% AMBEx14_2b_aliasing  Test aliasing Ambardar p 450; 
%  Use fft and label graph with gtext
ts=1/10         % S=10 so Fmax is 5 Hz
t=[0:ts:100];   % The time period is 100 seconds so the resolution 
%                   in f is 1/100 hertz.
%  Note: The point 100 would represent 1Hz and the point 400 is 4Hz.
%
N=length(t)     % N=101
xt=8*cos(2*pi*t)+6*cos(8*pi*t)+4*cos(22*pi*t);  % f=1,4,11 Hz
%
% Check spectrum
% Approximate the Fourier series with 1/N * |FFT|; Amb p547
Xf=(1/N)*abs(fft(xt));
Nplot=ceil(N/2+1)       % Make sure number of points is an integer
plot(2*Xf(1:Nplot))     % Plot 2x |FFT| 
title('Aliased result: f actual= 1,4,11 Hz; S=10; fa=11-10=1Hz')
ylabel('Amplitude')
xlabel('Frequency in Hz is 1/100 * index')
gtext('xt=8*cos(2*pi*t)+6*cos(8*pi*t)+4*cos(22*pi*t); f=1,4,11 Hz')
gtext('Note that the 11Hz signal is added to the 1Hz result (8+4=12)')