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## Copyright (C) 2008 Eric Chassande-Mottin, CNRS (France) <ecm@apc.univ-paris7.fr>
##
## 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 3 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, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{y} @var{h}]=} resample(@var{x},@var{p},@var{q})
## @deftypefnx {Function File} {@var{y} =} resample(@var{x},@var{p},@var{q},@var{h})
## Change the sample rate of @var{x} by a factor of @var{p}/@var{q}. This is
## performed using a polyphase algorithm. The impulse response @var{h} of the antialiasing
## filter is either specified or either designed with a Kaiser-windowed sinecard.
##
## Ref [1] J. G. Proakis and D. G. Manolakis,
## Digital Signal Processing: Principles, Algorithms, and Applications,
## 4th ed., Prentice Hall, 2007. Chap. 6
##
## Ref [2] A. V. Oppenheim, R. W. Schafer and J. R. Buck,
## Discrete-time signal processing, Signal processing series,
## Prentice-Hall, 1999
## @end deftypefn
function [y, h] = resample( x, p, q, h )
if nargchk(3,4,nargin)
print_usage;
elseif any([p q]<=0) || any([p q]~=floor([p q])),
error("resample.m: p and q must be positive integers");
endif
## simplify decimation and interpolation factors
great_common_divisor=gcd(p,q);
if (great_common_divisor>1)
p = double (p) / double (great_common_divisor);
q = double (q) / double (great_common_divisor);
else
p = double (p);
q = double (q);
endif
## filter design if required
if (nargin < 4)
## properties of the antialiasing filter
log10_rejection = -3.0;
stopband_cutoff_f = 1 / (2 * max (p, q));
roll_off_width = stopband_cutoff_f / 10.0;
## determine filter length
## use empirical formula from [2] Chap 7, Eq. (7.63) p 476
rejection_dB = -20.0*log10_rejection;
L = ceil((rejection_dB-8.0) / (28.714 * roll_off_width));
## ideal sinc filter
t=(-L:L)';
ideal_filter=2*p*stopband_cutoff_f*sinc(2*stopband_cutoff_f*t);
## determine parameter of Kaiser window
## use empirical formula from [2] Chap 7, Eq. (7.62) p 474
if ((rejection_dB>=21) && (rejection_dB<=50))
beta = 0.5842 * (rejection_dB-21.0)^0.4 + 0.07886 * (rejection_dB-21.0);
elseif (rejection_dB>50)
beta = 0.1102 * (rejection_dB-8.7);
else
beta = 0.0;
endif
## apodize ideal filter response
h=kaiser(2*L+1,beta).*ideal_filter;
endif
## check if input is a row vector
isrowvector=false;
if ((rows(x)==1) && (columns(x)>1))
x=x(:);
isrowvector=true;
endif
## check if filter is a vector
if ~isvector(h)
error("resample.m: the filter h should be a vector");
endif
Lx = rows(x);
Lh = length(h);
L = ( Lh - 1 )/2.0;
Ly = ceil(Lx*p/q);
## pre and postpad filter response
nz_pre = floor(q-mod(L,q));
hpad = prepad(h,Lh+nz_pre);
offset = floor((L+nz_pre)/q);
nz_post = 0;
while ceil( ( (Lx-1)*p + nz_pre + Lh + nz_post )/q ) - offset < Ly
nz_post++;
endwhile
hpad = postpad(hpad,Lh + nz_pre + nz_post);
## filtering
xfilt = upfirdn(x,hpad,p,q);
y = xfilt(offset+1:offset+Ly,:);
if isrowvector,
y=y.';
endif
endfunction
%!test
%! N=512;
%! p=3; q=5;
%! r=p/q;
%! NN=ceil(r*N);
%! t=0:N-1;
%! tt=0:NN-1;
%! err=zeros(N/2,1);
%! for n = 0:N/2-1,
%! phi0=2*pi*rand;
%! f0=n/N;
%! x=sin(2*pi*f0*t' + phi0);
%! [y,h]=resample(x,p,q);
%! xx=sin(2*pi*f0/r*tt' + phi0);
%! t0=ceil((length(h)-1)/2/q);
%! idx=t0+1:NN-t0;
%! err(n+1)=max(abs(y(idx)-xx(idx)));
%! endfor;
%! rolloff=.1;
%! rejection=10^-3;
%! idx_inband=1:ceil((1-rolloff/2)*r*N/2)-1;
%! assert(max(err(idx_inband))<rejection);
%!test
%! N=512;
%! p=3; q=5;
%! r=p/q;
%! NN=ceil(r*N);
%! t=0:N-1;
%! tt=0:NN-1;
%! reject=zeros(N/2,1);
%! for n = 0:N/2-1,
%! phi0=2*pi*rand;
%! f0=n/N;
%! x=sin(2*pi*f0*t' + phi0);
%! [y,h]=resample(x,p,q);
%! xx=sin(2*pi*f0/r*tt' + phi0);
%! t0=ceil((length(h)-1)/2/q);
%! idx=t0+1:NN-t0;
%! reject(n+1)=max(abs(y(idx)));
%! endfor;
%! rolloff=.1;
%! rejection=10^-3;
%! idx_stopband=ceil((1+rolloff/2)*r*N/2)+1:N/2;
%! assert(max(reject(idx_stopband))<=rejection);
%!test
%! N=1024;
%! p=2; q=7;
%! r=p/q;
%! NN=ceil(r*N);
%! t=0:N-1;
%! tt=0:NN-1;
%! err=zeros(N/2,1);
%! for n = 0:N/2-1,
%! phi0=2*pi*rand;
%! f0=n/N;
%! x=sin(2*pi*f0*t' + phi0);
%! [y,h]=resample(x,p,q);
%! xx=sin(2*pi*f0/r*tt' + phi0);
%! t0=ceil((length(h)-1)/2/q);
%! idx=t0+1:NN-t0;
%! err(n+1)=max(abs(y(idx)-xx(idx)));
%! endfor;
%! rolloff=.1;
%! rejection=10^-3;
%! idx_inband=1:ceil((1-rolloff/2)*r*N/2)-1;
%! assert(max(err(idx_inband))<rejection);
%% Test integer-type arguments
%!test
%! N = 512;
%! f = 0.1;
%! x = sin (2*pi*f*[0:N-1]);
%! y1 = resample (x, 3, 2);
%! y2 = resample (x, uint8 (3), 2);
%! assert (y1, y2);