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Initial revision
author pkienzle
date Wed, 10 Oct 2001 19:54:49 +0000
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1 ## Copyright (C) 2001 Paul Kienzle
2 ##
3 ## This program is free software; you can redistribute it and/or modify
4 ## it under the terms of the GNU General Public License as published by
5 ## the Free Software Foundation; either version 2 of the License, or
6 ## (at your option) any later version.
7 ##
8 ## This program is distributed in the hope that it will be useful,
9 ## but WITHOUT ANY WARRANTY; without even the implied warranty of
10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
11 ## GNU General Public License for more details.
12 ##
13 ## You should have received a copy of the GNU General Public License
14 ## along with this program; if not, write to the Free Software
15 ## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
16
17 ## y = sgolayfilt (x, p, n)
18 ## Smooth the data in x with a Savitsky-Golay smoothing filter of
19 ## polynomial order p and length n, n odd, n > p. By default, p=3
20 ## and n=p+2 or n=p+3 if p is even.
21 ##
22 ## y = sgolayfilt (x, F)
23 ## Smooth the data in x with smoothing filter F computed by sgolay.
24 ##
25 ## These filters are particularly good at preserving lineshape while
26 ## removing high frequency squiggles. Particularly, compare a 5 sample
27 ## averager, an order 5 butterworth lowpass filter (cutoff 1/3) and
28 ## sgolayfilt(x, 3, 5), the best cubic estimated from 5 points:
29 ##
30 ## [b, a] = butter(5,1/3);
31 ## x=[zeros(1,15), 10*ones(1,10), zeros(1,15)];
32 ## plot(sgolayfilt(x),"r;sgolayfilt;",...
33 ## filtfilt(ones(1,5)/5,1,x),"g;5 sample average;",...
34 ## filtfilt(b,a,x),"c;order 5 butterworth;",...
35 ## x,"+b;original data;");
36 ##
37 ## See also: sgolay
38
39 ## TODO: Doesn't accept "weight vector" as fourth parameter.
40 ## TODO: Patch filter.cc so that it accepts matrix arguments
41
42 function y = sgolayfilt (x, p, n)
43
44 if nargin < 1 || nargin > 3
45 usage("y = sgolayfilt(x,p,n) or y = sgolayfilt(x,F)");
46 endif
47
48 if (nargin < 2)
49 p = 3;
50 endif
51 if (nargin == 3)
52 F = sgolay(p, n);
53 elseif (prod(size(p)) == 1)
54 n = p+3-rem(p,2);
55 F = sgolay(p, n);
56 else
57 F = p;
58 n = size(F,1);
59 if (size(F,1) != size(F,2))
60 error("sgolayfilt(x,F): F is not a Savitzsky-Golay filter set");
61 endif
62 endif
63
64 transpose = (size(x,1) == 1);
65 if (transpose) x = x.'; endif;
66 len = size(x,1);
67 if (len < n)
68 error("sgolayfilt: insufficient data for filter");
69 endif
70
71 ## The first k rows of F are used to filter the first k points
72 ## of the data set based on the first n points of the data set.
73 ## The last k rows of F are used to filter the last k points
74 ## of the data set based on the last n points of the dataset.
75 ## The remaining data is filtered using the central row of F.
76 k = floor(n/2);
77 z = filter(F(k+1,:), 1, x);
78 y = [ F(1:k,:)*x(1:n,:) ; z(n:len,:) ; F(k+2:n,:)*x(len-n+1:len,:) ];
79
80 if (transpose) y = y.'; endif
81
82 endfunction
83
84 %!demo
85 %! [b, a] = butter(5,1/3);
86 %! x=[zeros(1,15), 10*ones(1,10), zeros(1,15)];
87 %! subplot(121); title("boxcar");
88 %! axis([1 40 -2 15]);
89 %! plot(sgolayfilt(x),"r;sgolay(3,5);",...
90 %! filtfilt(ones(1,5)/5,1,x),"g;5 sample average;",...
91 %! filtfilt(b,a,x),"c;order 5 butterworth;",...
92 %! x,"+b;original data;"); title("");
93 %!
94 %! x=x+randn(size(x))/2;
95 %! subplot(122); title("boxcar+noise");
96 %! plot(sgolayfilt(x,3,5),"r;sgolay(3,5);",...
97 %! filtfilt(ones(1,5)/5,1,x),"g;5 sample average;",...
98 %! filtfilt(b,a,x),"c;order 5 butterworth;",...
99 %! x,"+b;original data;"); title("");
100
101 %!demo
102 %! [b, a] = butter(5,1/3);
103 %! t = 0:0.01:1.0; % 1 second sample
104 %! x=cos(2*pi*t*3); % 3 Hz sinusoid
105 %! subplot(121); title("sinusoid");
106 %! axis([0 1 -1.5 2.5]);
107 %! plot(t,sgolayfilt(x,3,5),"r;sgolay(3,5);",...
108 %! t,filtfilt(ones(1,5)/5,1,x),"g;5 sample average;",...
109 %! t,filtfilt(b,a,x),"c;order 5 butterworth;",...
110 %! t,x,"+b;original data;"); title("");
111 %!
112 %! x=x+0.2*randn(size(x)); % signal+noise
113 %! subplot(122); title("sinusoid+noise");
114 %! plot(t,sgolayfilt(x',3,5),"r;sgolay(3,5);",...
115 %! t,filtfilt(ones(1,5)/5,1,x),"g;5 sample average;",...
116 %! t,filtfilt(b,a,x),"c;order 5 butterworth;",...
117 %! t,x,"+b;original data;"); title("");
118 %!
119 %! oneplot();