code by Jake Janovetz to find FIR filter coefficients using the Parks-McClellan algorithm

git-svn-id: svn://svn.mplayerhq.hu/mplayer/trunk@3483 b3059339-0415-0410-9bf9-f77b7e298cf2

2 files changed, 749 insertions, 0 deletions

diff --git a/libao2/remez.c b/libao2/remez.c
new file mode 100644
index 0000000000..afdce2c088
--- /dev/null
+++ b/libao2/remez.c
@@ -0,0 +1,704 @@
+/**************************************************************************
+ * Parks-McClellan algorithm for FIR filter design (C version)
+ *-------------------------------------------------
+ *  Copyright (c) 1995,1998  Jake Janovetz (janovetz@uiuc.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;
+   }
+
+/*
+ * 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)<0.00001)
+          denom = 0.00001;
+       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-7)
+      {
+         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[])
+{
+   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;
+   }
+   if (((max-min)/max) < 0.0001)
+      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 *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);
+   }
+   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))
+         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);
+}
+
diff --git a/libao2/remez.h b/libao2/remez.h
new file mode 100644
index 0000000000..3c51bd46aa
--- /dev/null
+++ b/libao2/remez.h
@@ -0,0 +1,45 @@
+/**************************************************************************
+ * Parks-McClellan algorithm for FIR filter design (C version)
+ *-------------------------------------------------
+ *  Copyright (c) 1995,1998  Jake Janovetz (janovetz@uiuc.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__ */
+