From octave-sources-request at bevo dot che dot wisc dot edu Thu Oct 18 21:19:42 2001
Subject: An octave port of Remez algorithm to design linear phase FIR filters
From: Chee-Kiang dot Goh at infineon dot com
To: octave-sources at bevo dot che dot wisc dot edu
Date: Fri, 19 Oct 2001 10:19:22 +0800

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Good day,

I have created an octave DLD interface to the remez algorithm by Jake Janovetz.

This algorithm can be used to design linear phase FIR filters. The interface is

similar to that in Matlab.

The original C source is by Jake Janovetz (janovetz at uiuc dot edu) dot  I guess

all the GPL stuff should apply to his code.

Tested on solaris-2.5.1 with gcc 2.95.2 and octave 2.1.34 only. From my

personal experience, it is not as numerically stable as that in Matlab, but

does the job well for most cases with <=100 taps FIR filters.

Please see attached files. On my system, the command to generate the oct file

is

mkoctfile remez.cc

Hope you find it useful.

Best Regards.

--
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    Goh Chee Kiang      \e/   email: Chee-Kiang dot Goh at infineon dot com
  __o          __o       I      Tel: +65-840-0334
 `\<,         `\<,      `\\,  Infineon Technologies Asia Pacific Pte Ltd
_O/ O_________O/_O______O/_O_ 168, Kallang Way. Singapore 349253
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




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/**************************************************************************
 * Parks-McClellan algorithm for FIR filter design (C version)
 *-------------------------------------------------
 *  Copyright (c) 1995,1998  Jake Janovetz (janovetz at uiuc dot edu)
 *
 *  This library is free software; you can redistribute it and/or
 *  modify it under the terms of the GNU Library General Public
 *  License as published by the Free Software Foundation; either
 *  version 2 of the License, or (at your option) any later version.
 *
 *  This library 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
 *  Library General Public License for more details.
 *
 *  You should have received a copy of the GNU Library General Public
 *  License along with this library; if not, write to the Free
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 *
 *************************************************************************/


#include "remez.h"
#include <math.h>

/*******************
 * CreateDenseGrid
 *=================
 * Creates the dense grid of frequencies from the specified bands.
 * Also creates the Desired Frequency Response function (D[]) and
 * the Weight function (W[]) on that dense grid
 *
 *
 * INPUT:
 * ------
 * int      r        - 1/2 the number of filter coefficients
 * int      numtaps  - Number of taps in the resulting filter
 * int      numband  - Number of bands in user specification
 * double   bands[]  - User-specified band edges [2*numband]
 * double   des[]    - Desired response per band [numband]
 * double   weight[] - Weight per band [numband]
 * int      symmetry - Symmetry of filter - used for grid check
 *
 * OUTPUT:
 * -------
 * int    gridsize   - Number of elements in the dense frequency grid
 * double Grid[]     - Frequencies (0 to 0.5) on the dense grid [gridsize]
 * double D[]        - Desired response on the dense grid [gridsize]
 * double W[]        - Weight function on the dense grid [gridsize]
 *******************/

void CreateDenseGrid(int r, int numtaps, int numband, double bands[],
                     double des[], double weight[], int *gridsize,
                     double Grid[], double D[], double W[],
                     int symmetry)
{
   int i, j, k, band;
   double delf, lowf, highf;

   delf = 0.5/(GRIDDENSITY*r);

/*
 * For differentiator, hilbert,
 *   symmetry is odd and Grid[0] = max(delf, band[0])
 */

   if ((symmetry == NEGATIVE) && (delf > bands[0]))
      bands[0] = delf;

   j=0;
   for (band=0; band < numband; band++)
   {
      Grid[j] = bands[2*band];
      lowf = bands[2*band];
      highf = bands[2*band + 1];
      k = (int)((highf - lowf)/delf + 0.5);   /* .5 for rounding */
      for (i=0; i<k; i++)
      {
         D[j] = des[band];
         W[j] = weight[band];
         Grid[j] = lowf;
         lowf += delf;
         j++;
      }
      Grid[j-1] = highf;
   }
   *gridsize=j-1;

/*
 * Similar to above, if odd symmetry, last grid point can't be .5
 *  - but, if there are even taps, leave the last grid point at .5
 */
   if ((symmetry == NEGATIVE) &&
       (Grid[*gridsize-1] > (0.5 - delf)) &&
       (numtaps % 2))
   {
      Grid[*gridsize-1] = 0.5-delf;
   }
}


/********************
 * InitialGuess
 *==============
 * Places Extremal Frequencies evenly throughout the dense grid.
 *
 *
 * INPUT: 
 * ------
 * int r        - 1/2 the number of filter coefficients
 * int gridsize - Number of elements in the dense frequency grid
 *
 * OUTPUT:
 * -------
 * int Ext[]    - Extremal indexes to dense frequency grid [r+1]
 ********************/

void InitialGuess(int r, int Ext[], int gridsize)
{
   int i;

   for (i=0; i<=r; i++)
      Ext[i] = i * (gridsize-1) / r;
}


/***********************
 * CalcParms
 *===========
 *
 *
 * INPUT:
 * ------
 * int    r      - 1/2 the number of filter coefficients
 * int    Ext[]  - Extremal indexes to dense frequency grid [r+1]
 * double Grid[] - Frequencies (0 to 0.5) on the dense grid [gridsize]
 * double D[]    - Desired response on the dense grid [gridsize]
 * double W[]    - Weight function on the dense grid [gridsize]
 *
 * OUTPUT:
 * -------
 * double ad[]   - 'b' in Oppenheim & Schafer [r+1]
 * double x[]    - [r+1]
 * double y[]    - 'C' in Oppenheim & Schafer [r+1]
 ***********************/

void CalcParms(int r, int Ext[], double Grid[], double D[], double W[],
                double ad[], double x[], double y[])
{
   int i, j, k, ld;
   double sign, xi, delta, denom, numer;

/*
 * Find x[]
 */
   for (i=0; i<=r; i++)
      x[i] = cos(Pi2 * Grid[Ext[i]]);

/*
 * Calculate ad[]  - Oppenheim & Schafer eq 7.132
 */
   ld = (r-1)/15 + 1;         /* Skips around to avoid round errors */
   for (i=0; i<=r; i++)
   {
       denom = 1.0;
       xi = x[i];
       for (j=0; j<ld; j++)
       {
          for (k=j; k<=r; k+=ld)
             if (k != i)
                denom *= 2.0*(xi - x[k]);
       }
       if (fabs(denom)<0.00000001)
          denom = 0.00000001;
       ad[i] = 1.0/denom;
   }

/*
 * Calculate delta  - Oppenheim & Schafer eq 7.131
 */
   numer = denom = 0;
   sign = 1;
   for (i=0; i<=r; i++)
   {
      numer += ad[i] * D[Ext[i]];
      denom += sign * ad[i]/W[Ext[i]];
      sign = -sign;
   }
   delta = numer/denom;
   sign = 1;

/*
 * Calculate y[]  - Oppenheim & Schafer eq 7.133b
 */
   for (i=0; i<=r; i++)
   {
      y[i] = D[Ext[i]] - sign * delta/W[Ext[i]];
      sign = -sign;
   }
}


/*********************
 * ComputeA
 *==========
 * Using values calculated in CalcParms, ComputeA calculates the
 * actual filter response at a given frequency (freq).  Uses
 * eq 7.133a from Oppenheim & Schafer.
 *
 *
 * INPUT:
 * ------
 * double freq - Frequency (0 to 0.5) at which to calculate A
 * int    r    - 1/2 the number of filter coefficients
 * double ad[] - 'b' in Oppenheim & Schafer [r+1]
 * double x[]  - [r+1]
 * double y[]  - 'C' in Oppenheim & Schafer [r+1]
 *
 * OUTPUT:
 * -------
 * Returns double value of A[freq]
 *********************/

double ComputeA(double freq, int r, double ad[], double x[], double y[])
{
   int i;
   double xc, c, denom, numer;

   denom = numer = 0;
   xc = cos(Pi2 * freq);
   for (i=0; i<=r; i++)
   {
      c = xc - x[i];
      if (fabs(c) < 1.0e-9)
      {
         numer = y[i];
         denom = 1;
         break;
      }
      c = ad[i]/c;
      denom += c;
      numer += c*y[i];
   }
   return numer/denom;
}


/************************
 * CalcError
 *===========
 * Calculates the Error function from the desired frequency response
 * on the dense grid (D[]), the weight function on the dense grid (W[]),
 * and the present response calculation (A[])
 *
 *
 * INPUT:
 * ------
 * int    r      - 1/2 the number of filter coefficients
 * double ad[]   - [r+1]
 * double x[]    - [r+1]
 * double y[]    - [r+1]
 * int gridsize  - Number of elements in the dense frequency grid
 * double Grid[] - Frequencies on the dense grid [gridsize]
 * double D[]    - Desired response on the dense grid [gridsize]
 * double W[]    - Weight function on the desnse grid [gridsize]
 *
 * OUTPUT:
 * -------
 * double E[]    - Error function on dense grid [gridsize]
 ************************/

void CalcError(int r, double ad[], double x[], double y[],
               int gridsize, double Grid[],
               double D[], double W[], double E[])
{
   int i;
   double A;

   for (i=0; i<gridsize; i++)
   {
      A = ComputeA(Grid[i], r, ad, x, y);
      E[i] = W[i] * (D[i] - A);
   }
}

/************************
 * Search
 *========
 * Searches for the maxima/minima of the error curve.  If more than
 * r+1 extrema are found, it uses the following heuristic (thanks
 * Chris Hanson):
 * 1) Adjacent non-alternating extrema deleted first.
 * 2) If there are more than one excess extrema, delete the
 *    one with the smallest error.  This will create a non-alternation
 *    condition that is fixed by 1).
 * 3) If there is exactly one excess extremum, delete the smaller
 *    of the first/last extremum
 *
 *
 * INPUT:
 * ------
 * int    r        - 1/2 the number of filter coefficients
 * int    Ext[]    - Indexes to Grid[] of extremal frequencies [r+1]
 * int    gridsize - Number of elements in the dense frequency grid
 * double E[]      - Array of error values.  [gridsize]
 * OUTPUT:
 * -------
 * int    Ext[]    - New indexes to extremal frequencies [r+1]
 ************************/

void Search(int r, int Ext[],
            int gridsize, double E[])
{
   int i, j, k, l, extra;     /* Counters */
   int up, alt;
   int *foundExt;             /* Array of found extremals */

/*
 * Allocate enough space for found extremals.
 */
   foundExt = (int *)malloc((2*r) * sizeof(int));
   k = 0;

/*
 * Check for extremum at 0.
 */
   if (((E[0]>0.0) && (E[0]>E[1])) ||
       ((E[0]<0.0) && (E[0]<E[1])))
      foundExt[k++] = 0;

/*
 * Check for extrema inside dense grid
 */
   for (i=1; i<gridsize-1; i++)
   {
      if (((E[i]>=E[i-1]) && (E[i]>E[i+1]) && (E[i]>0.0)) ||
          ((E[i]<=E[i-1]) && (E[i]<E[i+1]) && (E[i]<0.0)))
         foundExt[k++] = i;
   }

/*
 * Check for extremum at 0.5
 */
   j = gridsize-1;
   if (((E[j]>0.0) && (E[j]>E[j-1])) ||
       ((E[j]<0.0) && (E[j]<E[j-1])))
      foundExt[k++] = j;


/*
 * Remove extra extremals
 */
   extra = k - (r+1);

   while (extra > 0)
   {
      if (E[foundExt[0]] > 0.0)
         up = 1;                /* first one is a maxima */
      else
         up = 0;                /* first one is a minima */

      l=0;
      alt = 1;
      for (j=1; j<k; j++)
      {
         if (fabs(E[foundExt[j]]) < fabs(E[foundExt[l]]))
            l = j;               /* new smallest error. */
         if ((up) && (E[foundExt[j]] < 0.0))
            up = 0;             /* switch to a minima */
         else if ((!up) && (E[foundExt[j]] > 0.0))
            up = 1;             /* switch to a maxima */
         else
	 { 
            alt = 0;
            break;              /* Ooops, found two non-alternating */
         }                      /* extrema.  Delete smallest of them */
      }  /* if the loop finishes, all extrema are alternating */

/*
 * If there's only one extremal and all are alternating,
 * delete the smallest of the first/last extremals.
 */
      if ((alt) && (extra == 1))
      {
         if (fabs(E[foundExt[k-1]]) < fabs(E[foundExt[0]]))
            l = foundExt[k-1];   /* Delete last extremal */
         else
            l = foundExt[0];     /* Delete first extremal */
      }

      for (j=l; j<k; j++)        /* Loop that does the deletion */
      {
         foundExt[j] = foundExt[j+1];
      }
      k--;
      extra--;
   }

   for (i=0; i<=r; i++)
   {
      Ext[i] = foundExt[i];       /* Copy found extremals to Ext[] */
   }

   free(foundExt);
}


/*********************
 * FreqSample
 *============
 * Simple frequency sampling algorithm to determine the impulse
 * response h[] from A's found in ComputeA
 *
 *
 * INPUT:
 * ------
 * int      N        - Number of filter coefficients
 * double   A[]      - Sample points of desired response [N/2]
 * int      symmetry - Symmetry of desired filter
 *
 * OUTPUT:
 * -------
 * double h[] - Impulse Response of final filter [N]
 *********************/
void FreqSample(int N, double A[], double h[], int symm)
{
   int n, k;
   double x, val, M;

   M = (N-1.0)/2.0;
   if (symm == POSITIVE)
   {
      if (N%2)
      {
         for (n=0; n<N; n++)
         {
            val = A[0];
            x = Pi2 * (n - M)/N;
            for (k=1; k<=M; k++)
               val += 2.0 * A[k] * cos(x*k);
            h[n] = val/N;
         }
      }
      else
      {
         for (n=0; n<N; n++)
         {
            val = A[0];
            x = Pi2 * (n - M)/N;
            for (k=1; k<=(N/2-1); k++)
               val += 2.0 * A[k] * cos(x*k);
            h[n] = val/N;
         }
      }
   }
   else
   {
      if (N%2)
      {
         for (n=0; n<N; n++)
         {
            val = 0;
            x = Pi2 * (n - M)/N;
            for (k=1; k<=M; k++)
               val += 2.0 * A[k] * sin(x*k);
            h[n] = val/N;
         }
      }
      else
      {
          for (n=0; n<N; n++)
          {
             val = A[N/2] * sin(Pi * (n - M));
             x = Pi2 * (n - M)/N;
             for (k=1; k<=(N/2-1); k++)
                val += 2.0 * A[k] * sin(x*k);
             h[n] = val/N;
          }
      }
   }
}

/*******************
 * isDone
 *========
 * Checks to see if the error function is small enough to consider
 * the result to have converged.
 *
 * INPUT:
 * ------
 * int    r     - 1/2 the number of filter coeffiecients
 * int    Ext[] - Indexes to extremal frequencies [r+1]
 * double E[]   - Error function on the dense grid [gridsize]
 *
 * OUTPUT:
 * -------
 * Returns 1 if the result converged
 * Returns 0 if the result has not converged
 ********************/

short isDone(int r, int Ext[], double E[], double *maxErr)
{
   int i;
   double min, max, current;

   min = max = fabs(E[Ext[0]]);
   for (i=1; i<=r; i++)
   {
      current = fabs(E[Ext[i]]);
      if (current < min)
         min = current;
      if (current > max)
         max = current;
   }
   *maxErr=max;
   if (((max-min)/max) < 0.001)
      return 1;
   return 0;
}

/********************
 * remez
 *=======
 * Calculates the optimal (in the Chebyshev/minimax sense)
 * FIR filter impulse response given a set of band edges,
 * the desired reponse on those bands, and the weight given to
 * the error in those bands.
 *
 * INPUT:
 * ------
 * int     numtaps     - Number of filter coefficients
 * int     numband     - Number of bands in filter specification
 * double  bands[]     - User-specified band edges [2 * numband]
 * double  des[]       - User-specified band responses [numband]
 * double  weight[]    - User-specified error weights [numband]
 * int     type        - Type of filter
 *
 * OUTPUT:
 * -------
 * double h[]      - Impulse response of final filter [numtaps]
 ********************/

void remez(double h[], int numtaps,
           int numband, double bands[], double des[], double weight[],
           int type, double *maxErr)
{
   double *Grid, *W, *D, *E;
   int    i, iter, gridsize, r, *Ext;
   double *taps, c;
   double *x, *y, *ad;
   int    symmetry;

   if (type == BANDPASS)
      symmetry = POSITIVE;
   else
      symmetry = NEGATIVE;

   r = numtaps/2;                  /* number of extrema */
   if ((numtaps%2) && (symmetry == POSITIVE))
      r++;

/*
 * Predict dense grid size in advance for memory allocation
 *   .5 is so we round up, not truncate
 */
   gridsize = 0;
   for (i=0; i<numband; i++)
   {
      gridsize += (int)(2*r*GRIDDENSITY*(bands[2*i+1] - bands[2*i]) + .5)+2;
   }
   if (symmetry == NEGATIVE)
   {
      gridsize--;
   }

/*
 * Dynamically allocate memory for arrays with proper sizes
 */
   Grid = (double *)malloc(gridsize * sizeof(double));
   D = (double *)malloc(gridsize * sizeof(double));
   W = (double *)malloc(gridsize * sizeof(double));
   E = (double *)malloc(gridsize * sizeof(double));
   Ext = (int *)malloc((r+1) * sizeof(int));
   taps = (double *)malloc((r+1) * sizeof(double));
   x = (double *)malloc((r+1) * sizeof(double));
   y = (double *)malloc((r+1) * sizeof(double));
   ad = (double *)malloc((r+1) * sizeof(double));


   /*
 * Create dense frequency grid
 */
   CreateDenseGrid(r, numtaps, numband, bands, des, weight,
                   &gridsize, Grid, D, W, symmetry);
   InitialGuess(r, Ext, gridsize);

/*
 * For Differentiator: (fix grid)
 */
   if (type == DIFFERENTIATOR)
   {
      for (i=0; i<gridsize; i++)
      {
/* D[i] = D[i]*Grid[i]; */
         if (D[i] > 0.0001)
            W[i] = W[i]/Grid[i];
      }
   }

/*
 * For odd or Negative symmetry filters, alter the
 * D[] and W[] according to Parks McClellan
 */
   if (symmetry == POSITIVE)
   {
      if (numtaps % 2 == 0)
      {
         for (i=0; i<gridsize; i++)
         {
            c = cos(Pi * Grid[i]);
            D[i] /= c;
            W[i] *= c; 
         }
      }
   }
   else
   {
      if (numtaps % 2)
      {
         for (i=0; i<gridsize; i++)
         {
            c = sin(Pi2 * Grid[i]);
            D[i] /= c;
            W[i] *= c;
         }
      }
      else
      {
         for (i=0; i<gridsize; i++)
         {
            c = sin(Pi * Grid[i]);
            D[i] /= c;
            W[i] *= c;
         }
      }
   }

/*
 * Perform the Remez Exchange algorithm
 */
   for (iter=0; iter<MAXITERATIONS; iter++)
   {
      CalcParms(r, Ext, Grid, D, W, ad, x, y);
      CalcError(r, ad, x, y, gridsize, Grid, D, W, E);
      Search(r, Ext, gridsize, E);
      if (isDone(r, Ext, E,maxErr))
         break;
   }
   if (iter == MAXITERATIONS)
   {
      printf("Reached maximum iteration count.\nResults may be bad.\n");
   }

   CalcParms(r, Ext, Grid, D, W, ad, x, y);

/*
 * Find the 'taps' of the filter for use with Frequency
 * Sampling.  If odd or Negative symmetry, fix the taps
 * according to Parks McClellan
 */
   for (i=0; i<=numtaps/2; i++)
   {
      if (symmetry == POSITIVE)
      {
         if (numtaps%2)
            c = 1;
         else
            c = cos(Pi * (double)i/numtaps);
      }
      else
      {
         if (numtaps%2)
            c = sin(Pi2 * (double)i/numtaps);
         else
            c = sin(Pi * (double)i/numtaps);
      }
      taps[i] = ComputeA((double)i/numtaps, r, ad, x, y)*c;
   }

/*
 * Frequency sampling design with calculated taps
 */
   FreqSample(numtaps, taps, h, symmetry);

/*
 * Delete allocated memory
 */
   free(Grid);
   free(W);
   free(D);
   free(E);
   free(Ext);
   free(x);
   free(y);
   free(ad);
   free(taps);
}


--------------3E3A35CA73E3429EAB62C0FD
Content-Type: text/plain; charset=us-ascii;
 name="remez.h"
Content-Transfer-Encoding: 7bit
Content-Disposition: inline;
 filename="remez.h"

/**************************************************************************
 * Parks-McClellan algorithm for FIR filter design (C version)
 *-------------------------------------------------
 *  Copyright (c) 1995,1998  Jake Janovetz (janovetz at uiuc dot edu)
 *
 *  This library is free software; you can redistribute it and/or
 *  modify it under the terms of the GNU Library General Public
 *  License as published by the Free Software Foundation; either
 *  version 2 of the License, or (at your option) any later version.
 *
 *  This library 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
 *  Library General Public License for more details.

 *  You should have received a copy of the GNU Library General Public
 *  License along with this library; if not, write to the Free
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 *
 *************************************************************************/
#ifndef __REMEZ_H__
#define __REMEZ_H__

#define BANDPASS       1
#define DIFFERENTIATOR 2
#define HILBERT        3

#define NEGATIVE       0
#define POSITIVE       1

#define Pi             3.1415926535897932
#define Pi2            6.2831853071795865

#define GRIDDENSITY    16
#define MAXITERATIONS  40

/* Function prototype for remez() - the only function that should need be
 * called from external code
 */
void remez(double h[], int numtaps,
           int numband, double bands[], double des[], double weight[],
           int type);

#endif /* __REMEZ_H__ */


--------------3E3A35CA73E3429EAB62C0FD
Content-Type: text/plain; charset=us-ascii;
 name="remez.cc"
Content-Transfer-Encoding: 7bit
Content-Disposition: inline;
 filename="remez.cc"

/**************************************************************************
 * Parks-McClellan algorithm for FIR filter design (C version)
 *-------------------------------------------------
 *  Copyright (C) 1995  Jake Janovetz (janovetz at coewl dot cen dot uiuc dot 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 2 of the License, or
 *  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., 675 Mass Ave, Cambridge, MA 02139, USA.
 *
 *************************************************************************/

/**************************************************************************
 * Ported to Octave Oct file by
 * Chee-Kiang Goh (Chee-Kiang dot Goh at infineon dot com)
 * October 2001
 * For your free usage only :>
 * Share your ideas and innovation !
 *************************************************************************/
#include <malloc.h>

#include "remez.c"
#include <math.h>
#include <octave/oct.h>
DEFUN_DLD ( remez, args, , "\
 remez(): Remez (AKA Parks-McCellan) algorithm for linear phase\n\
         FIR filter design.\n\
 Usages:\n\
 [h,err]=remez(N,F,A)\n\
 [h,err]=remez(N,F,A,'Hilbert')\n\
 [h,err]=remez(N,F,A,'differentiator')\n\
 [h,err]=remez(N,F,A,W)\n\
 [h,err]=remez(N,F,A,W,'Hilbert')\n\
 [h,err]=remez(N,F,A,W,'differentiator')\n\
 \n\
 N: FIR filter length\n\
 F: Vector of frequency band edges (0-1) in pairs.\n\
    e.g. F=[0 0.5 0.7 1] specifies two bands 0-0.5 and 0.7-1. 0.5-0.7 \n\
    is considered as a transition band (don't care).\n\
 A: Vector of the desired amplitude at each band edge.\n\
    Should be same length as F. e.g. A=[1 1 0 0] specifies 0-0.5 have\n\
    gain of 1, and 0.7-0.1 have gain of 0. NB: only flat gain function is\n\
    implemented for now (10-2001)\n\
 W: Vector of weighting function for the ripple ratio between each band.\n\
    Same specification as A.\n\
 'Hilbert', 'differentiator': specifies either a hilbert transformer or\n\
    differentiator\n")
{
    octave_value_list retval;
    double *weights, *desired, *bands;
    double *h, maxErr;
    int i,type=BANDPASS, flagweight=0;
    int nargin=(args.length());


    if (nargin<3)
    {
        print_usage("remez");
        return retval;
    }

    int fl (args(0).int_value());
    if (fl<2)
    {
        printf("remez problem: we need at least an FIR filter of 2 taps !!\n");
        return retval;
    }


    ColumnVector X ( fl );

    int nband (args(1).length()/2);

    if (args(2).vector_value().length()<nband)
    {
        printf("remez problem: desired mag. specified is less than number of bands\n");
        return retval;
    }

    if (nargin>=4)
    {
        if (args(3).is_string())
        {
            if (strcmp(args(3).string_value().data(),"Hilbert")==0) type = HILBERT;
            else if (strcmp(args(3).string_value().data(),"differentiator")==0) type = DIFFERENTIATOR;
        }
        else
        {
            if (args(3).vector_value().length()<nband)
            {
                printf("remez problem: desired weights specified is less than number of bands\n");
                return retval;
            }
            flagweight=1;
            if (nargin>4)
                if (strcmp(args(4).string_value().data(),"Hilbert")==0) type = HILBERT;
                else if (strcmp(args(4).string_value().data(),"differentiator")==0) type = DIFFERENTIATOR;
        }
    }




   bands = (double *)malloc(nband*2 * sizeof(double));
   weights = (double *)malloc(nband * sizeof(double));
   desired = (double *)malloc(nband * sizeof(double));
   h = (double *)malloc(fl * sizeof(double));

   if (h==NULL || desired ==NULL || weights==NULL || bands ==NULL)
   {
       if (h) free(h);
       if (desired) free(desired);
       if (weights) free(weights);
       if (bands) free(bands);
       printf("remez problem: can't allocate memory !\n");
       return retval;
   }


   for (i=0;i<nband*2;i++)
   {
       bands[i]=(double) args(1).vector_value().elem(i)/2;
       if (bands[i]<0 || bands[i]>0.5)
       {
           printf("remez problem: found a -ve freq. band edge !!\n");
           return retval;
       }
   }
   for (i=0;i<nband;i++)
       desired[i]=(double) args(2).vector_value().elem(i*2);
   for (i=0;i<nband;i++)
   {
       weights[i]=(flagweight==1?(double) args(3).vector_value().elem(i*2):1);
       if (weights[i]<0)
       {
           printf("remez problem: found a -ve weight value !!\n");
           return retval;
       }
   }

   remez(h, fl, nband, bands, desired, weights, type, &maxErr);
   for (i=0;i<fl;i++) X.elem(i)=h[i];
   free(bands);
   free(weights);
   free(desired);
   free(h);
   retval(0)=X;
   retval(1)=maxErr;
   return retval;
}


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