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/* -*- c++ -*- */
/*
* Copyright 2002,2007,2008,2012,2013,2018 Free Software Foundation, Inc.
*
* This file is part of GNU Radio
*
* SPDX-License-Identifier: GPL-3.0-or-later
*
*/
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <gnuradio/fft/window.h>
#include <gnuradio/math.h>
#include <stdexcept>
namespace gr {
namespace fft {
#define IzeroEPSILON 1E-21 /* Max error acceptable in Izero */
static double Izero(double x)
{
double sum, u, halfx, temp;
int n;
sum = u = n = 1;
halfx = x / 2.0;
do {
temp = halfx / (double)n;
n += 1;
temp *= temp;
u *= temp;
sum += u;
} while (u >= IzeroEPSILON * sum);
return (sum);
}
double midn(int ntaps) { return ntaps / 2.0; }
double midm1(int ntaps) { return (ntaps - 1.0) / 2.0; }
double midp1(int ntaps) { return (ntaps + 1.0) / 2.0; }
double freq(int ntaps) { return 2.0 * GR_M_PI / ntaps; }
double rate(int ntaps) { return 1.0 / (ntaps >> 1); }
double window::max_attenuation(win_type type, double beta)
{
switch (type) {
case (WIN_HAMMING):
return 53;
break;
case (WIN_HANN):
return 44;
break;
case (WIN_BLACKMAN):
return 74;
break;
case (WIN_RECTANGULAR):
return 21;
break;
case (WIN_KAISER):
return (beta / 0.1102 + 8.7);
break;
case (WIN_BLACKMAN_hARRIS):
return 92;
break;
case (WIN_BARTLETT):
return 27;
break;
case (WIN_FLATTOP):
return 93;
break;
default:
throw std::out_of_range("window::max_attenuation: unknown window type provided.");
}
}
std::vector<float> window::coswindow(int ntaps, float c0, float c1, float c2)
{
std::vector<float> taps(ntaps);
float M = static_cast<float>(ntaps - 1);
for (int n = 0; n < ntaps; n++)
taps[n] = c0 - c1 * cosf((2.0f * GR_M_PI * n) / M) +
c2 * cosf((4.0f * GR_M_PI * n) / M);
return taps;
}
std::vector<float> window::coswindow(int ntaps, float c0, float c1, float c2, float c3)
{
std::vector<float> taps(ntaps);
float M = static_cast<float>(ntaps - 1);
for (int n = 0; n < ntaps; n++)
taps[n] = c0 - c1 * cosf((2.0f * GR_M_PI * n) / M) +
c2 * cosf((4.0f * GR_M_PI * n) / M) -
c3 * cosf((6.0f * GR_M_PI * n) / M);
return taps;
}
std::vector<float>
window::coswindow(int ntaps, float c0, float c1, float c2, float c3, float c4)
{
std::vector<float> taps(ntaps);
float M = static_cast<float>(ntaps - 1);
for (int n = 0; n < ntaps; n++)
taps[n] = c0 - c1 * cosf((2.0f * GR_M_PI * n) / M) +
c2 * cosf((4.0f * GR_M_PI * n) / M) -
c3 * cosf((6.0f * GR_M_PI * n) / M) +
c4 * cosf((8.0f * GR_M_PI * n) / M);
return taps;
}
std::vector<float> window::rectangular(int ntaps)
{
std::vector<float> taps(ntaps);
for (int n = 0; n < ntaps; n++)
taps[n] = 1;
return taps;
}
std::vector<float> window::hamming(int ntaps)
{
std::vector<float> taps(ntaps);
float M = static_cast<float>(ntaps - 1);
for (int n = 0; n < ntaps; n++)
taps[n] = 0.54 - 0.46 * cos((2 * GR_M_PI * n) / M);
return taps;
}
std::vector<float> window::hann(int ntaps)
{
std::vector<float> taps(ntaps);
float M = static_cast<float>(ntaps - 1);
for (int n = 0; n < ntaps; n++)
taps[n] = 0.5 - 0.5 * cos((2 * GR_M_PI * n) / M);
return taps;
}
std::vector<float> window::hanning(int ntaps) { return hann(ntaps); }
std::vector<float> window::blackman(int ntaps)
{
return coswindow(ntaps, 0.42, 0.5, 0.08);
}
std::vector<float> window::blackman2(int ntaps)
{
return coswindow(ntaps, 0.34401, 0.49755, 0.15844);
}
std::vector<float> window::blackman3(int ntaps)
{
return coswindow(ntaps, 0.21747, 0.45325, 0.28256, 0.04672);
}
std::vector<float> window::blackman4(int ntaps)
{
return coswindow(ntaps, 0.084037, 0.29145, 0.375696, 0.20762, 0.041194);
}
std::vector<float> window::blackman_harris(int ntaps, int atten)
{
switch (atten) {
case (61):
return coswindow(ntaps, 0.42323, 0.49755, 0.07922);
case (67):
return coswindow(ntaps, 0.44959, 0.49364, 0.05677);
case (74):
return coswindow(ntaps, 0.40271, 0.49703, 0.09392, 0.00183);
case (92):
return coswindow(ntaps, 0.35875, 0.48829, 0.14128, 0.01168);
default:
throw std::out_of_range("window::blackman_harris: unknown attenuation value "
"(must be 61, 67, 74, or 92)");
}
}
std::vector<float> window::blackmanharris(int ntaps, int atten)
{
return blackman_harris(ntaps, atten);
}
std::vector<float> window::nuttal(int ntaps) { return nuttall(ntaps); }
std::vector<float> window::nuttall(int ntaps)
{
return coswindow(ntaps, 0.3635819, 0.4891775, 0.1365995, 0.0106411);
}
std::vector<float> window::blackman_nuttal(int ntaps) { return nuttall(ntaps); }
std::vector<float> window::blackman_nuttall(int ntaps) { return nuttall(ntaps); }
std::vector<float> window::nuttal_cfd(int ntaps) { return nuttall_cfd(ntaps); }
std::vector<float> window::nuttall_cfd(int ntaps)
{
return coswindow(ntaps, 0.355768, 0.487396, 0.144232, 0.012604);
}
std::vector<float> window::flattop(int ntaps)
{
double scale = 4.63867;
return coswindow(
ntaps, 1.0 / scale, 1.93 / scale, 1.29 / scale, 0.388 / scale, 0.028 / scale);
}
std::vector<float> window::kaiser(int ntaps, double beta)
{
if (beta < 0)
throw std::out_of_range("window::kaiser: beta must be >= 0");
std::vector<float> taps(ntaps);
double IBeta = 1.0 / Izero(beta);
double inm1 = 1.0 / ((double)(ntaps - 1));
double temp;
/* extracting first and last element out of the loop, since
sqrt(1.0-temp*temp) might trigger unexpected floating point behaviour
if |temp| = 1.0+epsilon, which can happen for i==0 and
1/i==1/(ntaps-1)==inm1 ; compare
https://github.com/gnuradio/gnuradio/issues/1348 .
In any case, the 0. Bessel function of first kind is 1 at point 0.
*/
taps[0] = IBeta;
for (int i = 1; i < ntaps - 1; i++) {
temp = 2 * i * inm1 - 1;
taps[i] = Izero(beta * sqrt(1.0 - temp * temp)) * IBeta;
}
taps[ntaps - 1] = IBeta;
return taps;
}
std::vector<float> window::bartlett(int ntaps)
{
std::vector<float> taps(ntaps);
float M = static_cast<float>(ntaps - 1);
for (int n = 0; n < ntaps / 2; n++)
taps[n] = 2 * n / M;
for (int n = ntaps / 2; n < ntaps; n++)
taps[n] = 2 - 2 * n / M;
return taps;
}
std::vector<float> window::welch(int ntaps)
{
std::vector<float> taps(ntaps);
double m1 = midm1(ntaps);
double p1 = midp1(ntaps);
for (int i = 0; i < midn(ntaps) + 1; i++) {
taps[i] = 1.0 - pow((i - m1) / p1, 2);
taps[ntaps - i - 1] = taps[i];
}
return taps;
}
std::vector<float> window::parzen(int ntaps)
{
std::vector<float> taps(ntaps);
double m1 = midm1(ntaps);
double m = midn(ntaps);
int i;
for (i = ntaps / 4; i < 3 * ntaps / 4; i++) {
taps[i] = 1.0 - 6.0 * pow((i - m1) / m, 2.0) * (1.0 - fabs(i - m1) / m);
}
for (; i < ntaps; i++) {
taps[i] = 2.0 * pow(1.0 - fabs(i - m1) / m, 3.0);
taps[ntaps - i - 1] = taps[i];
}
return taps;
}
std::vector<float> window::exponential(int ntaps, double d)
{
if (d < 0)
throw std::out_of_range("window::exponential: d must be >= 0");
double m1 = midm1(ntaps);
double p = 1.0 / (8.69 * ntaps / (2.0 * d));
std::vector<float> taps(ntaps);
for (int i = 0; i < midn(ntaps) + 1; i++) {
taps[i] = exp(-fabs(i - m1) * p);
taps[ntaps - i - 1] = taps[i];
}
return taps;
}
std::vector<float> window::riemann(int ntaps)
{
double cx;
double sr1 = freq(ntaps);
double mid = midn(ntaps);
std::vector<float> taps(ntaps);
for (int i = 0; i < mid; i++) {
if (i == midn(ntaps)) {
taps[i] = 1.0;
taps[ntaps - i - 1] = 1.0;
} else {
cx = sr1 * (i - mid);
taps[i] = sin(cx) / cx;
taps[ntaps - i - 1] = sin(cx) / cx;
}
}
return taps;
}
std::vector<float> window::tukey(int ntaps, float a)
{
if ((a < 0) || (a > 1))
throw std::out_of_range("window::tukey: alpha must be between 0 and 1");
float N = static_cast<float>(ntaps - 1);
float aN = a * N;
float p1 = aN / 2.0;
float mid = midn(ntaps);
std::vector<float> taps(ntaps);
for (int i = 0; i < mid; i++) {
if (abs(i) < p1) {
taps[i] = 0.5 * (1.0 - cos((2 * GR_M_PI * i) / (aN)));
taps[ntaps - 1 - i] = taps[i];
} else {
taps[i] = 1.0;
taps[ntaps - i - 1] = 1.0;
}
}
return taps;
}
std::vector<float> window::gaussian(int ntaps, float sigma)
{
if (sigma <= 0)
throw std::out_of_range("window::gaussian: sigma must be > 0");
float a = 2 * sigma * sigma;
double m1 = midm1(ntaps);
std::vector<float> taps(ntaps);
for (int i = 0; i < midn(ntaps); i++) {
float N = (i - m1);
taps[i] = exp(-(N * N / a));
taps[ntaps - 1 - i] = taps[i];
}
return taps;
}
std::vector<float> window::build(win_type type, int ntaps, double beta)
{
switch (type) {
case WIN_RECTANGULAR:
return rectangular(ntaps);
case WIN_HAMMING:
return hamming(ntaps);
case WIN_HANN:
return hann(ntaps);
case WIN_BLACKMAN:
return blackman(ntaps);
case WIN_BLACKMAN_hARRIS:
return blackman_harris(ntaps);
case WIN_KAISER:
return kaiser(ntaps, beta);
case WIN_BARTLETT:
return bartlett(ntaps);
case WIN_FLATTOP:
return flattop(ntaps);
default:
throw std::out_of_range("window::build: type out of range");
}
}
} /* namespace fft */
} /* namespace gr */
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