## 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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