This file is indexed.

/usr/share/octave/packages/signal-1.3.2/grpdelay.m is in octave-signal 1.3.2-5.

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
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
## Copyright (C) 2000 Paul Kienzle  <pkienzle@users.sf.net>
## Copyright (C) 2004 Julius O. Smith III <jos@ccrma.stanford.edu>
##
## 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{g}, @var{w}] =} grpdelay (@var{b})
## @deftypefnx {Function File} {[@var{g}, @var{w}] =} grpdelay (@var{b}, @var{a})
## @deftypefnx {Function File} {[@var{g}, @var{w}] =} grpdelay (@dots{}, @var{n})
## @deftypefnx {Function File} {[@var{g}, @var{w}] =} grpdelay (@dots{}, @var{n}, "whole")
## @deftypefnx {Function File} {[@var{g}, @var{f}] =} grpdelay (@dots{}, @var{n}, @var{Fs})
## @deftypefnx {Function File} {[@var{g}, @var{f}] =} grpdelay (@dots{}, @var{n}, "whole", @var{Fs})
## @deftypefnx {Function File} {[@var{g}, @var{w}] =} grpdelay (@dots{}, @var{w})
## @deftypefnx {Function File} {[@var{g}, @var{f}] =} grpdelay (@dots{}, @var{f}, @var{Fs})
## @deftypefnx {Function File} {} grpdelay (@dots{})
## Compute the group delay of a filter.
##
## [g, w] = grpdelay(b)
##   returns the group delay g of the FIR filter with coefficients b.
##   The response is evaluated at 512 angular frequencies between 0 and
##   pi. w is a vector containing the 512 frequencies.
##   The group delay is in units of samples.  It can be converted
##   to seconds by multiplying by the sampling period (or dividing by
##   the sampling rate fs).
##
## [g, w] = grpdelay(b,a)
##   returns the group delay of the rational IIR filter whose numerator
##   has coefficients b and denominator coefficients a.
##
## [g, w] = grpdelay(b,a,n)
##   returns the group delay evaluated at n angular frequencies.  For fastest
##   computation n should factor into a small number of small primes.
##
## [g, w] = grpdelay(b,a,n,'whole')
##   evaluates the group delay at n frequencies between 0 and 2*pi.
##
## [g, f] = grpdelay(b,a,n,Fs)
##   evaluates the group delay at n frequencies between 0 and Fs/2.
##
## [g, f] = grpdelay(b,a,n,'whole',Fs)
##   evaluates the group delay at n frequencies between 0 and Fs.
##
## [g, w] = grpdelay(b,a,w)
##   evaluates the group delay at frequencies w (radians per sample).
##
## [g, f] = grpdelay(b,a,f,Fs)
##   evaluates the group delay at frequencies f (in Hz).
##
## grpdelay(...)
##   plots the group delay vs. frequency.
##
## If the denominator of the computation becomes too small, the group delay
## is set to zero.  (The group delay approaches infinity when
## there are poles or zeros very close to the unit circle in the z plane.)
##
## Theory: group delay, g(w) = -d/dw [arg@{H(e^jw)@}],  is the rate of change of
## phase with respect to frequency.  It can be computed as:
##
## @example
##               d/dw H(e^-jw)
##        g(w) = -------------
##                 H(e^-jw)
## @end example
##
## where
##
## @example
##         H(z) = B(z)/A(z) = sum(b_k z^k)/sum(a_k z^k).
## @end example
##
## By the quotient rule,
##
## @example
##                    A(z) d/dw B(z) - B(z) d/dw A(z)
##        d/dw H(z) = -------------------------------
##                               A(z) A(z)
## @end example
##
## Substituting into the expression above yields:
##
## @example
##                A dB - B dA
##        g(w) =  ----------- = dB/B - dA/A
##                    A B
## @end example
##
## Note that,
##
## @example
##        d/dw B(e^-jw) = sum(k b_k e^-jwk)
##        d/dw A(e^-jw) = sum(k a_k e^-jwk)
## @end example
##
## which is just the FFT of the coefficients multiplied by a ramp.
##
## As a further optimization when nfft>>length(a), the IIR filter (b,a)
## is converted to the FIR filter conv(b,fliplr(conj(a))).
## For further details, see
## http://ccrma.stanford.edu/~jos/filters/Numerical_Computation_Group_Delay.html
## @end deftypefn

function [gd, w] = grpdelay (b, a = 1, nfft = 512, whole, Fs)

  if (nargin < 1 || nargin > 5)
    print_usage ();
  endif

  HzFlag = false;
  if (length (nfft) > 1)
    if (nargin > 4)
      print_usage ();
    elseif (nargin > 3)
      ## grpdelay (B, A, F, Fs)
      Fs     = whole;
      HzFlag = true;
    else
      ## grpdelay (B, A, W)
      Fs = 1;
    endif
    w     = 2*pi*nfft/Fs;
    nfft  = length (w) * 2;
    whole = "";
  else
    if (nargin < 5)
      Fs = 1; # return w in radians per sample
      if (nargin < 4)
        whole = "";
      elseif (! ischar (whole))
        Fs      = whole;
        HzFlag  = true;
        whole   = "";
      endif
      if (nargin < 3)
        nfft = 512;
      endif
      if (nargin < 2)
        a = 1;
      endif
    else
      HzFlag = true;
    endif

    if (isempty (nfft))
      nfft = 512;
    endif
    if (! strcmp (whole, "whole"))
      nfft = 2*nfft;
    endif
    w = Fs*[0:nfft-1]/nfft;
  endif

  if (! HzFlag)
    w = w * 2 * pi;
  endif

  ## Make sure both are row vector
  a = a(:).';
  b = b(:).';

  oa = length (a) -1;     # order of a(z)
  if (oa < 0)             # a can be []
    a  = 1;
    oa = 0;
  endif
  ob = length (b) -1;     # order of b(z)
  if (ob < 0)             # b can be [] as well
    b  = 1;
    ob = 0;
  endif
  oc = oa + ob;           # order of c(z)

  c   = conv (b, fliplr (conj (a)));  # c(z) = b(z)*conj(a)(1/z)*z^(-oa)
  cr  = c.*(0:oc);                    # cr(z) = derivative of c wrt 1/z
  num = fft (cr, nfft);
  den = fft (c, nfft);
  minmag    = 10*eps;
  polebins  = find (abs (den) < minmag);
  for b = polebins
    warning ("grpdelay: setting group delay to 0 at singularity");
    num(b) = 0;
    den(b) = 1;
    ## try to preserve angle:
    ## db = den(b);
    ## den(b) = minmag*abs(num(b))*exp(j*atan2(imag(db),real(db)));
    ## warning(sprintf('grpdelay: den(b) changed from %f to %f',db,den(b)));
  endfor
  gd = real (num ./ den) - oa;

  if (! strcmp (whole, "whole"))
    ns = nfft/2; # Matlab convention ... should be nfft/2 + 1
    gd = gd(1:ns);
    w  = w(1:ns);
  else
    ns = nfft; # used in plot below
  endif

  ## compatibility
  gd = gd(:);
  w  = w(:);

  if (nargout == 0)
    unwind_protect
      grid ("on"); # grid() should return its previous state
      if (HzFlag)
        funits = "Hz";
      else
        funits = "radian/sample";
      endif
      xlabel (["Frequency (" funits ")"]);
      ylabel ("Group delay (samples)");
      plot (w(1:ns), gd(1:ns), ";;");
    unwind_protect_cleanup
      grid ("on");
    end_unwind_protect
  endif

endfunction

## ------------------------ DEMOS -----------------------

%!demo % 1
%! %--------------------------------------------------------------
%! % From Oppenheim and Schafer, a single zero of radius r=0.9 at
%! % angle pi should have a group delay of about -9 at 1 and 1/2
%! % at zero and 2*pi.
%! %--------------------------------------------------------------
%! grpdelay([1 0.9],[],512,'whole',1);
%! hold on;
%! xlabel('Normalized Frequency (cycles/sample)');
%! stem([0, 0.5, 1],[0.5, -9, 0.5],'*b;target;');
%! hold off;
%! title ('Zero at z = -0.9');
%!
%!demo % 2
%! %--------------------------------------------------------------
%! % confirm the group delays approximately meet the targets
%! % don't worry that it is not exact, as I have not entered
%! % the exact targets.
%! %--------------------------------------------------------------
%! b = poly([1/0.9*exp(1i*pi*0.2), 0.9*exp(1i*pi*0.6)]);
%! a = poly([0.9*exp(-1i*pi*0.6), 1/0.9*exp(-1i*pi*0.2)]);
%! grpdelay(b,a,512,'whole',1);
%! hold on;
%! xlabel('Normalized Frequency (cycles/sample)');
%! stem([0.1, 0.3, 0.7, 0.9], [9, -9, 9, -9],'*b;target;');
%! hold off;
%! title ('Two Zeros and Two Poles');

%!demo % 3
%! %--------------------------------------------------------------
%! % fir lowpass order 40 with cutoff at w=0.3 and details of
%! % the transition band [.3, .5]
%! %--------------------------------------------------------------
%! subplot(211);
%! Fs = 8000;     % sampling rate
%! Fc = 0.3*Fs/2; % lowpass cut-off frequency
%! nb = 40;
%! b = fir1(nb,2*Fc/Fs); % matlab freq normalization: 1=Fs/2
%! [H,f] = freqz(b,1,[],1);
%! [gd,f] = grpdelay(b,1,[],1);
%! plot(f,20*log10(abs(H)));
%! title(sprintf('b = fir1(%d,2*%d/%d);',nb,Fc,Fs));
%! xlabel('Normalized Frequency (cycles/sample)');
%! ylabel('Amplitude Response (dB)');
%! grid('on');
%! subplot(212);
%! del = nb/2; % should equal this
%! plot(f,gd);
%! title(sprintf('Group Delay in Pass-Band (Expect %d samples)',del));
%! ylabel('Group Delay (samples)');
%! axis([0, 0.2, del-1, del+1]);

%!demo % 4
%! %--------------------------------------------------------------
%! % IIR bandstop filter has delays at [1000, 3000]
%! %--------------------------------------------------------------
%! Fs = 8000;
%! [b, a] = cheby1(3, 3, 2*[1000, 3000]/Fs, 'stop');
%! [H,f] = freqz(b,a,[],Fs);
%! [gd,f] = grpdelay(b,a,[],Fs);
%! subplot(211);
%! plot(f,abs(H));
%! title('[b,a] = cheby1(3, 3, 2*[1000, 3000]/Fs, "stop");');
%! xlabel('Frequency (Hz)');
%! ylabel('Amplitude Response');
%! grid('on');
%! subplot(212);
%! plot(f,gd);
%! title('[gd,f] = grpdelay(b,a,[],Fs);');
%! ylabel('Group Delay (samples)');


% ------------------------ TESTS -----------------------

%!test % 00
%! [gd1,w] = grpdelay([0,1]);
%! [gd2,w] = grpdelay([0,1],1);
%! assert(gd1,gd2,10*eps);

%!test % 0A
%! [gd,w] = grpdelay([0,1],1,4);
%! assert(gd,[1;1;1;1]);
%! assert(w,pi/4*[0:3]',10*eps);

%!test % 0B
%! [gd,w] = grpdelay([0,1],1,4,'whole');
%! assert(gd,[1;1;1;1]);
%! assert(w,pi/2*[0:3]',10*eps);

%!test % 0C
%! [gd,f] = grpdelay([0,1],1,4,0.5);
%! assert(gd,[1;1;1;1]);
%! assert(f,1/16*[0:3]',10*eps);

%!test % 0D
%! [gd,w] = grpdelay([0,1],1,4,'whole',1);
%! assert(gd,[1;1;1;1]);
%! assert(w,1/4*[0:3]',10*eps);

%!test % 0E
%! [gd,f] = grpdelay([1 -0.9j],[],4,'whole',1);
%! gd0 = 0.447513812154696; gdm1 =0.473684210526316;
%! assert(gd,[gd0;-9;gd0;gdm1],20*eps);
%! assert(f,1/4*[0:3]',10*eps);

%!test % 1A:
%! gd= grpdelay(1,[1,.9],2*pi*[0,0.125,0.25,0.375]);
%! assert(gd, [-0.47368;-0.46918;-0.44751;-0.32316],1e-5);

%!test % 1B:
%! gd= grpdelay(1,[1,.9],[0,0.125,0.25,0.375],1);
%! assert(gd, [-0.47368;-0.46918;-0.44751;-0.32316],1e-5);

%!test % 2:
%! gd = grpdelay([1,2],[1,0.5,.9],4);
%! assert(gd,[-0.29167;-0.24218;0.53077;0.40658],1e-5);

%!test % 3
%! b1=[1,2];a1f=[0.25,0.5,1];a1=fliplr(a1f);
%! % gd1=grpdelay(b1,a1,4);
%! gd=grpdelay(conv(b1,a1f),1,4)-2;
%! assert(gd, [0.095238;0.239175;0.953846;1.759360],1e-5);

%!test % 4
%! Fs = 8000;
%! [b, a] = cheby1(3, 3, 2*[1000, 3000]/Fs, 'stop');
%! [h, w] = grpdelay(b, a, 256, 'half', Fs);
%! [h2, w2] = grpdelay(b, a, 512, 'whole', Fs);
%! assert (size(h), size(w));
%! assert (length(h), 256);
%! assert (size(h2), size(w2));
%! assert (length(h2), 512);
%! assert (h, h2(1:256));
%! assert (w, w2(1:256));

%!test % 5
%! a = [1 0 0.9];
%! b = [0.9 0 1];
%! [dh, wf] = grpdelay(b, a, 512, 'whole');
%! [da, wa] = grpdelay(1, a, 512, 'whole');
%! [db, wb] = grpdelay(b, 1, 512, 'whole');
%! assert(dh,db+da,1e-5);

## test for bug #39133 (do not fail for row or column vector)
%!test
%! DR= [1.00000 -0.00000 -3.37219 0.00000 ...
%!      5.45710 -0.00000 -5.24394 0.00000 ...
%!      3.12049 -0.00000 -1.08770 0.00000 0.17404];
%! N = [-0.0139469 -0.0222376 0.0178631 0.0451737 ...
%!       0.0013962 -0.0259712 0.0016338 0.0165189 ...
%!       0.0115098 0.0095051 0.0043874];
%! assert (nthargout (1:2, @grpdelay, N,  DR,  1024),
%!         nthargout (1:2, @grpdelay, N', DR', 1024));