function vtb3_3(N)
%VTB3_3  Fourier Series approximation to a triangle wave.
% VTB3_3(N) displays the N term Fourier approximation to a 
% triangular input.  The approximation is plotted versus time 
% normalized by the period of the wave.  The Fourier series is 
% the solid line and the actual wave is the dotted line.


%Creates triangular wave
tau1=0:.01:.5;
Ftr1=(4*tau1-1);

tau2=.51:.01:1;
Ftr2=3-4*tau2;

%Creates Fourier approximation

tau=[tau1 tau2];
F=zeros(1,length(tau));

for i=1:N
			k=2*i-1;
   Ftmp=(1/k^2)*cos(k*2*pi*tau);
   F=F+Ftmp;
end

F=-(8/pi^2)*F;

plot(tau1,Ftr1,'--',tau2,Ftr2,'--',tau,F,'-')
title([int2str(N),' term Fourier series approximation to a triangular input'])
ylabel('F(t)');
xlabel('time / period')