% This code is based on Example 23.1 and demonstrates the Gibbs 
% phenomenon occuring whenever the set of continuous functions is used
% to approximate a discontinuous one.

close all     % closes all windows opened during the previous runs
clear all     % clears the memory from the results of previous runs
clc           % clears screen

% The following part of the code produces a large scale picture.

m=100;        % 2*m is the number of terms in the truncated Fourier
x=linspace(-10,10,200);
k=(-m:m)';
kk=repmat(k,1,length(x));
f=sinh(pi)/pi*sum((-1).^kk./(1+i*kk).*exp(i*k*x));
subplot(2,1,1)
plot(x,real(f))
xlabel('x')

pause

% Now zoom into the region near the discontinuity:

dx=10/m;
x1=linspace(pi-dx,pi+dx);
n=length(x1);
ileft=find(x1<=pi);
irght=find(x1>pi);
g(1:n/2)=exp(-x1(ileft));
g(n/2+1:n)=exp(2*pi-x1(irght));
k=(-m:m)';
kk=repmat(k,1,n);
f1=sinh(pi)/pi*sum((-1).^kk./(1+i*kk).*exp(i*k*x1));

subplot(2,1,2)                            % Observe the overshoot. It 
     plot(x1,real(f1),x1,g),axis('tight') % does not disappear no matter
xlabel('x')                               % how big m is. This is the
                                          % Gibbs phenomenon.

ovsht=max(real(f1)-max(g)) % Use different values of m and see that 
                           % ovsht, the magnitude of the overshoot, does
                           % not decrease as m increases, while the 
                           % width of the region where the overshoot is 
                           % felt does decrease.