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/*
* lingot, a musical instrument tuner.
*
* Copyright (C) 2004-2011 Ibán Cereijo Graña, Jairo Chapela Martínez.
*
* This file is part of lingot.
*
* lingot is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* lingot is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with lingot; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#include <memory.h>
#include <math.h>
#include "lingot-complex.h"
#include "lingot-filter.h"
#define max(a,b) (((a)<(b))?(b):(a))
// given each polynomial order and coefs, with optional initial status.
LingotFilter* lingot_filter_new(unsigned int Na, unsigned int Nb, FLT* a,
FLT* b) {
unsigned int i;
LingotFilter* filter = malloc(sizeof(LingotFilter));
filter->N = max(Na, Nb);
filter->a = malloc((filter->N + 1) * sizeof(FLT));
filter->b = malloc((filter->N + 1) * sizeof(FLT));
filter->s = malloc((filter->N + 1) * sizeof(FLT));
for (i = 0; i < filter->N + 1; i++)
filter->a[i] = filter->b[i] = filter->s[i] = 0.0;
memcpy(filter->a, a, (Na + 1) * sizeof(FLT));
memcpy(filter->b, b, (Nb + 1) * sizeof(FLT));
for (i = 0; i < filter->N + 1; i++) {
filter->a[i] /= a[0]; // polynomial normalization.
filter->b[i] /= a[0];
}
return filter;
}
void lingot_filter_destroy(LingotFilter* filter) {
free(filter->a);
free(filter->b);
free(filter->s);
free(filter);
}
// Digital Filter Implementation II, in & out overlapables.
void lingot_filter_filter(LingotFilter* filter, unsigned int n, FLT* in,
FLT* out) {
FLT w, y;
register unsigned int i;
register int j;
for (i = 0; i < n; i++) {
w = in[i];
y = 0.0;
for (j = filter->N - 1; j >= 0; j--) {
w -= filter->a[j + 1] * filter->s[j];
y += filter->b[j + 1] * filter->s[j];
filter->s[j + 1] = filter->s[j];
}
y += w * filter->b[0];
filter->s[0] = w;
out[i] = y;
}
}
// single sample filtering
FLT lingot_filter_filter_sample(LingotFilter* filter, FLT in) {
FLT result;
lingot_filter_filter(filter, 1, &in, &result);
return result;
}
// vector prod
void lingot_filter_vector_product(int n, LingotComplex* vector,
LingotComplex* result) {
register int i;
LingotComplex aux1;
result->r = 1.0;
result->i = 0.0;
for (i = 0; i < n; i++) {
aux1.r = -vector[i].r;
aux1.i = -vector[i].i;
lingot_complex_mul(result, &aux1, result);
}
}
// Chebyshev filters
LingotFilter* lingot_filter_cheby_design(unsigned int n, FLT Rp, FLT wc) {
int i; // loops
int k;
int p;
FLT a[n + 1];
FLT b[n + 1];
FLT new_a[n + 1];
FLT new_b[n + 1];
// locate poles
LingotComplex pole[n];
for (i = 0; i < n; i++) {
pole[i].r = 0.0;
pole[i].i = 0.0;
}
FLT T = 2.0;
// 2Hz
FLT W = 2.0 / T * tan(M_PI * wc / T);
FLT epsilon = sqrt(pow(10.0, 0.1 * Rp) - 1);
FLT v0 = asinh(1 / epsilon) / n;
FLT sv0 = sinh(v0);
FLT cv0 = cosh(v0);
FLT t;
for (i = -(n - 1), k = 0; k < n; i += 2, k++) {
t = M_PI * i / (2.0 * n);
pole[k].r = -sv0 * cos(t);
pole[k].i = cv0 * sin(t);
}
LingotComplex gain;
lingot_filter_vector_product(n, pole, &gain);
if ((n & 1) == 0) {// even
FLT f = pow(10.0, -0.05 * Rp);
gain.r *= f;
gain.i *= f;
}
FLT f = pow(W, n);
gain.r *= f;
gain.i *= f;
for (i = 0; i < n; i++) {
pole[i].r *= W;
pole[i].i *= W;
}
// bilinear transform
LingotComplex sp[n];
for (i = 0; i < n; i++) {
sp[i].r = (2.0 - pole[i].r * T) / T;
sp[i].i = (0.0 - pole[i].i * T) / T;
}
LingotComplex tmp1;
LingotComplex aux2;
lingot_filter_vector_product(n, sp, &tmp1);
lingot_complex_div(&gain, &tmp1, &gain);
for (i = 0; i < n; i++) {
tmp1.r = (2.0 + pole[i].r * T);
tmp1.i = (0.0 + pole[i].i * T);
aux2.r = (2.0 - pole[i].r * T);
aux2.i = (0.0 - pole[i].i * T);
lingot_complex_div(&tmp1, &aux2, &pole[i]);
}
// compute filter coefficients from pole/zero values
a[0] = 1.0;
b[0] = 1.0;
new_a[0] = 1.0;
new_b[0] = 1.0;
for (i = 1; i <= n; i++) {
a[i] = 0.0;
b[i] = 0.0;
new_a[i] = 0.0;
new_b[i] = 0.0;
}
if ((n & 1) == 1) // odd
{
// first subfilter is first order
a[1] = -pole[n / 2].r;
b[1] = 1.0;
}
// iterate over the conjugate pairs
for (p = 0; p < n / 2; p++) {
FLT b1 = 2.0;
FLT b2 = 1.0;
FLT a1 = -2.0 * pole[p].r;
FLT a2 = pole[p].r * pole[p].r + pole[p].i * pole[p].i;
// 2nd order subfilter per each pair
new_a[1] = a[1] + a1 * a[0];
new_b[1] = b[1] + b1 * b[0];
// poly multiplication
for (i = 2; i <= n; i++) {
new_a[i] = a[i] + a1 * a[i - 1] + a2 * a[i - 2];
new_b[i] = b[i] + b1 * b[i - 1] + b2 * b[i - 2];
}
for (i = 1; i <= n; i++) {
a[i] = new_a[i];
b[i] = new_b[i];
}
}
gain.r = fabs(gain.r);
for (i = 0; i <= n; i++) {
b[i] *= gain.r;
}
return lingot_filter_new(n, n, a, b);
}
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