/usr/share/octave/packages/signal-1.3.2/sgolayfilt.m is in octave-signal 1.3.2-1+b1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 | ## Copyright (C) 2001 Paul Kienzle <pkienzle@users.sf.net>
## Copyright (C) 2004 Pascal Dupuis <Pascal.Dupuis@esat.kuleuven.ac.be>
##
## 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} =} sgolayfilt (@var{x})
## @deftypefnx {Function File} {@var{y} =} sgolayfilt (@var{x}, @var{p})
## @deftypefnx {Function File} {@var{y} =} sgolayfilt (@var{x}, @var{p}, @var{n})
## @deftypefnx {Function File} {@var{y} =} sgolayfilt (@var{x}, @var{p}, @var{n}, @var{m})
## @deftypefnx {Function File} {@var{y} =} sgolayfilt (@var{x}, @var{p}, @var{n}, @var{m}, @var{ts})
## @deftypefnx {Function File} {@var{y} =} sgolayfilt (@var{x}, @var{p}, @var{n}, @var{m}, @var{ts})
## @deftypefnx {Function File} {@var{y} =} sgolayfilt (@var{x}, @var{f})
## Smooth the data in x with a Savitsky-Golay smoothing filter of
## polynomial order p and length n, n odd, n > p. By default, p=3
## and n=p+2 or n=p+3 if p is even.
##
## If @var{f} is given as a matrix, it is expected to be a filter as
## computed by @code{sgolay}.
##
## These filters are particularly good at preserving lineshape while
## removing high frequency squiggles. Particularly, compare a 5 sample
## averager, an order 5 butterworth lowpass filter (cutoff 1/3) and
## sgolayfilt(x, 3, 5), the best cubic estimated from 5 points:
##
## @example
## @group
## [b, a] = butter (5, 1/3);
## x = [zeros(1,15), 10*ones(1,10), zeros(1,15)];
## plot (sgolayfilt (x), "r;sgolayfilt;", ...
## filtfilt (ones (1,5)/5, 1, x), "g;5 sample average;", ...
## filtfilt (b, a, x), "c;order 5 butterworth;", ...
## x, "+b;original data;");
## @end group
## @end example
##
## @seealso{sgolay}
## @end deftypefn
## FIXME: Patch filter.cc so that it accepts matrix arguments
function y = sgolayfilt (x, p = 3, n, m = 0, ts = 1)
if nargin < 1 || nargin > 5
print_usage;
endif
if (nargin >= 3)
F = sgolay(p, n, m, ts);
elseif (prod(size(p)) == 1)
n = p+3-rem(p,2);
F = sgolay(p, n);
else
F = p;
n = size(F,1);
if (size(F,1) != size(F,2))
error("sgolayfilt(x,F): F is not a Savitzsky-Golay filter set");
endif
endif
transpose = (size(x,1) == 1);
if (transpose) x = x.'; endif;
len = size(x,1);
if (len < n)
error("sgolayfilt: insufficient data for filter");
endif
## The first k rows of F are used to filter the first k points
## of the data set based on the first n points of the data set.
## The last k rows of F are used to filter the last k points
## of the data set based on the last n points of the dataset.
## The remaining data is filtered using the central row of F.
## As the filter coefficients are used in the reverse order of what
## seems the logical notation, reverse F(k+1, :) so that antisymmetric
## sequences are used with the right sign.
k = floor(n/2);
z = filter(F(k+1,n:-1:1), 1, x);
y = [ F(1:k,:)*x(1:n,:) ; z(n:len,:) ; F(k+2:n,:)*x(len-n+1:len,:) ];
if (transpose) y = y.'; endif
endfunction
%!demo
%! [b, a] = butter(5,1/3);
%! x=[zeros(1,15), 10*ones(1,10), zeros(1,15)];
%! subplot(121);
%! plot(sgolayfilt(x),"r;sgolay(3,5);",...
%! filtfilt(ones(1,5)/5,1,x),"g;5 sample average;",...
%! filtfilt(b,a,x),"c;order 5 butterworth;",...
%! x,"+b;original data;");
%! axis([1 40 -2 15]);
%! title("boxcar");
%!
%! x=x+randn(size(x))/2;
%! subplot(122);
%! plot(sgolayfilt(x,3,5),"r;sgolay(3,5);",...
%! filtfilt(ones(1,5)/5,1,x),"g;5 sample average;",...
%! filtfilt(b,a,x),"c;order 5 butterworth;",...
%! x,"+b;original data;");
%! axis([1 40 -2 15]);
%! title("boxcar+noise");
%!demo
%! [b, a] = butter(5,1/3);
%! t = 0:0.01:1.0; % 1 second sample
%! x=cos(2*pi*t*3); % 3 Hz sinusoid
%! subplot(121);
%! plot(t,sgolayfilt(x,3,5),"r;sgolay(3,5);",...
%! t,filtfilt(ones(1,5)/5,1,x),"g;5 sample average;",...
%! t,filtfilt(b,a,x),"c;order 5 butterworth;",...
%! t,x,"+b;original data;");
%! axis([0 1 -1.5 2.5]);
%! title("sinusoid");
%!
%! x=x+0.2*randn(size(x)); % signal+noise
%! subplot(122);
%! plot(t,sgolayfilt(x',3,5),"r;sgolay(3,5);",...
%! t,filtfilt(ones(1,5)/5,1,x),"g;5 sample average;",...
%! t,filtfilt(b,a,x),"c;order 5 butterworth;",...
%! t,x,"+b;original data;");
%! axis([0 1 -1.5 2.5]);
%! title("sinusoid+noise");
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