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/************************************************************************** |
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* Parks-McClellan algorithm for FIR filter design (C version) |
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*------------------------------------------------- |
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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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#include <stdio.h> |
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#include <math.h> |
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#include "xlib.h" |
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#include "remez.h" |
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/******************* |
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* CreateDenseGrid |
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*================= |
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* Creates the dense grid of frequencies from the specified bands. |
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* Also creates the Desired Frequency Response function (D[]) and |
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* the Weight function (W[]) on that 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 numtaps - Number of taps in the resulting filter |
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* int numband - Number of bands in user specification |
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* double bands[] - User-specified band edges [2*numband] |
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* 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: |
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* ------- |
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* 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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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, |
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double Grid[], double D[], double W[], |
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int symmetry) |
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{ |
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int i, j, k, band; |
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double delf, lowf, highf; |
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delf = 0.5/(GRIDDENSITY*r); |
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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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if ((symmetry == NEGATIVE) && (delf > bands[0])) |
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bands[0] = delf; |
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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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* 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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* 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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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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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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* 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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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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* 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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* 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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* 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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* 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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* 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] |
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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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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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* 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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static |
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void CalcError(int r, double ad[], double x[], double y[], |
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int gridsize, double Grid[], |
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double D[], double W[], double E[]) |
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{ |
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int i; |
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double A; |
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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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* 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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* |
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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[] - Indexes to Grid[] of extremal frequencies [r+1] |
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* int gridsize - Number of elements in the dense frequency grid |
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* double E[] - Array of error values. [gridsize] |
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* OUTPUT: |
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* ------- |
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* int Ext[] - New indexes to extremal frequencies [r+1] |
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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[]) |
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{ |
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int i, j, k, l, extra; /* Counters */ |
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int up, alt; |
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int *foundExt; /* Array of found extremals */ |
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/* |
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* Allocate enough space for found extremals. |
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*/ |
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foundExt = (int *)malloc((2*r) * sizeof(int)); |
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k = 0; |
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/* |
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* Check for extremum at 0. |
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*/ |
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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]))) |
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foundExt[k++] = 0; |
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/* |
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* Check for extrema inside dense grid |
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*/ |
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for (i=1; i<gridsize-1; i++) |
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{ |
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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))) |
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foundExt[k++] = i; |
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} |
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/* |
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* Check for extremum at 0.5 |
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*/ |
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j = gridsize-1; |
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if (((E[j]>0.0) && (E[j]>E[j-1])) || |
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((E[j]<0.0) && (E[j]<E[j-1]))) |
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foundExt[k++] = j; |
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/* |
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* Remove extra extremals |
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*/ |
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extra = k - (r+1); |
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while (extra > 0) |
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{ |
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if (E[foundExt[0]] > 0.0) |
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up = 1; /* first one is a maxima */ |
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else |
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up = 0; /* first one is a minima */ |
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l=0; |
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alt = 1; |
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for (j=1; j<k; j++) |
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{ |
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if (fabs(E[foundExt[j]]) < fabs(E[foundExt[l]])) |
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l = j; /* new smallest error. */ |
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if ((up) && (E[foundExt[j]] < 0.0)) |
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up = 0; /* switch to a minima */ |
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else if ((!up) && (E[foundExt[j]] > 0.0)) |
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up = 1; /* switch to a maxima */ |
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else |
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{ |
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alt = 0; |
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break; /* Ooops, found two non-alternating */ |
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} /* extrema. Delete smallest of them */ |
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} /* if the loop finishes, all extrema are alternating */ |
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/* |
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* If there's only one extremal and all are alternating, |
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* delete the smallest of the first/last extremals. |
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*/ |
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if ((alt) && (extra == 1)) |
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{ |
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if (fabs(E[foundExt[k-1]]) < fabs(E[foundExt[0]])) |
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l = foundExt[k-1]; /* Delete last extremal */ |
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else |
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l = foundExt[0]; /* Delete first extremal */ |
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} |
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for (j=l; j<k; j++) /* Loop that does the deletion */ |
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{ |
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|
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 |
|
|
|