Mercurial > octave-nkf
view src/DLD-FUNCTIONS/filter.cc @ 4776:adf8d68d7143 ss-2-1-54
[project @ 2004-02-16 20:32:20 by jwe]
author | jwe |
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date | Mon, 16 Feb 2004 20:32:20 +0000 |
parents | 6b96ce9f5743 |
children | 9f7ef92b50b0 |
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/* Copyright (C) 1996, 1997 John W. Eaton This file is part of Octave. Octave 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, or (at your option) any later version. Octave 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 Octave; see the file COPYING. If not, write to the Free Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ // Based on Tony Richardson's filter.m. // // Originally translated to C++ by KH (Kurt.Hornik@ci.tuwien.ac.at) // with help from Fritz Leisch and Andreas Weingessel on Oct 20, 1994. // // Rewritten to use templates to handle both real and complex cases by // jwe, Wed Nov 1 19:15:29 1995. #ifdef HAVE_CONFIG_H #include <config.h> #endif #include "quit.h" #include "defun-dld.h" #include "error.h" #include "oct-obj.h" #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) extern MArray<double> filter (MArray<double>&, MArray<double>&, MArray<double>&); extern MArray<Complex> filter (MArray<Complex>&, MArray<Complex>&, MArray<Complex>&); #endif template <class T> MArray<T> filter (MArray<T>& b, MArray<T>& a, MArray<T>& x, MArray<T>& si) { MArray<T> y; int a_len = a.length (); int b_len = b.length (); int x_len = x.length (); int si_len = si.length (); int ab_len = a_len > b_len ? a_len : b_len; b.resize (ab_len, 0.0); if (si.length () != ab_len - 1) { error ("filter: si must be a vector of length max (length (a), length (b)) - 1"); return y; } T norm = a (0); if (norm == 0.0) { error ("filter: the first element of a must be non-zero"); return y; } y.resize (x_len, 0.0); if (norm != 1.0) b = b / norm; if (a_len > 1) { a.resize (ab_len, 0.0); if (norm != 1.0) a = a / norm; for (int i = 0; i < x_len; i++) { y (i) = si (0) + b (0) * x (i); if (si_len > 1) { for (int j = 0; j < si_len - 1; j++) { OCTAVE_QUIT; si (j) = si (j+1) - a (j+1) * y (i) + b (j+1) * x (i); } si (si_len-1) = b (si_len) * x (i) - a (si_len) * y (i); } else si (0) = b (si_len) * x (i) - a (si_len) * y (i); } } else if (si_len > 0) { for (int i = 0; i < x_len; i++) { y (i) = si (0) + b (0) * x (i); if (si_len > 1) { for (int j = 0; j < si_len - 1; j++) { OCTAVE_QUIT; si (j) = si (j+1) + b (j+1) * x (i); } si (si_len-1) = b (si_len) * x (i); } else si (0) = b (1) * x (i); } } else y = b (0) * x; return y; } #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) extern MArray<double> filter (MArray<double>&, MArray<double>&, MArray<double>&, MArray<double>&); extern MArray<Complex> filter (MArray<Complex>&, MArray<Complex>&, MArray<Complex>&, MArray<Complex>&); #endif template <class T> MArray<T> filter (MArray<T>& b, MArray<T>& a, MArray<T>& x) { int a_len = a.length (); int b_len = b.length (); int si_len = (a_len > b_len ? a_len : b_len) - 1; MArray<T> si (si_len, T (0.0)); return filter (b, a, x, si); } DEFUN_DLD (filter, args, nargout, "-*- texinfo -*-\n\ @deftypefn {Loadable Function} {y =} filter (@var{b}, @var{a}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, @var{si})\n\ Return the solution to the following linear, time-invariant difference\n\ equation:\n\ @iftex\n\ @tex\n\ $$\n\ \\sum_{k=0}^N a_{k+1} y_{n-k} = \\sum_{k=0}^M b_{k+1} x_{n-k}, \\qquad\n\ 1 \\le n \\le P\n\ $$\n\ @end tex\n\ @end iftex\n\ @ifinfo\n\ \n\ @smallexample\n\ N M\n\ SUM a(k+1) y(n-k) = SUM b(k+1) x(n-k) for 1<=n<=length(x)\n\ k=0 k=0\n\ @end smallexample\n\ @end ifinfo\n\ \n\ @noindent\n\ where\n\ @ifinfo\n\ N=length(a)-1 and M=length(b)-1.\n\ @end ifinfo\n\ @iftex\n\ @tex\n\ $a \\in \\Re^{N-1}$, $b \\in \\Re^{M-1}$, and $x \\in \\Re^P$.\n\ @end tex\n\ @end iftex\n\ An equivalent form of this equation is:\n\ @iftex\n\ @tex\n\ $$\n\ y_n = -\\sum_{k=1}^N c_{k+1} y_{n-k} + \\sum_{k=0}^M d_{k+1} x_{n-k}, \\qquad\n\ 1 \\le n \\le P\n\ $$\n\ @end tex\n\ @end iftex\n\ @ifinfo\n\ \n\ @smallexample\n\ N M\n\ y(n) = - SUM c(k+1) y(n-k) + SUM d(k+1) x(n-k) for 1<=n<=length(x)\n\ k=1 k=0\n\ @end smallexample\n\ @end ifinfo\n\ \n\ @noindent\n\ where\n\ @ifinfo\n\ c = a/a(1) and d = b/a(1).\n\ @end ifinfo\n\ @iftex\n\ @tex\n\ $c = a/a_1$ and $d = b/a_1$.\n\ @end tex\n\ @end iftex\n\ \n\ If the fourth argument @var{si} is provided, it is taken as the\n\ initial state of the system and the final state is returned as\n\ @var{sf}. The state vector is a column vector whose length is\n\ equal to the length of the longest coefficient vector minus one.\n\ If @var{si} is not supplied, the initial state vector is set to all\n\ zeros.\n\ \n\ In terms of the z-transform, y is the result of passing the discrete-\n\ time signal x through a system characterized by the following rational\n\ system function:\n\ @iftex\n\ @tex\n\ $$\n\ H(z) = {\\displaystyle\\sum_{k=0}^M d_{k+1} z^{-k}\n\ \\over 1 + \\displaystyle\\sum_{k+1}^N c_{k+1} z^{-k}}\n\ $$\n\ @end tex\n\ @end iftex\n\ @ifinfo\n\ \n\ @example\n\ M\n\ SUM d(k+1) z^(-k)\n\ k=0\n\ H(z) = ----------------------\n\ N\n\ 1 + SUM c(k+1) z(-k)\n\ k=1\n\ @end example\n\ @end ifinfo\n\ @end deftypefn") { octave_value_list retval; int nargin = args.length (); if (nargin < 3 || nargin > 4) { print_usage ("filter"); return retval; } const char *errmsg = "filter: arguments must be vectors"; bool x_is_row_vector = (args(2).rows () == 1); bool si_is_row_vector = (nargin == 4 && args(3).rows () == 1); if (args(0).is_complex_type () || args(1).is_complex_type () || args(2).is_complex_type () || (nargin == 4 && args(3).is_complex_type ())) { ComplexColumnVector b (args(0).complex_vector_value ()); ComplexColumnVector a (args(1).complex_vector_value ()); ComplexColumnVector x (args(2).complex_vector_value ()); if (! error_state) { ComplexColumnVector si; if (nargin == 3) { int a_len = a.length (); int b_len = b.length (); int si_len = (a_len > b_len ? a_len : b_len) - 1; si.resize (si_len, 0.0); } else si = ComplexColumnVector (args(3).complex_vector_value ()); if (! error_state) { ComplexColumnVector y (filter (b, a, x, si)); if (nargout == 2) { if (si_is_row_vector) retval(1) = si.transpose (); else retval(1) = si; } if (x_is_row_vector) retval(0) = y.transpose (); else retval(0) = y; } else error (errmsg); } else error (errmsg); } else { ColumnVector b (args(0).vector_value ()); ColumnVector a (args(1).vector_value ()); ColumnVector x (args(2).vector_value ()); if (! error_state) { ColumnVector si; if (nargin == 3) { int a_len = a.length (); int b_len = b.length (); int si_len = (a_len > b_len ? a_len : b_len) - 1; si.resize (si_len, 0.0); } else si = ColumnVector (args(3).vector_value ()); if (! error_state) { ColumnVector y (filter (b, a, x, si)); if (nargout == 2) { if (si_is_row_vector) retval(1) = si.transpose (); else retval(1) = si; } if (x_is_row_vector) retval(0) = y.transpose (); else retval(0) = y; } else error (errmsg); } else error (errmsg); } return retval; } template MArray<double> filter (MArray<double>&, MArray<double>&, MArray<double>&, MArray<double>&); template MArray<double> filter (MArray<double>&, MArray<double>&, MArray<double>&); template MArray<Complex> filter (MArray<Complex>&, MArray<Complex>&, MArray<Complex>&, MArray<Complex>&); template MArray<Complex> filter (MArray<Complex>&, MArray<Complex>&, MArray <Complex>&); /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */