| 1 |
/************************************************************************** |
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* Parks-McClellan algorithm for FIR filter design (C version) |
| 3 |
*------------------------------------------------- |
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* Copyright (c) 1995,1998 Jake Janovetz (janovetz@uiuc.edu) |
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* |
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* This library is free software; you can redistribute it and/or |
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* modify it under the terms of the GNU Library General Public |
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* License as published by the Free Software Foundation; either |
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* version 2 of the License, or (at your option) any later version. |
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* |
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* This library is distributed in the hope that it will be useful, |
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* but WITHOUT ANY WARRANTY; without even the implied warranty of |
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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* Library General Public License for more details. |
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* |
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* You should have received a copy of the GNU Library General Public |
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* License along with this library; if not, write to the Free |
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA |
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* |
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*************************************************************************/ |
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|
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|
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#include <stdio.h> |
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#include <math.h> |
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|
| 26 |
#include "xlib.h" |
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#include "remez.h" |
| 28 |
|
| 29 |
/******************* |
| 30 |
* CreateDenseGrid |
| 31 |
*================= |
| 32 |
* Creates the dense grid of frequencies from the specified bands. |
| 33 |
* Also creates the Desired Frequency Response function (D[]) and |
| 34 |
* the Weight function (W[]) on that dense grid |
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* |
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* |
| 37 |
* INPUT: |
| 38 |
* ------ |
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* int r - 1/2 the number of filter coefficients |
| 40 |
* int numtaps - Number of taps in the resulting filter |
| 41 |
* int numband - Number of bands in user specification |
| 42 |
* double bands[] - User-specified band edges [2*numband] |
| 43 |
* double des[] - Desired response per band [numband] |
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* double weight[] - Weight per band [numband] |
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* int symmetry - Symmetry of filter - used for grid check |
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* |
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* OUTPUT: |
| 48 |
* ------- |
| 49 |
* int gridsize - Number of elements in the dense frequency grid |
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* double Grid[] - Frequencies (0 to 0.5) on the dense grid [gridsize] |
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* double D[] - Desired response on the dense grid [gridsize] |
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* double W[] - Weight function on the dense grid [gridsize] |
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*******************/ |
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|
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static |
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void CreateDenseGrid(int r, int numtaps, int numband, double bands[], |
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double des[], double weight[], int *gridsize, |
| 58 |
double Grid[], double D[], double W[], |
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int symmetry) |
| 60 |
{ |
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int i, j, k, band; |
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double delf, lowf, highf; |
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|
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delf = 0.5/(GRIDDENSITY*r); |
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|
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/* |
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* For differentiator, hilbert, |
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* symmetry is odd and Grid[0] = max(delf, band[0]) |
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*/ |
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|
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if ((symmetry == NEGATIVE) && (delf > bands[0])) |
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bands[0] = delf; |
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|
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j=0; |
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for (band=0; band < numband; band++) |
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{ |
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Grid[j] = bands[2*band]; |
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lowf = bands[2*band]; |
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highf = bands[2*band + 1]; |
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k = (int)((highf - lowf)/delf + 0.5); /* .5 for rounding */ |
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for (i=0; i<k; i++) |
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{ |
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D[j] = des[band]; |
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W[j] = weight[band]; |
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Grid[j] = lowf; |
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lowf += delf; |
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j++; |
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} |
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Grid[j-1] = highf; |
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} |
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|
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/* |
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* Similar to above, if odd symmetry, last grid point can't be .5 |
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* - but, if there are even taps, leave the last grid point at .5 |
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*/ |
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if ((symmetry == NEGATIVE) && |
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(Grid[*gridsize-1] > (0.5 - delf)) && |
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(numtaps % 2)) |
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{ |
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Grid[*gridsize-1] = 0.5-delf; |
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} |
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} |
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|
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|
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/******************** |
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* InitialGuess |
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*============== |
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* Places Extremal Frequencies evenly throughout the dense grid. |
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* |
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* |
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* INPUT: |
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* ------ |
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* int r - 1/2 the number of filter coefficients |
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* int gridsize - Number of elements in the dense frequency grid |
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* |
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* OUTPUT: |
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* ------- |
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* int Ext[] - Extremal indexes to dense frequency grid [r+1] |
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********************/ |
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|
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static |
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void InitialGuess(int r, int Ext[], int gridsize) |
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{ |
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int i; |
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|
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for (i=0; i<=r; i++) |
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Ext[i] = i * (gridsize-1) / r; |
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} |
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|
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|
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/*********************** |
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* CalcParms |
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*=========== |
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* |
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* |
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* INPUT: |
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* ------ |
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* int r - 1/2 the number of filter coefficients |
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* int Ext[] - Extremal indexes to dense frequency grid [r+1] |
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* double Grid[] - Frequencies (0 to 0.5) on the dense grid [gridsize] |
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* double D[] - Desired response on the dense grid [gridsize] |
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* double W[] - Weight function on the dense grid [gridsize] |
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* |
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* OUTPUT: |
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* ------- |
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* double ad[] - 'b' in Oppenheim & Schafer [r+1] |
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* double x[] - [r+1] |
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* double y[] - 'C' in Oppenheim & Schafer [r+1] |
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***********************/ |
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|
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static |
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void CalcParms(int r, int Ext[], double Grid[], double D[], double W[], |
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double ad[], double x[], double y[]) |
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{ |
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int i, j, k, ld; |
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double sign, xi, delta, denom, numer; |
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|
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/* |
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* Find x[] |
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*/ |
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for (i=0; i<=r; i++) |
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x[i] = cos(M_2PI * Grid[Ext[i]]); |
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|
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/* |
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* Calculate ad[] - Oppenheim & Schafer eq 7.132 |
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*/ |
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ld = (r-1)/15 + 1; /* Skips around to avoid round errors */ |
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for (i=0; i<=r; i++) |
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{ |
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denom = 1.0; |
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xi = x[i]; |
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for (j=0; j<ld; j++) |
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{ |
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for (k=j; k<=r; k+=ld) |
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if (k != i) |
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denom *= 2.0*(xi - x[k]); |
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} |
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if (fabs(denom)<0.00001) |
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denom = 0.00001; |
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ad[i] = 1.0/denom; |
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} |
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|
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/* |
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* Calculate delta - Oppenheim & Schafer eq 7.131 |
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*/ |
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numer = denom = 0; |
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sign = 1; |
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for (i=0; i<=r; i++) |
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{ |
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numer += ad[i] * D[Ext[i]]; |
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denom += sign * ad[i]/W[Ext[i]]; |
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sign = -sign; |
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} |
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delta = numer/denom; |
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sign = 1; |
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|
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/* |
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* Calculate y[] - Oppenheim & Schafer eq 7.133b |
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*/ |
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for (i=0; i<=r; i++) |
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{ |
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y[i] = D[Ext[i]] - sign * delta/W[Ext[i]]; |
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sign = -sign; |
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} |
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} |
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|
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|
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/********************* |
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* ComputeA |
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*========== |
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* Using values calculated in CalcParms, ComputeA calculates the |
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* actual filter response at a given frequency (freq). Uses |
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* eq 7.133a from Oppenheim & Schafer. |
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* |
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* |
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* INPUT: |
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* ------ |
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* double freq - Frequency (0 to 0.5) at which to calculate A |
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* int r - 1/2 the number of filter coefficients |
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* double ad[] - 'b' in Oppenheim & Schafer [r+1] |
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* double x[] - [r+1] |
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* double y[] - 'C' in Oppenheim & Schafer [r+1] |
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* |
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* OUTPUT: |
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* ------- |
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* Returns double value of A[freq] |
| 227 |
*********************/ |
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|
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static |
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double ComputeA(double freq, int r, double ad[], double x[], double y[]) |
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{ |
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int i; |
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double xc, c, denom, numer; |
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|
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denom = numer = 0; |
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xc = cos(M_2PI * freq); |
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for (i=0; i<=r; i++) |
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{ |
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c = xc - x[i]; |
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if (fabs(c) < 1.0e-7) |
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{ |
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numer = y[i]; |
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denom = 1; |
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break; |
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} |
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c = ad[i]/c; |
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denom += c; |
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numer += c*y[i]; |
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} |
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return numer/denom; |
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} |
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|
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|
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/************************ |
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* CalcError |
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*=========== |
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* Calculates the Error function from the desired frequency response |
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* on the dense grid (D[]), the weight function on the dense grid (W[]), |
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* and the present response calculation (A[]) |
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* |
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* |
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* INPUT: |
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* ------ |
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* int r - 1/2 the number of filter coefficients |
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* double ad[] - [r+1] |
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* double x[] - [r+1] |
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* double y[] - [r+1] |
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* int gridsize - Number of elements in the dense frequency grid |
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* double Grid[] - Frequencies on the dense grid [gridsize] |
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* double D[] - Desired response on the dense grid [gridsize] |
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* double W[] - Weight function on the desnse grid [gridsize] |
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* |
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* OUTPUT: |
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* ------- |
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* double E[] - Error function on dense grid [gridsize] |
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************************/ |
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|
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static |
| 279 |
void CalcError(int r, double ad[], double x[], double y[], |
| 280 |
int gridsize, double Grid[], |
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double D[], double W[], double E[]) |
| 282 |
{ |
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int i; |
| 284 |
double A; |
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|
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for (i=0; i<gridsize; i++) |
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{ |
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A = ComputeA(Grid[i], r, ad, x, y); |
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E[i] = W[i] * (D[i] - A); |
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} |
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} |
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|
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/************************ |
| 294 |
* Search |
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*======== |
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* Searches for the maxima/minima of the error curve. If more than |
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* r+1 extrema are found, it uses the following heuristic (thanks |
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* Chris Hanson): |
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* 1) Adjacent non-alternating extrema deleted first. |
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* 2) If there are more than one excess extrema, delete the |
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* one with the smallest error. This will create a non-alternation |
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* condition that is fixed by 1). |
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* 3) If there is exactly one excess extremum, delete the smaller |
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* of the first/last extremum |
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* |
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* |
| 307 |
* INPUT: |
| 308 |
* ------ |
| 309 |
* int r - 1/2 the number of filter coefficients |
| 310 |
* int Ext[] - Indexes to Grid[] of extremal frequencies [r+1] |
| 311 |
* int gridsize - Number of elements in the dense frequency grid |
| 312 |
* double E[] - Array of error values. [gridsize] |
| 313 |
* OUTPUT: |
| 314 |
* ------- |
| 315 |
* int Ext[] - New indexes to extremal frequencies [r+1] |
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************************/ |
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|
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static |
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void Search(int r, int Ext[], |
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int gridsize, double E[]) |
| 321 |
{ |
| 322 |
int i, j, k, l, extra; /* Counters */ |
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int up, alt; |
| 324 |
int *foundExt; /* Array of found extremals */ |
| 325 |
|
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/* |
| 327 |
* Allocate enough space for found extremals. |
| 328 |
*/ |
| 329 |
foundExt = (int *)malloc((2*r) * sizeof(int)); |
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k = 0; |
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|
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/* |
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* Check for extremum at 0. |
| 334 |
*/ |
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if (((E[0]>0.0) && (E[0]>E[1])) || |
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((E[0]<0.0) && (E[0]<E[1]))) |
| 337 |
foundExt[k++] = 0; |
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|
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/* |
| 340 |
* Check for extrema inside dense grid |
| 341 |
*/ |
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for (i=1; i<gridsize-1; i++) |
| 343 |
{ |
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if (((E[i]>=E[i-1]) && (E[i]>E[i+1]) && (E[i]>0.0)) || |
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((E[i]<=E[i-1]) && (E[i]<E[i+1]) && (E[i]<0.0))) |
| 346 |
foundExt[k++] = i; |
| 347 |
} |
| 348 |
|
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/* |
| 350 |
* Check for extremum at 0.5 |
| 351 |
*/ |
| 352 |
j = gridsize-1; |
| 353 |
if (((E[j]>0.0) && (E[j]>E[j-1])) || |
| 354 |
((E[j]<0.0) && (E[j]<E[j-1]))) |
| 355 |
foundExt[k++] = j; |
| 356 |
|
| 357 |
|
| 358 |
/* |
| 359 |
* Remove extra extremals |
| 360 |
*/ |
| 361 |
extra = k - (r+1); |
| 362 |
|
| 363 |
while (extra > 0) |
| 364 |
{ |
| 365 |
if (E[foundExt[0]] > 0.0) |
| 366 |
up = 1; /* first one is a maxima */ |
| 367 |
else |
| 368 |
up = 0; /* first one is a minima */ |
| 369 |
|
| 370 |
l=0; |
| 371 |
alt = 1; |
| 372 |
for (j=1; j<k; j++) |
| 373 |
{ |
| 374 |
if (fabs(E[foundExt[j]]) < fabs(E[foundExt[l]])) |
| 375 |
l = j; /* new smallest error. */ |
| 376 |
if ((up) && (E[foundExt[j]] < 0.0)) |
| 377 |
up = 0; /* switch to a minima */ |
| 378 |
else if ((!up) && (E[foundExt[j]] > 0.0)) |
| 379 |
up = 1; /* switch to a maxima */ |
| 380 |
else |
| 381 |
{ |
| 382 |
alt = 0; |
| 383 |
break; /* Ooops, found two non-alternating */ |
| 384 |
} /* extrema. Delete smallest of them */ |
| 385 |
} /* if the loop finishes, all extrema are alternating */ |
| 386 |
|
| 387 |
/* |
| 388 |
* If there's only one extremal and all are alternating, |
| 389 |
* delete the smallest of the first/last extremals. |
| 390 |
*/ |
| 391 |
if ((alt) && (extra == 1)) |
| 392 |
{ |
| 393 |
if (fabs(E[foundExt[k-1]]) < fabs(E[foundExt[0]])) |
| 394 |
l = foundExt[k-1]; /* Delete last extremal */ |
| 395 |
else |
| 396 |
l = foundExt[0]; /* Delete first extremal */ |
| 397 |
} |
| 398 |
|
| 399 |
for (j=l; j<k; j++) /* Loop that does the deletion */ |
| 400 |
{ |
| 401 |
foundExt[j] = foundExt[j+1]; |
| 402 |
} |
| 403 |
k--; |
| 404 |
extra--; |
| 405 |
} |
| 406 |
|
| 407 |
for (i=0; i<=r; i++) |
| 408 |
{ |
| 409 |
Ext[i] = foundExt[i]; /* Copy found extremals to Ext[] */ |
| 410 |
} |
| 411 |
|
| 412 |
free(foundExt); |
| 413 |
} |
| 414 |
|
| 415 |
|
| 416 |
/********************* |
| 417 |
* FreqSample |
| 418 |
*============ |
| 419 |
* Simple frequency sampling algorithm to determine the impulse |
| 420 |
* response h[] from A's found in ComputeA |
| 421 |
* |
| 422 |
* |
| 423 |
* INPUT: |
| 424 |
* ------ |
| 425 |
* int N - Number of filter coefficients |
| 426 |
* double A[] - Sample points of desired response [N/2] |
| 427 |
* int symmetry - Symmetry of desired filter |
| 428 |
* |
| 429 |
* OUTPUT: |
| 430 |
* ------- |
| 431 |
* double h[] - Impulse Response of final filter [N] |
| 432 |
*********************/ |
| 433 |
static |
| 434 |
void FreqSample(int N, double A[], double h[], int symm) |
| 435 |
{ |
| 436 |
int n, k; |
| 437 |
double x, val, M; |
| 438 |
|
| 439 |
M = (N-1.0)/2.0; |
| 440 |
if (symm == POSITIVE) |
| 441 |
{ |
| 442 |
if (N%2) |
| 443 |
{ |
| 444 |
for (n=0; n<N; n++) |
| 445 |
{ |
| 446 |
val = A[0]; |
| 447 |
x = M_2PI * (n - M)/N; |
| 448 |
for (k=1; k<=M; k++) |
| 449 |
val += 2.0 * A[k] * cos(x*k); |
| 450 |
h[n] = val/N; |
| 451 |
} |
| 452 |
} |
| 453 |
else |
| 454 |
{ |
| 455 |
for (n=0; n<N; n++) |
| 456 |
{ |
| 457 |
val = A[0]; |
| 458 |
x = M_2PI * (n - M)/N; |
| 459 |
for (k=1; k<=(N/2-1); k++) |
| 460 |
val += 2.0 * A[k] * cos(x*k); |
| 461 |
h[n] = val/N; |
| 462 |
} |
| 463 |
} |
| 464 |
} |
| 465 |
else |
| 466 |
{ |
| 467 |
if (N%2) |
| 468 |
{ |
| 469 |
for (n=0; n<N; n++) |
| 470 |
{ |
| 471 |
val = 0; |
| 472 |
x = M_2PI * (n - M)/N; |
| 473 |
for (k=1; k<=M; k++) |
| 474 |
val += 2.0 * A[k] * sin(x*k); |
| 475 |
h[n] = val/N; |
| 476 |
} |
| 477 |
} |
| 478 |
else |
| 479 |
{ |
| 480 |
for (n=0; n<N; n++) |
| 481 |
{ |
| 482 |
val = A[N/2] * sin(M_PI * (n - M)); |
| 483 |
x = M_2PI * (n - M)/N; |
| 484 |
for (k=1; k<=(N/2-1); k++) |
| 485 |
val += 2.0 * A[k] * sin(x*k); |
| 486 |
h[n] = val/N; |
| 487 |
} |
| 488 |
} |
| 489 |
} |
| 490 |
} |
| 491 |
|
| 492 |
/******************* |
| 493 |
* isDone |
| 494 |
*======== |
| 495 |
* Checks to see if the error function is small enough to consider |
| 496 |
* the result to have converged. |
| 497 |
* |
| 498 |
* INPUT: |
| 499 |
* ------ |
| 500 |
* int r - 1/2 the number of filter coeffiecients |
| 501 |
* int Ext[] - Indexes to extremal frequencies [r+1] |
| 502 |
* double E[] - Error function on the dense grid [gridsize] |
| 503 |
* |
| 504 |
* OUTPUT: |
| 505 |
* ------- |
| 506 |
* Returns 1 if the result converged |
| 507 |
* Returns 0 if the result has not converged |
| 508 |
********************/ |
| 509 |
|
| 510 |
static |
| 511 |
short isDone(int r, int Ext[], double E[]) |
| 512 |
{ |
| 513 |
int i; |
| 514 |
double min, max, current; |
| 515 |
|
| 516 |
min = max = fabs(E[Ext[0]]); |
| 517 |
for (i=1; i<=r; i++) |
| 518 |
{ |
| 519 |
current = fabs(E[Ext[i]]); |
| 520 |
if (current < min) |
| 521 |
min = current; |
| 522 |
if (current > max) |
| 523 |
max = current; |
| 524 |
} |
| 525 |
if (((max-min)/max) < 0.0001) |
| 526 |
return 1; |
| 527 |
return 0; |
| 528 |
} |
| 529 |
|
| 530 |
/******************** |
| 531 |
* remez |
| 532 |
*======= |
| 533 |
* Calculates the optimal (in the Chebyshev/minimax sense) |
| 534 |
* FIR filter impulse response given a set of band edges, |
| 535 |
* the desired reponse on those bands, and the weight given to |
| 536 |
* the error in those bands. |
| 537 |
* |
| 538 |
* INPUT: |
| 539 |
* ------ |
| 540 |
* int numtaps - Number of filter coefficients |
| 541 |
* int numband - Number of bands in filter specification |
| 542 |
* double bands[] - User-specified band edges [2 * numband] |
| 543 |
* double des[] - User-specified band responses [numband] |
| 544 |
* double weight[] - User-specified error weights [numband] |
| 545 |
* int type - Type of filter |
| 546 |
* |
| 547 |
* OUTPUT: |
| 548 |
* ------- |
| 549 |
* double h[] - Impulse response of final filter [numtaps] |
| 550 |
********************/ |
| 551 |
|
| 552 |
void remez(double h[], int numtaps, |
| 553 |
int numband, double bands[], double des[], double weight[], |
| 554 |
int type) |
| 555 |
{ |
| 556 |
double *Grid, *W, *D, *E; |
| 557 |
int i, iter, gridsize, r, *Ext; |
| 558 |
double *taps, c; |
| 559 |
double *x, *y, *ad; |
| 560 |
int symmetry; |
| 561 |
|
| 562 |
if (type == BANDPASS) |
| 563 |
symmetry = POSITIVE; |
| 564 |
else |
| 565 |
symmetry = NEGATIVE; |
| 566 |
|
| 567 |
r = numtaps/2; /* number of extrema */ |
| 568 |
if ((numtaps%2) && (symmetry == POSITIVE)) |
| 569 |
r++; |
| 570 |
|
| 571 |
/* |
| 572 |
* Predict dense grid size in advance for memory allocation |
| 573 |
* .5 is so we round up, not truncate |
| 574 |
*/ |
| 575 |
gridsize = 0; |
| 576 |
for (i=0; i<numband; i++) |
| 577 |
{ |
| 578 |
gridsize += (int)(2*r*GRIDDENSITY*(bands[2*i+1] - bands[2*i]) + .5); |
| 579 |
} |
| 580 |
if (symmetry == NEGATIVE) |
| 581 |
{ |
| 582 |
gridsize--; |
| 583 |
} |
| 584 |
|
| 585 |
/* |
| 586 |
* Dynamically allocate memory for arrays with proper sizes |
| 587 |
*/ |
| 588 |
Grid = (double *)malloc(gridsize * sizeof(double)); |
| 589 |
D = (double *)malloc(gridsize * sizeof(double)); |
| 590 |
W = (double *)malloc(gridsize * sizeof(double)); |
| 591 |
E = (double *)malloc(gridsize * sizeof(double)); |
| 592 |
Ext = (int *)malloc((r+1) * sizeof(int)); |
| 593 |
taps = (double *)malloc((r+1) * sizeof(double)); |
| 594 |
x = (double *)malloc((r+1) * sizeof(double)); |
| 595 |
y = (double *)malloc((r+1) * sizeof(double)); |
| 596 |
ad = (double *)malloc((r+1) * sizeof(double)); |
| 597 |
|
| 598 |
/* |
| 599 |
* Create dense frequency grid |
| 600 |
*/ |
| 601 |
CreateDenseGrid(r, numtaps, numband, bands, des, weight, |
| 602 |
&gridsize, Grid, D, W, symmetry); |
| 603 |
InitialGuess(r, Ext, gridsize); |
| 604 |
|
| 605 |
/* |
| 606 |
* For Differentiator: (fix grid) |
| 607 |
*/ |
| 608 |
if (type == DIFFERENTIATOR) |
| 609 |
{ |
| 610 |
for (i=0; i<gridsize; i++) |
| 611 |
{ |
| 612 |
/* D[i] = D[i]*Grid[i]; */ |
| 613 |
if (D[i] > 0.0001) |
| 614 |
W[i] = W[i]/Grid[i]; |
| 615 |
} |
| 616 |
} |
| 617 |
|
| 618 |
/* |
| 619 |
* For odd or Negative symmetry filters, alter the |
| 620 |
* D[] and W[] according to Parks McClellan |
| 621 |
*/ |
| 622 |
if (symmetry == POSITIVE) |
| 623 |
{ |
| 624 |
if (numtaps % 2 == 0) |
| 625 |
{ |
| 626 |
for (i=0; i<gridsize; i++) |
| 627 |
{ |
| 628 |
c = cos(M_PI * Grid[i]); |
| 629 |
D[i] /= c; |
| 630 |
W[i] *= c; |
| 631 |
} |
| 632 |
} |
| 633 |
} |
| 634 |
else |
| 635 |
{ |
| 636 |
if (numtaps % 2) |
| 637 |
{ |
| 638 |
for (i=0; i<gridsize; i++) |
| 639 |
{ |
| 640 |
c = sin(M_2PI * Grid[i]); |
| 641 |
D[i] /= c; |
| 642 |
W[i] *= c; |
| 643 |
} |
| 644 |
} |
| 645 |
else |
| 646 |
{ |
| 647 |
for (i=0; i<gridsize; i++) |
| 648 |
{ |
| 649 |
c = sin(M_PI * Grid[i]); |
| 650 |
D[i] /= c; |
| 651 |
W[i] *= c; |
| 652 |
} |
| 653 |
} |
| 654 |
} |
| 655 |
|
| 656 |
/* |
| 657 |
* Perform the Remez Exchange algorithm |
| 658 |
*/ |
| 659 |
for (iter=0; iter<MAXITERATIONS; iter++) |
| 660 |
{ |
| 661 |
CalcParms(r, Ext, Grid, D, W, ad, x, y); |
| 662 |
CalcError(r, ad, x, y, gridsize, Grid, D, W, E); |
| 663 |
Search(r, Ext, gridsize, E); |
| 664 |
if (isDone(r, Ext, E)) |
| 665 |
break; |
| 666 |
} |
| 667 |
if (iter == MAXITERATIONS) |
| 668 |
{ |
| 669 |
fprintf(stderr, "design_remez_fir: reached maximum iteration count, results may be bad.\n"); |
| 670 |
} |
| 671 |
|
| 672 |
CalcParms(r, Ext, Grid, D, W, ad, x, y); |
| 673 |
|
| 674 |
/* |
| 675 |
* Find the 'taps' of the filter for use with Frequency |
| 676 |
* Sampling. If odd or Negative symmetry, fix the taps |
| 677 |
* according to Parks McClellan |
| 678 |
*/ |
| 679 |
for (i=0; i<=numtaps/2; i++) |
| 680 |
{ |
| 681 |
if (symmetry == POSITIVE) |
| 682 |
{ |
| 683 |
if (numtaps%2) |
| 684 |
c = 1; |
| 685 |
else |
| 686 |
c = cos(M_PI * (double)i/numtaps); |
| 687 |
} |
| 688 |
else |
| 689 |
{ |
| 690 |
if (numtaps%2) |
| 691 |
c = sin(M_2PI * (double)i/numtaps); |
| 692 |
else |
| 693 |
c = sin(M_PI * (double)i/numtaps); |
| 694 |
} |
| 695 |
taps[i] = ComputeA((double)i/numtaps, r, ad, x, y)*c; |
| 696 |
} |
| 697 |
|
| 698 |
/* |
| 699 |
* Frequency sampling design with calculated taps |
| 700 |
*/ |
| 701 |
FreqSample(numtaps, taps, h, symmetry); |
| 702 |
|
| 703 |
/* |
| 704 |
* Delete allocated memory |
| 705 |
*/ |
| 706 |
free(Grid); |
| 707 |
free(W); |
| 708 |
free(D); |
| 709 |
free(E); |
| 710 |
free(Ext); |
| 711 |
free(x); |
| 712 |
free(y); |
| 713 |
free(ad); |
| 714 |
} |
| 715 |
|
