% alias.m - aliasing due to undersampling
% HJSIII - 98.11.05

clear

% actual sampling rate 200 Hz
fs = 200;

% sampling rate for display
fsfast=2000;

% sampling times
dt = 1 / fs;
dtfast = 1 / fsfast;

% fill sample buffers
tend = 0.1;
ns = tend / dt;
nsfast = tend / dtfast;

  ts = (0:ns) * dt;
  v30 = sin( 2 * pi * 30 * ts );
  v60 = sin( 2 * pi * 60 * ts );
  v90 = sin( 2 * pi * 90 * ts );
  v120 = sin( 2 * pi * 120 * ts );
  v150 = sin( 2 * pi * 150 * ts );
  v180 = sin( 2 * pi * 180 * ts );
  v210 = sin( 2 * pi * 210 * ts );
  v240 = sin( 2 * pi * 240 * ts );
  
  tsfast = (0:nsfast) * dtfast;
  v30fast = sin( 2 * pi * 30 * tsfast );
  v60fast = sin( 2 * pi * 60 * tsfast );
  v90fast = sin( 2 * pi * 90 * tsfast );
  v120fast = sin( 2 * pi * 120 * tsfast );
  v150fast = sin( 2 * pi * 150 * tsfast );
  v180fast = sin( 2 * pi * 180 * tsfast );
  v210fast = sin( 2 * pi * 210 * tsfast );
  v240fast = sin( 2 * pi * 240 * tsfast );
  
% plot time domain
figure( 1 )  
subplot(4,2,1)
  plot( ts, v30, ts, v30, 'o', tsfast, v30fast, ':' )  
  title('30/60/90/120 Hz sampled at 200 Hz')
%  xlabel('Time (sec)')
%  ylabel('Amplitude')
subplot(4,2,3)
  plot( ts, v60, ts, v60, 'o', tsfast, v60fast, ':' )  
%  title('60 HZ sine sampled at 200 Hz')
%  xlabel('Time (sec)')
%  ylabel('Amplitude')
subplot(4,2,5)
  plot( ts, v90, ts, v90, 'o', tsfast, v90fast, ':' )  
%  title('90 HZ sine sampled at 200 Hz')
%  xlabel('Time (sec)')
%  ylabel('Amplitude')
subplot(4,2,7)
  plot( ts, v120, ts, v120, 'o', tsfast, v120fast, ':' )  
%  title('120 HZ sine sampled at 200 Hz')
  xlabel('Time (sec)')
%  ylabel('Amplitude')
subplot(4,2,2)
  plot( ts, v150, ts, v150, 'o', tsfast, v150fast, ':' )  
  title('150/180/210/240 Hz sampled at 200 Hz')
%  xlabel('Time (sec)')
%  ylabel('Amplitude')
subplot(4,2,4)
  plot( ts, v180, ts, v180, 'o', tsfast, v180fast, ':' )  
%  title('180 HZ sine sampled at 200 Hz')
%  xlabel('Time (sec)')
%  ylabel('Amplitude')
subplot(4,2,6)
  plot( ts, v210, ts, v210, 'o', tsfast, v210fast, ':' )  
%  title('210 HZ sine sampled at 200 Hz')
%  xlabel('Time (sec)')
%  ylabel('Amplitude')
subplot(4,2,8)
  plot( ts, v240, ts, v240, 'o', tsfast, v240fast, ':' )  
%  title('240 HZ sine sampled at 200 Hz')
  xlabel('Time (sec)')
%  ylabel('Amplitude')

% plot frequency domain
figure( 2 )
  f0 = fs / 2;
  f = 0 : 400;
  fsym = [ 30 60 90 120 150 180 210 240 270 300 330 360 390 ];
  a = f0 - abs( mod(f,fs) - f0 );
  asym = f0 - abs( mod(fsym,fs) - f0 );
  plot( f, a, fsym, asym, 'o' )
  title( 'Aliasing = fs/2 - abs( mod(f,fs) - fs/2 )' )
  xlabel( 'Actual frequency [Hz]' )
  ylabel( 'Apparent frequency [Hz] for fs=200 Hz' )