Question

Consider the system given by the input/output relationship 1.14. 32 1 2] n31+ 1 63 4 16 [Is- ]x+ [- u]x (a) When xn] is equal n5 (b) Write a MATLAB M-file to compute the output response y[n] resulting from the in- put x[n] = 5 sin(mn/10 +m/4) , for 0 s ns 69. Express your answer by giving the M-file and the MATLAB plot. to a constant c for all n 0, show that v[n] is equal to c for all

Answer 1

32 32. 31 CA C x C 32 CX 32 wchave, or 3 C 32 63 C x = ( C X 0) - Like wisc ) mathematical incluction thuorcm , Foom for Used Matlab for 0n69

MATLAB code is given below in bold letters.

clc;
close all;
clear all;

% define n
n = 0 : 69;

% define the filter h[n] as follows
h = 32/63*[1 1/2 1/4 1/8 1/16 1/32];

% define the input x[n]
x = 5*sin(n*pi/10+pi/4);

% compute y[n] using filter command
y = filter(h,1,x);

% plot the output
figure;
stem(n,y,'fill');grid on;
xlabel('n');title('y[n]');

yin 5 4 3 1 0 -1 -2 -3 -4 -5 0 70 60 50 10 40 30 20 o LO