Add a useful package (from Source forge) for octave

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

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+## Copyright (C) 2011 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 {Loadable Function} {y =} filter (@var{b}, @var{a}, @var{x})
+## @deftypefnx {Loadable Function} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, @var{si})
+## 
+## Digital filtering of vectors in a Galois Field. Returns the solution to
+## the following linear, time-invariant difference equation over a Galois
+## Field:
+## @iftex
+## @tex
+## $$
+## \\sum_{k=0}^N a_{k+1} y_{n-k} = \\sum_{k=0}^M b_{k+1} x_{n-k}, \\qquad
+##  1 \\le n \\le P
+## $$
+## @end tex
+## @end iftex
+## @ifinfo
+## 
+## @smallexample
+##    N                   M
+##   SUM a(k+1) y(n-k) = SUM b(k+1) x(n-k)      for 1<=n<=length(x)
+##   k=0                 k=0
+## @end smallexample
+## @end ifinfo
+## 
+## @noindent
+## where
+## @ifinfo
+##  N=length(a)-1 and M=length(b)-1.
+## @end ifinfo
+## @iftex
+## @tex
+##  $a \\in \\Re^{N-1}$, $b \\in \\Re^{M-1}$, and $x \\in \\Re^P$.
+## @end tex
+## @end iftex
+## An equivalent form of this equation is:
+## @iftex
+## @tex
+## $$
+## y_n = -\\sum_{k=1}^N c_{k+1} y_{n-k} + \\sum_{k=0}^M d_{k+1} x_{n-k}, \\qquad
+##  1 \\le n \\le P
+## $$
+## @end tex
+## @end iftex
+## @ifinfo
+## 
+## @smallexample
+##             N                   M
+##   y(n) = - SUM c(k+1) y(n-k) + SUM d(k+1) x(n-k)  for 1<=n<=length(x)
+##            k=1                 k=0
+## @end smallexample
+## @end ifinfo
+## 
+## @noindent
+## where
+## @ifinfo
+##  c = a/a(1) and d = b/a(1).
+## @end ifinfo
+## @iftex
+## @tex
+## $c = a/a_1$ and $d = b/a_1$.
+## @end tex
+## @end iftex
+## 
+## If the fourth argument @var{si} is provided, it is taken as the
+## initial state of the system and the final state is returned as
+## @var{sf}.  The state vector is a column vector whose length is
+## equal to the length of the longest coefficient vector minus one.
+## If @var{si} is not supplied, the initial state vector is set to all
+## zeros.
+## @end deftypefn
+
+function varargout = filter (varargin)
+  varargout = cell (1, max(1, nargout));
+  [varargout{:}] = gfilter (varargin{:});
+endfunction