1. ## Matlab: Plotting Fourier-Series

I'm doing some fourier transforms and I'm wondering how to plot this in Matlab to look at the graphs. I don't know how to plot the function, nor the series.

$\displaystyle f(x)=\Big\{_{ 1, \hspace{0.5cm} 0 \leq x < \pi}^{-1, \hspace{0.3cm} -\pi \leq x < 0}$; $\displaystyle f(x+2\pi)=f(x)$, for all x.

which has the fourier series (if calculated correctly):

$\displaystyle b_n=\frac{2}{n\pi}[1-(-1)^n]\to\frac{4}{\pi}\sum_{m=1}^{\infty}\frac{sin((2m-1)x)}{2m-1}$

I'd like to do a comparison of the Fourier-series and the original function by looking at the graphs. Also, how do you find the Fourier-series and their coefficients, from a function like the one I posted? It'd be great to use Matlab for that.

Any help would be appreciated

2. Originally Posted by cith
I'm doing some fourier transforms and I'm wondering how to plot this in Matlab to look at the graphs. I don't know how to plot the function, nor the series.

$\displaystyle f(x)=\Big\{_{ 1, \hspace{0.5cm} 0 \leq x < \pi}^{-1, \hspace{0.3cm} -\pi \leq x < 0}$; $\displaystyle f(x+2\pi)=f(x)$, for all x.

which has the fourier series (if calculated correctly):

$\displaystyle b_n=\frac{2}{n\pi}[1-(-1)^n]\to\frac{4}{\pi}\sum_{m=1}^{\infty}\frac{sin((2m-1)x)}{2m-1}$
x=0: pi/1000 :2*pi;

f=-1+(x>=0)*(2);

plot(x,f);

CB

3. $\displaystyle \sum_{m=1}^{\infty}\frac{sin((2m-1)x)}{2m-1}$
Is there a way to plot this too?

Thanks

4. Originally Posted by cith
$\displaystyle \sum_{m=1}^{\infty}\frac{sin((2m-1)x)}{2m-1}$
Is there a way to plot this too?

Thanks
By that I assume you mean the partial sums, then yes:

Code:
x=0:pi/100:2*pi
n=1:5;

[N,X]=meshgrid(n,x);

S=sin((2*N-1).*X)./(2*N-1);

SS=sum(S');

plot(x,SS);
and if you want this on the same plot as the other use "hold on" before the second plot (and "hold off" after the second).

CB