Question

In MATLAB, generate a square wave of period 1s and length of 8s, sampled at 1024HZ. The maximum value of the wave is 1 and the minimum value is -1. Take the fft of this data. Show both plots. The fft should represent Fourier series representation of the wave in lecture, comment on this aspect. Comment on the difference in FFT when I sample for 8.01 sec instead of 8 sec.

Answer 1

clc;
clear all;
close all;
%%%%%%generation of square wave%%%%%%%%%%%%%
f=1; %frequency of square wave
Fs=1024; %sampling frequency
ts=1/Fs;   
N=32*256; %we are using 256 point fft
t=0:ts:N*ts;
x=square(2*pi*f*t); %generating square wave
figure;
plot(t,x); %plotting square wave
xlabel('time');
ylabel('amplitude');
title('suqare wave');
%%%generating fourier transform
y=fft(x);
y=fftshift(y);
P2=abs(y/N);
P1 = P2(1:N);
P1(2:end-1) = P1(2:end-1);
f = Fs*((-N/2):(N/2-1))/N; %%%generating frequency
figure;
plot(f,P1);
title('N=256 point fft');
xlabel('frequency (Hz)');
ylabel('|X(f)|/N');

clc: clear all: close all 동동동동동몽genera tion of f-1; F3 1024; %sampling square wave 동동동동동동동동동동% frequency of square wave frequency N=32*256; %we are using 256 point fft x-square (2*pi*f*t); figure: plot (t, x); xlabel (time'); ylabel 'amplitude title (sugare wave' %generating square wave plotting square wave %%generating fourier transform y fft (x); P2=abs (y/N) ; P1 P2 ( 1: N) ; P1 (2:end-1P1 (2:end-1) f = Fs* ( (-N/2) : (N/2-1)) /N; figure: plot (f, P1): title ('N-256 point fft'); xlabel ('frequency (Hz) ylabel ('X (f) I/N) %\generating frequenc

suqare wave 0.8 0.6 0.4 0.2 ー0 0.2 0.4 0.6 0.8 4 8 time

N-256 point fft 0.7 r 0.6 0.5 0.4 0.3 0.2 0.1 0 -600 -400 -200 200 400 600 frequency (Hz)