Question

Discrete-Time Periodic Signal 4 1. Convolution and Discrete-Time Fourier Series (DTFS) (a) Generate a periodic signal r2n] with the fundamental period N n]sin(2Tn/10)sin(27n/20) sin(27n/30), for 0nN-1 Find the fundamental frequency 2T/N with the fundamental period N (b) Generate a periodic signal h2[nl with the fundamental period N h2[n](1/2)", for 0n< N - 1 (c) Using the conv function in Matlab, compute the convolution y2n x2n]h2[n] (d) Using the fft function in Matlab, find the DTFS X2k] of x2n] and H2k] of h2n] (e) Multiply the DTFSS of n and h2[n], that is Y2k] NX2[k]H2[k]. (f) Using the ifft function in Matlab, find the inverse DTFS (IDTFS) of Y2(k) to find y2[n] (g) Compare the signal y2n] found from the convolution in time domain and y2[n] found from the multiplication in frequency domain and IDTFS

It's about signals and systems. I need some help to make MATLAB codes of this problems. Thank you :)

Answer 1

MATLAB CODE:

clc
clear all
close all

N = 60;
Omega = 2*pi/N;

fprintf('Omega = %d',Omega)

n = 0:N-1;
x2 = sin(2*pi.*n/10)+sin(2*pi.*n/20)+sin(2*pi.*n/30);
h2 = (1/2).^n;
y2 = conv(x2,h2);

subplot(3,1,1)
stem(n,x2);
xlabel('n')
title('x_2[n]')

subplot(3,1,2)
stem(n,h2);
xlabel('n')
title('h_2[n]')

subplot(3,1,3)
stem(y2);
xlabel('n')
title('Convolution of x_2[n] and h_2[n] is y_2[n]')

X2 = fft(x2);
fprintf('DTFS of x2[n]:\n')
disp(X2)

H2 = fft(h2);
fprintf('DTFS of h2[n]:\n')
disp(H2)

Y2 = N.*X2.*H2;
fprintf('DTFS of y2[n]:\n')
disp(Y2)

y = ifft(Y2);
fprintf('Inverde fourier trsnsform of Y2:\n')
disp(y)

OUTPUT:

-1 -2 60 50 4С 30 20 10 n h2n 1 0.8 0.6 0.4 0.2 60 50 30 20 Convolution of x,[n] and h2[n] is y2[n] 120 100 80 60 40 20