--- /dev/null
+## 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}]=} fracshift(@var{x},@var{d})
+## @deftypefnx {Function File} {@var{y} =} fracshift(@var{x},@var{d},@var{h})
+## Shift the series @var{x} by a (possibly fractional) number of samples @var{d}.
+## The interpolator @var{h} is either specified or either designed with a Kaiser-windowed sinecard.
+## @end deftypefn
+## @seealso{circshift}
+
+## Ref [1] A. V. Oppenheim, R. W. Schafer and J. R. Buck,
+## Discrete-time signal processing, Signal processing series,
+## Prentice-Hall, 1999
+##
+## Ref [2] T.I. Laakso, V. Valimaki, M. Karjalainen and U.K. Laine
+## Splitting the unit delay, IEEE Signal Processing Magazine,
+## vol. 13, no. 1, pp 30--59 Jan 1996
+
+function [y, h] = fracshift( x, d, h )
+
+ if nargchk(2,3,nargin)
+ print_usage;
+ endif;
+
+ ## if the delay is an exact integer, use circshift
+ if d==fix(d)
+ y=circshift(x,d);
+ return
+ endif;
+
+ ## filter design if required
+
+ if (nargin < 4)
+
+ ## properties of the interpolation filter
+
+ log10_rejection = -3.0;
+ stopband_cutoff_f = 1.0 / 2.0;
+ roll_off_width = stopband_cutoff_f / 10;
+
+ ## determine filter length
+ ## use empirical formula from [1] 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*stopband_cutoff_f*sinc(2*stopband_cutoff_f*(t-(d-fix(d))));
+
+ ## determine parameter of Kaiser window
+ ## use empirical formula from [1] 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 (sincard) filter response
+
+ m = 2*L;
+ t = (0 : m)' - (d-fix(d));
+ t = 2 * beta / m * sqrt (t .* (m - t));
+ w = besseli (0, t) / besseli (0, beta);
+ h = w.*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("fracshift.m: the filter h should be a vector");
+ endif
+
+ Lx = length(x);
+ Lh = length(h);
+ L = ( Lh - 1 )/2.0;
+ Ly = Lx;
+
+ ## pre and postpad filter response
+ hpad = prepad(h,Lh);
+ offset = floor(L);
+ hpad = postpad(hpad,Ly + offset);
+
+ ## filtering
+ xfilt = upfirdn(x,hpad,1,1);
+ y = xfilt(offset+1:offset+Ly,:);
+
+ y=circshift(y,fix(d));
+
+ if isrowvector,
+ y=y.';
+ endif
+
+endfunction
+
+%!test
+%! N=1024;
+%! d=1.5;
+%! t=(0:N-1)-N/2;
+%! tt=t-d;
+%! err=zeros(N/2,1);
+%! for n = 0:N/2-1,
+%! phi0=2*pi*rand;
+%! f0=n/N;
+%! sigma=N/4;
+%! x=exp(-t'.^2/(2*sigma)).*sin(2*pi*f0*t' + phi0);
+%! [y,h]=fracshift(x,d);
+%! xx=exp(-tt'.^2/(2*sigma)).*sin(2*pi*f0*tt' + phi0);
+%! err(n+1)=max(abs(y-xx));
+%! endfor;
+%! rolloff=.1;
+%! rejection=10^-3;
+%! idx_inband=1:ceil((1-rolloff)*N/2)-1;
+%! assert(max(err(idx_inband))<rejection);
+
+%!test
+%! N=1024;
+%! d=7/6;
+%! t=(0:N-1)-N/2;
+%! tt=t-d;
+%! err=zeros(N/2,1);
+%! for n = 0:N/2-1,
+%! phi0=2*pi*rand;
+%! f0=n/N;
+%! sigma=N/4;
+%! x=exp(-t'.^2/(2*sigma)).*sin(2*pi*f0*t' + phi0);
+%! [y,h]=fracshift(x,d);
+%! xx=exp(-tt'.^2/(2*sigma)).*sin(2*pi*f0*tt' + phi0);
+%! err(n+1)=max(abs(y-xx));
+%! endfor;
+%! rolloff=.1;
+%! rejection=10^-3;
+%! idx_inband=1:ceil((1-rolloff)*N/2)-1;
+%! assert(max(err(idx_inband))<rejection);
+
+%!test
+%! N=1024;
+%! p=6;
+%! q=7;
+%! d1=64;
+%! d2=d1*p/q;
+%! t=128;
+%! n=zeros(N,1);
+%! n(N/2+(-t:t))=randn(2*t+1,1);
+%! [b a]=butter(10,.25);
+%! n=filter(b,a,n);
+%! n1=fracshift(n,d1);
+%! n1=resample(n1,p,q);
+%! n2=resample(n,p,q);
+%! n2=fracshift(n2,d2);
+%! err=abs(n2-n1);
+%! rejection=10^-3;
+%! assert(max(err)<rejection);
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff