Plotting Fourier series approximation for a square wave using MATLAB.

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Suppose $f(x)$ is a square wave of period $2\pi$ such that

$f(x)=1$ for $0<x<\pi$

$f(x)=-1$ for $\pi<x<2\pi$

The Fourier series for $f(x)$ is

$f(x)=\frac{4}{\pi}\left[\frac{\sin x}{1}+\frac{\sin 3x}{3}+\frac{\sin 5x}{5}+\ldots\right]$

I tried plotting this using MATLAB (using the first 10 terms):

Code:

x=linspace(-4*pi,4*pi,100); y=0; k=1; for n=1:10 y=y+4*sin(k*x)/pi*k; k=k+2; end plot(x,y) axis([-4*pi 4*pi -2 2]) xlabel('x') ylabel('Square wave approximation using first 10 terms')

I have attached my output but it doesn't look anything like a square wave. What am I doing wrong?

Re: Plotting Fourier series approximation for a square wave using MATLAB.

Hi alexmahone! :)

Perhaps you should write

y=y+4*sin(k*x)/(pi*k);

instead of:

y=y+4*sin(k*x)/pi*k;

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Re: Plotting Fourier series approximation for a square wave using MATLAB.

Quote:

Originally Posted by ILikeSerena

Hi alexmahone! :)

Perhaps you should write

y=y+4*sin(k*x)/(pi*k);

instead of:

y=y+4*sin(k*x)/pi*k;

You are just amazing!

I now get: