ref: c428282125ba0ccbd085c0cfdc061a55ee64208c
dir: /src/effects_i_dsp.c/
/* libSoX internal DSP functions.
* All public functions & data are prefixed with lsx_ .
*
* Copyright (c) 2008 robs@users.sourceforge.net
*
* This library is free software; you can redistribute it and/or modify it
* under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser
* General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this library; if not, write to the Free Software Foundation,
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#ifdef NDEBUG /* Enable assert always. */
#undef NDEBUG /* Must undef above assert.h or other that might include it. */
#endif
#include "sox_i.h"
#include <assert.h>
#include <string.h>
/* Numerical Recipes cubic spline */
void lsx_prepare_spline3(double const * x, double const * y, int n,
double start_1d, double end_1d, double * y_2d)
{
double p, qn, sig, un, * u = lsx_malloc((n - 1) * sizeof(*u));
int i;
if (start_1d == HUGE_VAL)
y_2d[0] = u[0] = 0; /* Start with natural spline or */
else { /* set the start first derivative */
y_2d[0] = -.5;
u[0] = (3 / (x[1] - x[0])) * ((y[1] - y[0]) / (x[1] - x[0]) - start_1d);
}
for (i = 1; i < n - 1; ++i) {
sig = (x[i] - x[i - 1]) / (x[i + 1] - x[i - 1]);
p = sig * y_2d[i - 1] + 2;
y_2d[i] = (sig - 1) / p;
u[i] = (y[i + 1] - y[i]) / (x[i + 1] - x[i]) -
(y[i] - y[i - 1]) / (x[i] - x[i - 1]);
u[i] = (6 * u[i] / (x[i + 1] - x[i - 1]) - sig * u[i - 1]) / p;
}
if (end_1d == HUGE_VAL)
qn = un = 0; /* End with natural spline or */
else { /* set the end first derivative */
qn = .5;
un = 3 / (x[n - 1] - x[n - 2]) * (end_1d - (y[n - 1] - y[n - 2]) / (x[n - 1] - x[n - 2]));
}
y_2d[n - 1] = (un - qn * u[n - 2]) / (qn * y_2d[n - 2] + 1);
for (i = n - 2; i >= 0; --i)
y_2d[i] = y_2d[i] * y_2d[i + 1] + u[i];
free(u);
}
double lsx_spline3(double const * x, double const * y, double const * y_2d,
int n, double x1)
{
int t, i[2] = {0, 0};
double d, a, b;
for (i[1] = n - 1; i[1] - i[0] > 1; t = (i[1] + i[0]) >> 1, i[x[t] > x1] = t);
d = x[i[1]] - x[i[0]];
assert(d != 0);
a = (x[i[1]] - x1) / d;
b = (x1 - x[i[0]]) / d;
return a * y[i[0]] + b * y[i[1]] +
((a * a * a - a) * y_2d[i[0]] + (b * b * b - b) * y_2d[i[1]]) * d * d / 6;
}
double lsx_bessel_I_0(double x)
{
double term = 1, sum = 1, last_sum, x2 = x / 2;
int i = 1;
do {
double y = x2 / i++;
last_sum = sum, sum += term *= y * y;
} while (sum != last_sum);
return sum;
}
int lsx_set_dft_length(int num_taps) /* Set to 4 x nearest power of 2 */
{
int result, n = num_taps;
for (result = 8; n > 2; result <<= 1, n >>= 1);
result = range_limit(result, 4096, 131072);
assert(num_taps * 2 < result);
return result;
}
#include "fft4g.h"
static int * lsx_fft_br;
static double * lsx_fft_sc;
static int fft_len = -1;
#ifdef HAVE_OPENMP
static omp_lock_t fft_cache_lock;
#endif
void init_fft_cache(void)
{
assert(lsx_fft_br == NULL);
assert(lsx_fft_sc == NULL);
assert(fft_len == -1);
omp_init_lock(&fft_cache_lock);
fft_len = 0;
}
void clear_fft_cache(void)
{
assert(fft_len >= 0);
omp_destroy_lock(&fft_cache_lock);
free(lsx_fft_br);
free(lsx_fft_sc);
lsx_fft_sc = NULL;
lsx_fft_br = NULL;
fft_len = -1;
}
static sox_bool is_power_of_2(int x)
{
return !(x < 2 || (x & (x - 1)));
}
static void update_fft_cache(int len)
{
assert(is_power_of_2(len));
assert(fft_len >= 0);
omp_set_lock(&fft_cache_lock);
if (len > fft_len) {
int old_n = fft_len;
fft_len = len;
lsx_fft_br = lsx_realloc(lsx_fft_br, dft_br_len(fft_len) * sizeof(*lsx_fft_br));
lsx_fft_sc = lsx_realloc(lsx_fft_sc, dft_sc_len(fft_len) * sizeof(*lsx_fft_sc));
if (!old_n)
lsx_fft_br[0] = 0;
}
}
void lsx_safe_rdft(int len, int type, double * d)
{
update_fft_cache(len);
lsx_rdft(len, type, d, lsx_fft_br, lsx_fft_sc);
omp_unset_lock(&fft_cache_lock);
}
void lsx_safe_cdft(int len, int type, double * d)
{
update_fft_cache(len);
lsx_cdft(len, type, d, lsx_fft_br, lsx_fft_sc);
omp_unset_lock(&fft_cache_lock);
}
void lsx_power_spectrum(int n, double const * in, double * out)
{
int i;
double * work = lsx_memdup(in, n * sizeof(*work));
lsx_safe_rdft(n, 1, work);
out[0] = sqr(work[0]);
for (i = 2; i < n; i += 2)
out[i >> 1] = sqr(work[i]) + sqr(work[i + 1]);
out[i >> 1] = sqr(work[1]);
free(work);
}
void lsx_power_spectrum_f(int n, float const * in, float * out)
{
int i;
double * work = lsx_malloc(n * sizeof(*work));
for (i = 0; i< n; ++i) work[i] = in[i];
lsx_safe_rdft(n, 1, work);
out[0] = sqr(work[0]);
for (i = 2; i < n; i += 2)
out[i >> 1] = sqr(work[i]) + sqr(work[i + 1]);
out[i >> 1] = sqr(work[1]);
free(work);
}
void lsx_apply_hann_f(float h[], const int num_points)
{
int i, m = num_points - 1;
for (i = 0; i < num_points; ++i) {
double x = 2 * M_PI * i / m;
h[i] *= .5 - .5 * cos(x);
}
}
void lsx_apply_hann(double h[], const int num_points)
{
int i, m = num_points - 1;
for (i = 0; i < num_points; ++i) {
double x = 2 * M_PI * i / m;
h[i] *= .5 - .5 * cos(x);
}
}
void lsx_apply_hamming(double h[], const int num_points)
{
int i, m = num_points - 1;
for (i = 0; i < num_points; ++i) {
double x = 2 * M_PI * i / m;
h[i] *= .53836 - .46164 * cos(x);
}
}
void lsx_apply_bartlett(double h[], const int num_points)
{
int i, m = num_points - 1;
for (i = 0; i < num_points; ++i) {
h[i] *= 2. / m * (m / 2. - fabs(i - m / 2.));
}
}
void lsx_apply_blackman(double h[], const int num_points, double alpha /*.16*/)
{
int i, m = num_points - 1;
for (i = 0; i < num_points; ++i) {
double x = 2 * M_PI * i / m;
h[i] *= (1 - alpha) *.5 - .5 * cos(x) + alpha * .5 * cos(2 * x);
}
}
void lsx_apply_blackman_nutall(double h[], const int num_points)
{
int i, m = num_points - 1;
for (i = 0; i < num_points; ++i) {
double x = 2 * M_PI * i / m;
h[i] *= .3635819 - .4891775 * cos(x) + .1365995 * cos(2 * x) - .0106411 * cos(3 * x);
}
}
double lsx_kaiser_beta(double att)
{
if (att > 100 ) return .1117 * att - 1.11;
if (att > 50 ) return .1102 * (att - 8.7);
if (att > 20.96) return .58417 * pow(att -20.96, .4) + .07886 * (att - 20.96);
return 0;
}
void lsx_apply_kaiser(double h[], const int num_points, double beta)
{
int i, m = num_points - 1;
for (i = 0; i <= m; ++i) {
double x = 2. * i / m - 1;
h[i] *= lsx_bessel_I_0(beta * sqrt(1 - x * x)) / lsx_bessel_I_0(beta);
}
}
double * lsx_make_lpf(int num_taps, double Fc, double beta, double scale, sox_bool dc_norm)
{
int i, m = num_taps - 1;
double * h = malloc(num_taps * sizeof(*h)), sum = 0;
double mult = scale / lsx_bessel_I_0(beta);
assert(Fc >= 0 && Fc <= 1);
lsx_debug("make_lpf(n=%i, Fc=%g beta=%g dc-norm=%i scale=%g)", num_taps, Fc, beta, dc_norm, scale);
for (i = 0; i <= m / 2; ++i) {
double x = M_PI * (i - .5 * m), y = 2. * i / m - 1;
h[i] = x? sin(Fc * x) / x : Fc;
sum += h[i] *= lsx_bessel_I_0(beta * sqrt(1 - y * y)) * mult;
if (m - i != i)
sum += h[m - i] = h[i];
}
for (i = 0; dc_norm && i < num_taps; ++i) h[i] *= scale / sum;
return h;
}
int lsx_lpf_num_taps(double att, double tr_bw, int k)
{ /* TODO this could be cleaner, esp. for k != 0 */
int n;
if (att <= 80)
n = .25 / M_PI * (att - 7.95) / (2.285 * tr_bw) + .5;
else {
double n160 = (.0425* att - 1.4) / tr_bw; /* Half order for att = 160 */
n = n160 * (16.556 / (att - 39.6) + .8625) + .5; /* For att [80,160) */
}
return k? 2 * n : 2 * (n + (n & 1)) + 1; /* =1 %4 (0 phase 1/2 band) */
}
double * lsx_design_lpf(
double Fp, /* End of pass-band; ~= 0.01dB point */
double Fc, /* Start of stop-band */
double Fn, /* Nyquist freq; e.g. 0.5, 1, PI */
sox_bool allow_aliasing,
double att, /* Stop-band attenuation in dB */
int * num_taps, /* (Single phase.) 0: value will be estimated */
int k) /* Number of phases; 0 for single-phase */
{
double tr_bw, beta;
if (allow_aliasing)
Fc += (Fc - Fp) * LSX_TO_3dB;
Fp /= Fn, Fc /= Fn; /* Normalise to Fn = 1 */
tr_bw = LSX_TO_6dB * (Fc-Fp); /* Transition band-width: 6dB to stop points */
if (!*num_taps)
*num_taps = lsx_lpf_num_taps(att, tr_bw, k);
beta = lsx_kaiser_beta(att);
if (k)
*num_taps = *num_taps * k - 1;
else k = 1;
lsx_debug("%g %g %g", Fp, tr_bw, Fc);
return lsx_make_lpf(*num_taps, (Fc - tr_bw) / k, beta, (double)k, sox_true);
}
static double safe_log(double x)
{
assert(x >= 0);
if (x)
return log(x);
lsx_debug("log(0)");
return -26;
}
void lsx_fir_to_phase(double * * h, int * len, int * post_len, double phase)
{
double * pi_wraps, * work, phase1 = (phase > 50 ? 100 - phase : phase) / 50;
int i, work_len, begin, end, imp_peak = 0, peak = 0;
double imp_sum = 0, peak_imp_sum = 0;
double prev_angle2 = 0, cum_2pi = 0, prev_angle1 = 0, cum_1pi = 0;
for (i = *len, work_len = 2 * 2 * 8; i > 1; work_len <<= 1, i >>= 1);
work = lsx_calloc((size_t)work_len + 2, sizeof(*work)); /* +2: (UN)PACK */
pi_wraps = lsx_malloc((((size_t)work_len + 2) / 2) * sizeof(*pi_wraps));
memcpy(work, *h, *len * sizeof(*work));
lsx_safe_rdft(work_len, 1, work); /* Cepstral: */
LSX_UNPACK(work, work_len);
for (i = 0; i <= work_len; i += 2) {
double angle = atan2(work[i + 1], work[i]);
double detect = 2 * M_PI;
double delta = angle - prev_angle2;
double adjust = detect * ((delta < -detect * .7) - (delta > detect * .7));
prev_angle2 = angle;
cum_2pi += adjust;
angle += cum_2pi;
detect = M_PI;
delta = angle - prev_angle1;
adjust = detect * ((delta < -detect * .7) - (delta > detect * .7));
prev_angle1 = angle;
cum_1pi += fabs(adjust); /* fabs for when 2pi and 1pi have combined */
pi_wraps[i >> 1] = cum_1pi;
work[i] = safe_log(sqrt(sqr(work[i]) + sqr(work[i + 1])));
work[i + 1] = 0;
}
LSX_PACK(work, work_len);
lsx_safe_rdft(work_len, -1, work);
for (i = 0; i < work_len; ++i) work[i] *= 2. / work_len;
for (i = 1; i < work_len / 2; ++i) { /* Window to reject acausal components */
work[i] *= 2;
work[i + work_len / 2] = 0;
}
lsx_safe_rdft(work_len, 1, work);
for (i = 2; i < work_len; i += 2) /* Interpolate between linear & min phase */
work[i + 1] = phase1 * i / work_len * pi_wraps[work_len >> 1] +
(1 - phase1) * (work[i + 1] + pi_wraps[i >> 1]) - pi_wraps[i >> 1];
work[0] = exp(work[0]), work[1] = exp(work[1]);
for (i = 2; i < work_len; i += 2) {
double x = exp(work[i]);
work[i ] = x * cos(work[i + 1]);
work[i + 1] = x * sin(work[i + 1]);
}
lsx_safe_rdft(work_len, -1, work);
for (i = 0; i < work_len; ++i) work[i] *= 2. / work_len;
/* Find peak pos. */
for (i = 0; i <= (int)(pi_wraps[work_len >> 1] / M_PI + .5); ++i) {
imp_sum += work[i];
if (fabs(imp_sum) > fabs(peak_imp_sum)) {
peak_imp_sum = imp_sum;
peak = i;
}
if (work[i] > work[imp_peak]) /* For debug check only */
imp_peak = i;
}
while (peak && fabs(work[peak-1]) > fabs(work[peak]) && work[peak-1] * work[peak] > 0)
--peak;
if (!phase1)
begin = 0;
else if (phase1 == 1)
begin = peak - *len / 2;
else {
begin = (.997 - (2 - phase1) * .22) * *len + .5;
end = (.997 + (0 - phase1) * .22) * *len + .5;
begin = peak - begin - (begin & 1);
end = peak + 1 + end + (end & 1);
*len = end - begin;
*h = lsx_realloc(*h, *len * sizeof(**h));
}
for (i = 0; i < *len; ++i) (*h)[i] =
work[(begin + (phase > 50 ? *len - 1 - i : i) + work_len) & (work_len - 1)];
*post_len = phase > 50 ? peak - begin : begin + *len - (peak + 1);
lsx_debug("nPI=%g peak-sum@%i=%g (val@%i=%g); len=%i post=%i (%g%%)",
pi_wraps[work_len >> 1] / M_PI, peak, peak_imp_sum, imp_peak,
work[imp_peak], *len, *post_len, 100 - 100. * *post_len / (*len - 1));
free(pi_wraps), free(work);
}
void lsx_plot_fir(double * h, int num_points, sox_rate_t rate, sox_plot_t type, char const * title, double y1, double y2)
{
int i, N = lsx_set_dft_length(num_points);
if (type == sox_plot_gnuplot) {
double * h1 = lsx_calloc(N, sizeof(*h1));
double * H = lsx_malloc((N / 2 + 1) * sizeof(*H));
memcpy(h1, h, sizeof(*h1) * num_points);
lsx_power_spectrum(N, h1, H);
printf(
"# gnuplot file\n"
"set title '%s'\n"
"set xlabel 'Frequency (Hz)'\n"
"set ylabel 'Amplitude Response (dB)'\n"
"set grid xtics ytics\n"
"set key off\n"
"plot '-' with lines\n"
, title);
for (i = 0; i <= N/2; ++i)
printf("%g %g\n", i * rate / N, 10 * log10(H[i]));
printf(
"e\n"
"pause -1 'Hit return to continue'\n");
free(H);
free(h1);
}
else if (type == sox_plot_octave) {
printf("%% GNU Octave file (may also work with MATLAB(R) )\nb=[");
for (i = 0; i < num_points; ++i)
printf("%24.16e\n", h[i]);
printf("];\n"
"[h,w]=freqz(b,1,%i);\n"
"plot(%g*w/pi,20*log10(h))\n"
"title('%s')\n"
"xlabel('Frequency (Hz)')\n"
"ylabel('Amplitude Response (dB)')\n"
"grid on\n"
"axis([0 %g %g %g])\n"
"disp('Hit return to continue')\n"
"pause\n"
, N, rate * .5, title, rate * .5, y1, y2);
}
else if (type == sox_plot_data) {
printf("# %s\n"
"# FIR filter\n"
"# rate: %g\n"
"# name: b\n"
"# type: matrix\n"
"# rows: %i\n"
"# columns: 1\n", title, rate, num_points);
for (i = 0; i < num_points; ++i)
printf("%24.16e\n", h[i]);
}
}