Question

Problem 2 (Spectrum of a rectangular signal): In this problem, the amplitude spectrum of the signal 1 or Ot 2 ms x(t)- 0 otherwise is to be analysed (b) Numerical calculation of the spectrum: (i) Use Matlab to generate and plot a vector containing the sample values of the rectangular signal defined in (2) sampled at f 8kHz. Choose the number N of sample values so that it is a power of 2 and that the signal duration is at least 4 ms. Do not forget to label the axes of your plot. Matlab's fft function to (ii) Use plot the amplitude spectrum in the frequency range [0, fs/2]. Make sure that the frequency axis is labelled correctly.

Answer 1

MATLAB:

clc;close all;clear all;
T=4*(10^(-3))
T1=2*(10^(-3))
t=0:T/200:T
x=(t<=T1)
subplot(221)
plot(t,x,'m')
title('Rectangular function')
xlabel('t')
ylabel('x(t)')

fs=8000
Ts=1/fs
n=0:1:T/Ts
x=(n<=T1/Ts)
subplot(222)
stem(n,x,'b')
title('Sampled Rectangular function')
xlabel('n')
ylabel('x(n)')

X=fft(x)
N=length(n)
f=0:fs/(2*(N-1)):fs/2
subplot(223)
stem(f,abs(X),'r')
hold on
plot(f,abs(X),'b--')
xlabel('f')
ylabel('|X(f)|')
title('Amplitude spectrum')
hold off

Rectangular function Sampled Rectangular function 0.8 0.6 0.4 0.2 0.8 0.6 0.4 0.2 0 0.001 0.002 0.003 0.004 0 5 10 15 20 25 30 35 Amplitude spectrum 20 15 1000 2000 3000 4000