Frequency spectrum of a square wave in MATLAB

Question

I need to plot the frequency spectrum for a square wave using MATLAB. The wave is HIGH (5mV) between 0 and -2 and LOW (omv) between 0 and 2. I have already obtained the fourier seires for this function and i have the first ten components of the series.

(5/2) + ((10/pi)*sin((pi*t)/2)) + ((10/(3*pi))*sin((3*pi*t)/2)) + ((10/(5*pi))*sin((5*pi*t)/2)) + ((10/(7*pi))*sin((7*pi*t)/2))+ ((10/(9*pi))*sin((9*pi*t)/2))+ ((10/(11*pi))*sin((11*pi*t)/2))+ ((10/(13*pi))*sin((13*pi*t)/2))+ ((10/(15*pi))*sin((15*pi*t)/2))+ ((10/(17*pi))*sin((17*pi*t)/2))+ ((10/(19*pi))*sin((19*pi*t)/2))

How do I plot the frequency spectrum for this wave using MATLAB? I have tried using FFTs, but I really don't know how it works to plot the graph.

Please share your square wave method and and also square wave frequency. — User1551892
The period of the square wave is 4ms, but doesn't the spectrum depend on the frequency of the individual components from the fourier's series? — user2802349

Dan Dan · Accepted Answer · 2013-11-20T08:26:54

This is adapted straight from the fft docs but using a square wave as the signal:

Fs = 1000;                    %// Sampling frequency
freq = 50;
T = 1/Fs;                     %// Sample time
L = 1000;                     %// Length of signal
t = (0:L-1)*T;                %// Time vector
A = 10;                       %// Amplitude

y = A*(sin(2*pi*freq*t) > 0); %// Make a square wave


plot(Fs*t,y);
xlabel('time (milliseconds)')

NFFT = 2^nextpow2(L);         %// Next power of 2 from length of y
Y = fft(y,NFFT)/L;
f = Fs/2*linspace(0,1,NFFT/2+1);

%// Plot single-sided amplitude spectrum.
plot(f,2*abs(Y(1:NFFT/2+1))) 
title('Single-Sided Amplitude Spectrum of y(t)')
xlabel('Frequency (Hz)') %// probably would be more meaningful if you convert this to radians per second, check out the xtickmark and xtickmarklabel properties of plot
ylabel('|Y(f)|')

Frequency spectrum of a square wave in MATLAB

1 Answers