# Impulse response of a given system

Aim:-  To write a MATLAB program to evaluate the impulse response of the system .

Objective:-  To write a MATLAB program to evaluate the impulse response of the system  using MATlab.

EQUIPMENTS:

Operating System - Windows XP

Constructor - Simulator

Software - CCStudio 3 & MATLAB 7.5

The Difference equation is given as

y(n) = x(n)+0.5x(n-1)+0.85x(n-2)+y(n-1)+y(n-2)

Program:-

clc;

clear all;

close all;

% Difference equation of a second order system

% y(n) = x(n)+0.5x(n-1)+0.85x(n-2)+y(n-1)+y(n-2)

b=input('enter the coefficients of x(n),x(n-1)-----');

a=input('enter the coefficients of y(n),y(n-1)----');

N=input('enter the number of samples of imp response ');

[h,t]=impz(b,a,N);

subplot(2,1,1);

% figure(1);

plot(t,h);

title('plot of impulse response');

ylabel('amplitude');

xlabel('time index----->N');

subplot(2,1,2);

% figure(2);

stem(t,h);

title('plot of impulse response');

ylabel('amplitude');

xlabel('time index----->N');

disp(h);

grid on;

Output

enter the coefficients of x(n),x(n-1)-----[1 0.5 0.85] enter the coefficients of y(n),y(n-1)-----[1 -1 -1] enter the number of samples of imp respons 4

1.0000

1.5000

3.3500

4.8500

Graph

Calculations:-

y(n) = x(n)+0.5x(n-1)+0.85x(n-2)+y(n-1)+y(n-2)

y(n) - y(n-1) - y(n-2) = x(n) + 0.5x(n-1) + 0.85x(n-2) Taking Z transform on both sides,

Y(Z) - Z-1 Y(Z)- Z-2 Y(Z) = X(Z) + 0.5 Z-1 X(Z) + 0.85 Z-2 X(Z) Y(Z)[1 - Z-1 - Z-2] = X(Z)[1 + 0.5 Z-1 + 0.85 Z-2 ]

But,  H(Z) = Y(Z)/X(Z)

= [1 + 0.5 Z-1 + 0.85 Z-2 ]/ [1 - Z-1 - Z-2] By dividing we get

H(Z) =  1 + 1.5 Z-1 + 3.35 Z-2 + 4.85 Z-3

h(n) = [1 1.5 3.35 4.85]

RESULT:  The impulse  response of given Differential  equation is obtained. Hence the theory and practical value are proved

Discussion /Viva questions:-

1)  Differentiate between linear and circular convolution.

2)  Determine the unit step response of the linear time invariant system with impulse

response  h(n)=a n u(n) a<1&-a<1

3)  Determine the range of values of the parameter a for which linear time invariant system with impulse response    h(n)=a n u(n)     is stable.

4)  Consider the special case of a finite duration sequence given as X(n)={2 4 0 3}, resolve the sequence x(n) into a sum of weighted sequences.

5) . Describe impulse response of a function?

6) . Where to use command filter or impz, and what is the difference between these two?

• Updated
Feb 03, 2020
• Views
2,619
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