This file is indexed.

/usr/share/octave/packages/signal-1.2.2/butter.m is in octave-signal 1.2.2-1build1.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  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
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
## Copyright (C) 1999 Paul Kienzle <pkienzle@users.sf.net>
## Copyright (C) 2003 Doug Stewart <dastew@sympatico.ca>
## Copyright (C) 2011 Alexander Klein <alexander.klein@math.uni-giessen.de>
##
## 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/>.

## Generate a butterworth filter.
## Default is a discrete space (Z) filter.
## 
## [b,a] = butter(n, Wc)
##    low pass filter with cutoff pi*Wc radians
##
## [b,a] = butter(n, Wc, 'high')
##    high pass filter with cutoff pi*Wc radians
##
## [b,a] = butter(n, [Wl, Wh])
##    band pass filter with edges pi*Wl and pi*Wh radians
##
## [b,a] = butter(n, [Wl, Wh], 'stop')
##    band reject filter with edges pi*Wl and pi*Wh radians
##
## [z,p,g] = butter(...)
##    return filter as zero-pole-gain rather than coefficients of the
##    numerator and denominator polynomials.
## 
## [...] = butter(...,'s')
##     return a Laplace space filter, W can be larger than 1.
## 
## [a,b,c,d] = butter(...)
##  return  state-space matrices 
##
## References: 
##
## Proakis & Manolakis (1992). Digital Signal Processing. New York:
## Macmillan Publishing Company.

function [a, b, c, d] = butter (n, W, varargin)
  
  if (nargin>4 || nargin<2) || (nargout>4 || nargout<2)
    print_usage;
  end

  ## interpret the input parameters
  if (!(length(n)==1 && n == round(n) && n > 0))
    error ("butter: filter order n must be a positive integer");
  end

  stop = 0;
  digital = 1;
  for i=1:length(varargin)
    switch varargin{i}
    case 's', digital = 0;
    case 'z', digital = 1;
    case { 'high', 'stop' }, stop = 1;
    case { 'low',  'pass' }, stop = 0;
    otherwise,  error ("butter: expected [high|stop] or [s|z]");
    endswitch
  endfor


  [r, c]=size(W);
  if (!(length(W)<=2 && (r==1 || c==1)))
    error ("butter: frequency must be given as w0 or [w0, w1]");
  elseif (!(length(W)==1 || length(W) == 2))
    error ("butter: only one filter band allowed");
  elseif (length(W)==2 && !(W(1) < W(2)))
    error ("butter: first band edge must be smaller than second");
  endif

  if ( digital && !all(W >= 0 & W <= 1))
    error ("butter: critical frequencies must be in (0 1)");
  elseif ( !digital && !all(W >= 0 ))
    error ("butter: critical frequencies must be in (0 inf)");
  endif

  ## Prewarp to the band edges to s plane
  if digital
    T = 2;       # sampling frequency of 2 Hz
    W = 2/T*tan(pi*W/T);
  endif

  ## Generate splane poles for the prototype butterworth filter
  ## source: Kuc
  C = 1; # default cutoff frequency
  pole = C*exp(1i*pi*(2*[1:n] + n - 1)/(2*n));
  if mod(n,2) == 1, pole((n+1)/2) = -1; end  # pure real value at exp(i*pi)
  zero = [];
  gain = C^n;

  ## splane frequency transform
  [zero, pole, gain] = sftrans(zero, pole, gain, W, stop);

  ## Use bilinear transform to convert poles to the z plane
  if digital
     [zero, pole, gain] = bilinear(zero, pole, gain, T);
  endif

  ## convert to the correct output form
  if nargout==2, 
    a = real(gain*poly(zero));
    b = real(poly(pole));
  elseif nargout==3,
    a = zero;
    b = pole;
    c = gain;
  else
    ## output ss results 
    [a, b, c, d] = zp2ss (zero, pole, gain);
  endif

endfunction

%!shared sf, sf2, off_db
%! off_db = 0.5;
%! ##Sampling frequency must be that high to make the low pass filters pass.
%! sf = 6000; sf2 = sf/2;
%! data=[sinetone(5,sf,10,1),sinetone(10,sf,10,1),sinetone(50,sf,10,1),sinetone(200,sf,10,1),sinetone(400,sf,10,1)];

%!test
%! ##Test low pass order 1 with 3dB @ 50Hz
%! data=[sinetone(5,sf,10,1),sinetone(10,sf,10,1),sinetone(50,sf,10,1),sinetone(200,sf,10,1),sinetone(400,sf,10,1)];
%! [b, a] = butter ( 1, 50 / sf2 );
%! filtered = filter ( b, a, data );
%! damp_db = 20 * log10 ( max ( filtered ( end - sf : end, : ) ) );
%! assert ( [ damp_db( 4 ) - damp_db( 5 ), damp_db( 1 : 3 ) ], [ 6 0 0 -3 ], off_db )

%!test
%! ##Test low pass order 4 with 3dB @ 50Hz
%! data=[sinetone(5,sf,10,1),sinetone(10,sf,10,1),sinetone(50,sf,10,1),sinetone(200,sf,10,1),sinetone(400,sf,10,1)];
%! [b, a] = butter ( 4, 50 / sf2 );
%! filtered = filter ( b, a, data );
%! damp_db = 20 * log10 ( max ( filtered ( end - sf : end, : ) ) );
%! assert ( [ damp_db( 4 ) - damp_db( 5 ), damp_db( 1 : 3 ) ], [ 24 0 0 -3 ], off_db )

%!test
%! ##Test high pass order 1 with 3dB @ 50Hz
%! data=[sinetone(5,sf,10,1),sinetone(10,sf,10,1),sinetone(50,sf,10,1),sinetone(200,sf,10,1),sinetone(400,sf,10,1)];
%! [b, a] = butter ( 1, 50 / sf2, "high" );
%! filtered = filter ( b, a, data );
%! damp_db = 20 * log10 ( max ( filtered ( end - sf : end, : ) ) );
%! assert ( [ damp_db( 2 ) - damp_db( 1 ), damp_db( 3 : end ) ], [ 6 -3 0 0 ], off_db )

%!test
%! ##Test high pass order 4 with 3dB @ 50Hz
%! data=[sinetone(5,sf,10,1),sinetone(10,sf,10,1),sinetone(50,sf,10,1),sinetone(200,sf,10,1),sinetone(400,sf,10,1)];
%! [b, a] = butter ( 4, 50 / sf2, "high" );
%! filtered = filter ( b, a, data );
%! damp_db = 20 * log10 ( max ( filtered ( end - sf : end, : ) ) );
%! assert ( [ damp_db( 2 ) - damp_db( 1 ), damp_db( 3 : end ) ], [ 24 -3 0 0 ], off_db )

%!demo
%! sf = 800; sf2 = sf/2;
%! data=[[1;zeros(sf-1,1)],sinetone(25,sf,1,1),sinetone(50,sf,1,1),sinetone(100,sf,1,1)];
%! [b,a]=butter ( 1, 50 / sf2 );
%! filtered = filter(b,a,data);
%!
%! clf
%! subplot ( columns ( filtered ), 1, 1) 
%! plot(filtered(:,1),";Impulse response;")
%! subplot ( columns ( filtered ), 1, 2 ) 
%! plot(filtered(:,2),";25Hz response;")
%! subplot ( columns ( filtered ), 1, 3 ) 
%! plot(filtered(:,3),";50Hz response;")
%! subplot ( columns ( filtered ), 1, 4 ) 
%! plot(filtered(:,4),";100Hz response;")