--- a/scripts/ChangeLog
+++ b/scripts/ChangeLog
@@ -1,3 +1,10 @@
+2005-06-02  Paul Kienzle  <pkienzle@users.sf.net>
+
+	* signal/freqz.m: Use correct calculations when given a vector of
+	frequencies.  Improve accuracy of returned frequency vector.
+	Improve speed for medium length filters (at a slight cost for slow
+	filters).  Add test cases.
+
 2005-05-27  "Dmitri A. Sergatskov"  <dasergatskov@gmail.com>
 
 	* plot/loglog.m: Fix set commands.

--- a/scripts/polynomial/polygcd.m
+++ b/scripts/polynomial/polygcd.m
@@ -1,3 +1,68 @@
+## Copyright (C) 2000 Paul Kienzle
+##
+## 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 2 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, write to the Free Software
+## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {[@var{q}]} polygcd (@var{b}, @var{a}, @var{tol})
+##
+## Find greatest common divisor of two polynomials.  This is equivalent
+## to the polynomial found by multiplying together all the common roots.
+## Together with deconv, you can reduce a ratio of two polynomials.
+## Tolerance defaults to 
+## @example 
+## sqrt(eps).
+## @end example
+##  Note that this is an unstable
+## algorithm, so don't try it on large polynomials.
+##
+## Example
+## @example
+##    polygcd(poly(1:8),poly(3:12)) - poly(3:8)
+##    deconv(poly(1:8),polygcd(poly(1:8),poly(3:12))) - poly(1:2)
+## @end example
+## @end deftypefn
+##
+## @seealso{poly, polyinteg, polyderiv, polyreduce, roots, conv, deconv,
+## residue, filter, polyval, and polyvalm}
+
+function x = polygcd(b,a,tol)
+  if (nargin<2 || nargin>3)
+    usage("x=polygcd(b,a [,tol])");
+  endif
+  if (nargin<3), tol=sqrt(eps); endif
+  if (length(a)==1 || length(b)==1)
+    if a==0, x=b;
+    elseif b==0, x=a;
+    else x=1;
+    endif
+    return;
+  endif
+  a = a./a(1);
+  while (1)
+    [d, r] = deconv(b, a);
+    nz = find(abs(r)>tol);
+    if isempty(nz)
+      x = a; 
+      return;
+    else
+      r = r(nz(1):length(r));
+    endif
+    b = a;
+    a = r./r(1);
+  endwhile
+endfunction
 ## Copyright (C) 2000 Paul Kienzle
 ##
 ## This program is free software; you can redistribute it and/or modify

--- a/scripts/signal/freqz.m
+++ b/scripts/signal/freqz.m
@@ -14,8 +14,8 @@
 ##
 ## You should have received a copy of the GNU General Public License
 ## along with Octave; see the file COPYING.  If not, write to the Free
-## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
-## 02110-1301, USA.
+## Software Foundation, 59 Temple Place - Suite 330, Boston, MA
+## 02111-1307, USA.
 
 ## -*- texinfo -*-
 ## @deftypefn {Function File} {[@var{h}, @var{w}] =} freqz (@var{b}, @var{a}, @var{n}, "whole")
@@ -70,7 +70,7 @@
 
 ## Author: jwe ???
 
-function [h_r, w_r] = freqz (b, a, n, region, Fs)
+function [h_r, f_r] = freqz (b, a, n, region, Fs)
 
   if (nargin < 1 || nargin > 5)
     usage ("[h, w] = freqz (b, a, n [, \"whole\"] [, Fs])");
@@ -90,6 +90,9 @@
     endif
   endif
 
+  if (isempty (b))
+    b = 1;
+  endif
   if (isempty (a)) 
     a = 1; 
   endif
@@ -111,56 +114,65 @@
     endif
   endif
 
-  la = length (a);
-  a = reshape (a, 1, la);
-  lb = length (b);
-  b = reshape (b, 1, lb);
-  k = max ([la, lb]);
+  a = a(:).';
+  b = b(:).';
 
-  if (! isscalar (n))
-    if (nargin == 4) ## Fs was specified
-      w = 2*pi*n/Fs;
-    else
-      w = n;
+  if (! isscalar (n)) ## Explicit frequency vector given
+    w = f = n;
+    if (nargin == 4)  ## Sampling rate Fs was specified
+      w = 2*pi*f/Fs;
     endif
-    n = length (n);
-    extent = 0;
+    hb = polyval (fliplr(b), exp(-j*w));
+    ha = polyval (fliplr(a), exp(-j*w));
   elseif (strcmp (region, "whole"))
-    w = 2 * pi * (0:n-1) / n;
-    extent = n;
+    f = Fs * (0:n-1) / n;
+    ## polyval(fliplr(P),exp(-jw)) is O(p n) and fft(x) is O(n log(n)),
+    ## where p is the order of the the polynomial P.  For small p it
+    ## would be faster to use polyval but in practice the overhead for
+    ## polyval is much higher and the little bit of time saved isn't
+    ## worth the extra code.
+    hb = fft (postpad (b, n));
+    ha = fft (postpad (a, n));
   else
-    w = pi * (0:n-1) / n;
-    extent = 2 * n;
+    f = Fs/2 * (0:n-1) / n;
+    hb = fft (postpad (b, 2*n))(1:n);
+    ha = fft (postpad (a, 2*n))(1:n);
   endif
 
-  if (length (b) == 1)
-    if (length (a) == 1)
-      hb = b * ones (1, n);
-    else
-      hb = b;
-    endif
-  elseif (extent >= k) 
-    hb = fft (postpad (b, extent));
-    hb = hb(1:n);
-  else
-    hb = polyval (postpad (b, k), exp (j*w));
-  endif
-  if (length (a) == 1)
-    ha = a;
-  elseif (extent >= k)
-    ha = fft (postpad (a, extent));
-    ha = ha(1:n);
-  else
-    ha = polyval (postpad (a, k), exp (j*w));
-  endif
   h = hb ./ ha;
-  w = Fs * w / (2*pi);
 
   if (nargout != 0), # return values and don't plot
     h_r = h;
-    w_r = w;
+    f_r = f;
   else             # plot and don't return values
-    freqz_plot (w, h);
+    freqz_plot (f, h);
   end
 
 endfunction
+
+%!test # correct values and fft-polyval consistency
+%! # butterworth filter, order 2, cutoff pi/2 radians
+%! b = [0.292893218813452  0.585786437626905  0.292893218813452];
+%! a = [1  0  0.171572875253810];
+%! [h,w] = freqz(b,a,32);
+%! assert(h(1),1,10*eps);
+%! assert(abs(h(17)).^2,0.5,10*eps);
+%! assert(h,freqz(b,a,w),10*eps); # fft should be consistent with polyval
+
+%!test # whole-half consistency
+%! b = [1 1 1]/3; # 3-sample average
+%! [h,w] = freqz(b,1,32,'whole');
+%! assert(h(2:16),conj(h(32:-1:18)),20*eps);
+%! [h2,w2] = freqz(b,1,16,'half');
+%! assert(h(1:16),h2,20*eps);
+%! assert(w(1:16),w2,20*eps);
+
+%!test # Sampling frequency properly interpreted
+%! b = [1 1 1]/3;
+%! [h,f] = freqz(b,1,16,320);
+%! assert(f,[0:15]*10,10*eps);
+%! [h2,f2] = freqz(b,1,[0:15]*10,320);
+%! assert(f2,[0:15]*10,10*eps);
+%! assert(h,h2,20*eps);
+%! [h3,f3] = freqz(b,1,32,'whole',320);
+%! assert(f3,[0:31]*10,10*eps);