## Copyright (C) 2000 Paul Kienzle
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; if not, write to the Free Software
## Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA

## usage: y = decimate(x, q [, n] [, ftype])
##
## Downsample the signal x by a factor of q, using an order n filter
## of ftype 'fir' or 'iir'.  By default, an order 8 Chebyshev type I
## filter is used or a 30 point FIR filter if ftype is 'fir'.  Note
## that q must be an integer for this rate change method.
##
## Example
##    ## Generate a signal that starts away from zero, is slowly varying
##    ## at the start and quickly varying at the end, decimate and plot.
##    ## Since it starts away from zero, you will see the boundary
##    ## effects of the antialiasing filter clearly.  Next you will see
##    ## how it follows the curve nicely in the slowly varying early
##    ## part of the signal, but averages the curve in the quickly
##    ## varying late part of the signal.
##    t=0:0.01:2; x=chirp(t,2,.5,10,'quadratic')+sin(2*pi*t*0.4); 
##    y = decimate(x,4);   # factor of 4 decimation
##    stem(t(1:121)*1000,x(1:121),"-g;Original;"); hold on; # plot original
##    stem(t(1:4:121)*1000,y(1:31),"-r;Decimated;"); hold off; # decimated

function y = decimate(x, q, n, ftype)

  if nargin < 1 || nargin > 4, 
    usage("y=decimate(x, q [, n] [, ftype])"); 
  endif
  if q != fix(q), error("decimate only works with integer q."); endif

  if nargin<3
    ftype='iir';
    n=[];
  elseif nargin==3
    if ischar(n)
      ftype=n; 
      n=[];
    else 
      ftype='iir';
    endif
  endif

  fir = strcmp(ftype, 'fir');
  if isempty(n)
    if fir, n=30; else n=8; endif
  endif

  if fir
    b = fir1(n, 1/q);
    y=fftfilt(b, x);
  else
    [b, a] = cheby1(n, 0.05, 0.8/q);
    y=filtfilt(b,a,x);
  endif
  y = y(1:q:length(x));
endfunction

%!demo
%! t=0:0.01:2; x=chirp(t,2,.5,10,'quadratic')+sin(2*pi*t*0.4); 
%! y = decimate(x,4);   # factor of 4 decimation
%! stem(t(1:121)*1000,x(1:121),"-g;Original;"); hold on; # plot original
%! stem(t(1:4:121)*1000,y(1:31),"-r;Decimated;"); hold off; # decimated
%! %------------------------------------------------------------------
%! % The signal to decimate starts away from zero, is slowly varying
%! % at the start and quickly varying at the end, decimate and plot.
%! % Since it starts away from zero, you will see the boundary
%! % effects of the antialiasing filter clearly.  You will also see
%! % how it follows the curve nicely in the slowly varying early
%! % part of the signal, but averages the curve in the quickly
%! % varying late part of the signal.
