M-file:
%% Filename: FourierSeriesExample7.m % Description: m-file to plot complex (exponential) Fourier Series % representation of a triangle wave. clear; clc; close all; % clear memory and command window, close all figures t = linspace(-2,3,1000); % times over which to plot FS N = [2, 4, 6, 50]; % upper limit (N) and lower limit (-N) for n in summation figure(1); % open figure in which to plot % Build triangle wave using increasing number of terms for in = 1:4, % loop over four different limits (in N) of Fourier Series f = -0.5*ones(1,length(t)); % initialize summation to c0 = a0 = -1/2 subplot(2,2,in); % open one of four subplots % brute force original triangle wave plot([-2, -1, 0, 1, 2, 3],... [ 0, -1, 0,-1, 0, -1],'k-.','LineWidth',2); hold on; for n = 1:1:N(in), % loop over different lengths of FS % compute +n term termpos = (((1 - cos( n*pi))/( n*pi)^2) - sin( n*pi)/( n*pi))*exp( j*n*pi*t); % compute -n term termneg = (((1 - cos(-n*pi))/(-n*pi)^2) - sin(-n*pi)/(-n*pi))*exp(-j*n*pi*t); terms = termpos + termneg; % add complex conjugate terms to get real terms f = f + terms; % add real terms to series plot(t,terms,'b--','LineWidth',1); % plot real terms (harmonics) end plot(t,f,'r-','LineWidth',2); % plot FS hold off; xlabel('time (sec)','FontSize',14); ylabel('FS Approx to f(t)','FontSize',14); title(['Fourier Series Approx w/n = ',num2str(-N(in)),'\ldots', num2str(N(in)),' Terms'],'FontSize',14); end
Figures/Plots Generated: