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Sourcecode: octave-matcompat version File versions

resample.m

## 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

## usage: y=resample(x,p,q,d)
##
## Change the sample rate of x by a factor of p/q.  Note that p and q do
## not need to be integers since this routine does not use a polyphase
## rate change algorithm, but instead uses bandlimited interpolation,
## wherein the continous time signal is estimated by summing the sinc
## functions of the nearest neighbouring points up to distance d.
##
## This is discussed in:
##     J. O. Smith and P. Gossett (1984). A flexible sampling-rate
##     conversion method. In ICASSP-84, Volume II, pp. 19.4.1-19.4.2. 
##     New York: IEEE Press.
## See the authors page at: http://www-ccrma.stanford.edu/~jos/resample/
##
## Note that the resampling is not yet very fast or very good, but it is
## very flexible.
##
## Example
##    ## Speech example
##    [x, fs] = auload(file_in_loadpath("sample.wav"));
##    sound(resample(x,16000,fs), 16000);  # resample at 16 kHz
##
##    ## Example from interp1
##    xf=0:0.05:10.95; yf = sin(2*pi*xf/5);
##    xp=0:10;         yp = sin(2*pi*xp/5);
##    r = resample(yp,xp(2),xf(2));
##    plot(xf,yf,';original;',xf,r,';resample;',xp,yp,'*;;');
##
## Note that resample computes all samples up to but not including time
## n+1. If you are increasing the sample rate, this means that it will
## generate samples beyond the end of the time range of the original
## signal. That is why xf must goes all the way to 10.95 in the example.
 
## TODO: Fix so that audible clicking goes away.
## TODO: Change to a faster algorithm.
## TODO: Test on a chirp signal.
   
function y=resample(x,p,q,order,beta)
  if (nargin < 2 || nargin > 5)
    usage("y=resample(x,p,q,order)");
  endif

  if (nargin < 3), q=1; endif
  if (nargin < 4), order = 5; endif

  ##  ## chain to decimate/interpolate if appropriate
  ##  if p==1 && q==fix(q)
  ##    y=decimate(x,q); order?
  ##    return;
  ##  elseif q==1 && p==fix(p)
  ##    y=interp(x,q); order?
  ##    return;
  ##  endif

  transpose = rows(x)==1;
  if transpose, x = x.'; endif

  ## if rate reduction, apply antialiasing filter first
  r=p/q;
  if (r < 1)                 
    b = fir1(2*order+1, r);
    x = fftfilt(b, x);
  endif

  ## Determine the new sampling times, and their distance to the old
  ## ones.  Note that the new series should be the maximum that can
  ## be contained in the old series without going over the time
  ## allotted to the old series.  In short, you have to go a little
  ## beyond the last sample of the old series if your new sampling
  ## rate is higher.
  t=[1:1/r:length(x)+1-1/r]';   # the sampling points of the new series
  idx = fix(t);                 # the nearest old point
  t = t-idx;                    # distance to the nearest old point

  ## generate the new series by summing the sinc functions of the
  ## nearest neighbour points implicit in the continuous time
  ## expansion of the old series.  This new series is truncated
  ## to +/- order nearest neighbours.  For convenience, the original
  ## series is zero-padded before and after, implicitly setting the
  ## neighbours at the start of the signal to zero.
  x = ;
  y = zeros(length(idx),columns(x));        # the new series
  for i=-order:order
    w = sinc(t-i).*(0.5+0.5*cos(pi*(t-i)/(order+0.5))); # hanning window
    y=y + x(idx+i+order,:).*w(:,ones(size(x,2),1));
  endfor

  if transpose, y=y.'; endif
endfunction

%!demo
%! xf=0:0.05:10.95; yf = sin(2*pi*xf/5);
%! xp=0:10;      yp = sin(2*pi*xp/5);
%! r = resample(yp,xp(2),xf(2));
%! oneplot();
%! title("confirm that the resampled function matches the original");
%! plot(xf,yf,';original;',...
%!    xf,r(1:length(xf)),';resample;',...
%!    xp,yp,'*;;');
%! title("");
%! [x, fs] = auload(file_in_loadpath("sample.wav"));
%! sound(resample(x,16000,fs), 16000);

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