[Mplayer-cvslog] CVS: main/libao2 remez.c,NONE,1.1 remez.h,NONE,1.1
Stephen Davies
steve at mplayer.dev.hu
Fri Dec 14 00:33:58 CET 2001
Update of /cvsroot/mplayer/main/libao2
In directory mplayer:/var/tmp.root/cvs-serv26885
Added Files:
remez.c remez.h
Log Message:
code by Jake Janovetz to find FIR filter coefficients using the Parks-McClellan algorithm
--- NEW FILE ---
/**************************************************************************
* Parks-McClellan algorithm for FIR filter design (C version)
*-------------------------------------------------
* Copyright (c) 1995,1998 Jake Janovetz (janovetz at 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);
}
--- NEW FILE ---
/**************************************************************************
* Parks-McClellan algorithm for FIR filter design (C version)
*-------------------------------------------------
* Copyright (c) 1995,1998 Jake Janovetz (janovetz at 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__ */
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