Find frequency response of a given system given in (Transfer Function/ Differential equation form

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

Objective: To  write a MATLAB program to evaluate the Frequency  response of the system .

EQUIPMENTS:  

Operating System - Windows XP

Constructor - Simulator

Software - CCStudio 3 & MATLAB 7.5

MATLAB PROGRAM:

clc;  

clear all;  

close all;  

% Difference equation of a second order system  

% y[n]-0.25y[n-1]+0.45y[n-2]=1.55x[n]+1.95x[n-1]+ 2.15x[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 frequency  response ');  

[h,t]=freqz(b,a,N);  

subplot(2,1,1);

% figure(1);

plot(t,h);  

subplot(2,1,2);

% figure(2);

stem(t,h);

title('plot of frequency  response');  

ylabel('amplitude');  

xlabel('time index----->N');  

disp(h);  

grid on;  

OUTPUT:  

enter the coefficients of x(n),x(n-1)-----[1.55 1.95 2.15]

enter the coefficients of y(n),y(n-1)----[1 -.25 .45]

enter the number of samples of frequency  response 1500

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

Objective: After finishing this experiment the students are able to  

calculate and plot a frequency response of given Differential  equation is obtained. Hence the theory and practical value are proved.

Viva QUESTIONS:

? Which built in function is used to solve a given difference equation?

? What is frequency response? Give equation for first order system and second order system?

? What is an LTI system?

? What is steady state response?

? Suppose we have a system with transfer function H(z) = 1 / ((z – 1.1)*(z – 0.9)). Is the system stable or unstable?

? What is Auto Regressive Model? How is the order of auto regressive model is decided?