% 
% Written by:
% -- 
% John L. Weatherwax                2008-11-24
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

% for a sampling of T=1.0: 
% 
T = 1.0; 
t = -6:+T:+6; 
x = exp( - abs(t) ); 

N = 500; 

dftx1 = T*fft( x, N ); 
domega = (2*pi)/(T*N); 
omega  = 0 : domega : (2*pi - domega); 

% find the value of omega_k that is closest to pi/2
[mv,mi] = min(abs(omega - pi/2));
fprintf( 'mi = %10d (zero based indexing)\n', mi-1 ); 
% what does our FFT give us at this index:
dftx1(mi)

clear; 

% for a sampling of T=0.2:
% 
T = 0.2;
t = -6:+T:+6; 
x = exp( - abs(t) ); 

N = 500; 

dftx2 = T*fft( x, N ); 
domega = (2*pi)/(T*N); 
omega  = 0 : domega : (2*pi/T - domega); 

% find the value of omega_k that is closest to pi/2
[mv,mi] = min(abs(omega - pi/2));
fprintf( 'mi = %10d (zero based indexing)\n', mi-1 ); 
% what does our FFT give us at this index:
dftx2(mi)

% the exact result: 
%
2/(1+(pi/2)^2)