%
%  ffttest.m -- djm, 30 june 2005
%

clear
N = 32;  dx = 2*pi/N;

%  matlab fft works well on 0 < x < 2*pi

x = (0:dx:2*pi-dx);
k0 = (-N/2:N/2-1);
k1 = fftshift(k0);

%  single fourier mode (note normalizations of fft & ifft !!!)
j = 4;
y0 = exp(i*j*x);
yf = fft(y0)/N;
y1 = ifft(yf)*N;

figure(1);  clf
subplot(2,1,1);  hold on
plot(x,real(y1),'y',x,imag(y1),'y')
plot(x,real(y0),'r--',x,real(y0),'k.',x,imag(y0),'b--',x,imag(y0),'k.')
axis([0 2*pi -1 1])
title('\bf real (r) & imag (b) parts of y(x)')
subplot(2,1,2)
plot(k1,real(yf),'r',k1,real(yf),'k.',k1,imag(yf),'b',k1,imag(yf),'k.')
axis([-N/2 N/2 -1 1])
title('\bf real & imag parts of fft of y(x)')