# An octave/MATLAB script to show the Fourier series of a string of impulse functions

From Class Wiki

This checks this identity.

% This is a script to see if the Fourier series with unity coefficients is % really a series of impulse functions. M=100; % Number of terms T=1e-3; % the period of the sampling function is 1 mS. t=0:T/1000:10*T; f=zeros(size(t)); for k=-M:M v = 1; f = f +v*exp(j*2*pi*k*t/T); end plot(t,f) title(strcat('\Sigma_{k=-\infty}^\infty \delta(t-kT) \approx \Sigma_{k=-M}^M e^{-j2\pi nt/T}' ,'(M = ',num2str(2*M),' Terms, and T =',num2str(T),')')) %title(strcat('Fourier Series of a Sum ofImpulse Functions with ',num2str(2*M),' Terms')) xlabel('Time (S)')