Question

matlab and comment please

In this exercise we learn how to solve constant-coefficient difference equation using Mat lab. Also, we investigate the response of systems to different kinds of inputs. (1) Consider the difference equation given as follows: y(n)= -0.9y(n 1)-0.81y(n 2)1.62x(n) +1.8r(n -1)+2x(n-2), n0 Find and plot r(n) and y(n) and hence find the energy of y(n) for the following cases: ( (d) a(n) r(n)r(n 25), where r(n) is the unit-ramp sequence.

only need (D)

Answer 1

(D) MATLAB CODE:

clc
clear all
close all

syms n z
% By the application of Z-Transform to given difference equation
% we got the transfer function H(z) as given below

H(z) = (1.62+1.8*z^(-1)+2*z^(-2))/(1+0.9*z^(-1)+0.81*z^(-2));

u(n) = heaviside(n)+(1/2)*kroneckerDelta(n,0);% Unit step sequence
r(n) = n*u(n); % Unit Ramp
x(n) = r(n) - r(n-25); % Given input x[n]

X(z) = ztrans(x(n),n,z);    % Z-Transform of x[n]
Y(z) = H(z)*X(z);
y(n) = iztrans(Y(z),z,n);

n = 0:24;

subplot(2,1,1)   % Plot of x[n]
stem(n,x(n))
xlabel('n')
title('x[n]')

subplot(2,1,2)   % Plot of y[n]
stem(n,y(n))
xlabel('n')
title('y[n]')

OUTPUT:

x[n] 25 20 15 10 5 25 20 15 10 n y[n] 50 45 40 35 30 25 20 15 10 25 20 15 10