel('Time index n');

ylabel('Amplitude');

title('delayed Output of System No. 2');grid;

OUTPUT: