# How can I plot an exponential Fourier series? [closed]

Iam triying to plot summatory of the next function:

(e^(i*n*t*wo)*Sin[n*Pi/2])/(n*pi)


I have no problem plotting a trigonometric fourier serie, so the only problem is plotting the complex i. I have watched several videos where they use an uppercase I instead of an lowercase i, I have already tried that but with no results. The functions that I use are:

s[i_,t_] := 1/2 + Sum[(e^(i*n*t*wo)*Sin[n*Pi/2])/(n*pi),{n,-i,-1}] + Sum[(e^(i*n*t*wo)*Sin[n*Pi/2])/(n*pi),{n,1,i}]

Plot[s,{t,-10,10}]


First I made a declaration of a function where the summatories are declared, the i in the Plot[] function is the number of iterations.

I offer an apologize my english is not the best one and I dont know how to make the ecuation look pretty. Anyway thanks a lot.

• You will want to use Re[] or Im[] to see the individual parts in Plot[], or use ReIm[] in conjunction with ParametricPlot[]. Also, the exponential constant is E (capitalization matters!) and the exponential function is Exp[]. – J. M. is in limbo Mar 11 '16 at 17:41
• First you should look at the Mathematica documentation for Exp, then also search for examples here. See this Q&A or this one, for instance. Your definition is incorrect because s uses two arguments but you in Plot you're calling it with just one. – Jens Mar 11 '16 at 17:46

This might be what you are after:

s[i_, t_] := 1/2 + Sum[(E^(I*n*t*wo)*Sin[n*Pi/2])/(n*Pi), {n, -i, -1}] +
Sum[(E^(I*n*t*wo)*Sin[n*Pi/2])/(n*Pi), {n, 1, i}];
wo = 1;
Plot[s[5, t], {t, -10, 10}] • yeeei!!! Thanks, but could you please explain me why you use the I and the E? – Mac Mar 11 '16 at 17:59
• Because as I said, capitalization matters, @Mac. Those are the symbols used by Mathematica for the constants you know. – J. M. is in limbo Mar 11 '16 at 18:14
• Consider the difference between ?E and ?e. – bill s Mar 11 '16 at 18:24