Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / communications-1.1.1 / @galois / dftmtx.m

diff --git a/octave_packages/communications-1.1.1/@galois/dftmtx.m b/octave_packages/communications-1.1.1/@galois/dftmtx.m
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+++ b/octave_packages/communications-1.1.1/@galois/dftmtx.m
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+## Copyright (C) 2002 David Bateman
+##
+## 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{d} = } dftmtx (@var{a})
+##
+## Form a matrix, that can be used to perform Fourier transforms in
+## a Galois Field.
+##
+## Given that @var{a} is an element of the Galois Field GF(2^m), and
+## that the minimum value for @var{k} for which @code{@var{a} ^ @var{k}} 
+## is equal to one is @code{2^m - 1}, then this function produces a 
+## @var{k}-by-@var{k} matrix representing the discrete Fourier transform    
+## over a Galois Field with respect to @var{a}. The Fourier transform of
+## a column vector is then given by @code{dftmtx(@var{a}) * @var{x}}.
+##
+## The inverse Fourier transform is given by @code{dftmtx(1/@var{a})}
+## @end deftypefn
+
+function d = dftmtx(a)
+
+  if (nargin != 1)
+    error ("usage: d = dftmtx (a)");
+  endif
+    
+  if (!isgalois(a))
+    error("dftmtx: argument must be a galois variable");
+  endif
+
+  m = a.m;
+  prim = a.prim_poly;
+  n = 2^a.m - 1;
+  if (n > 255)
+    error ([ "dftmtx: argument must be in Galois Field GF(2^m), where" ...
+           " m is not greater than 8"]); 
+  endif
+
+  if (length(a) ~= 1)
+    error ("dftmtx: argument must be a scalar");
+  endif
+
+  mp = minpol(a);
+  if ((mp(1) ~= 1) || !isprimitive(mp))
+    error("dftmtx: argument must be a primitive nth root of unity");
+  endif
+  
+  step = log(a);
+  step = step.x;
+  row = exp(gf([0:n-1], m, prim));
+  d = zeros(n);
+  for i=1:n;
+    d(i,:) = row .^ mod(step*(i-1),n);
+  end
+  
+endfunction