/* fft/signals_source.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough
*
* This program 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 3 of the License, or (at
* your option) any later version.
*
* This program 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 this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#include "signals.h"
int
FUNCTION(fft_signal,complex_pulse) (const size_t k,
const size_t n,
const size_t stride,
const BASE z_real,
const BASE z_imag,
BASE data[],
BASE fft[])
{
size_t j;
if (n == 0)
{
GSL_ERROR ("length n must be positive integer", GSL_EDOM);
}
/* gsl_complex pulse at position k, data[j] = z * delta_{jk} */
for (j = 0; j < n; j++)
{
REAL(data,stride,j) = 0.0;
IMAG(data,stride,j) = 0.0;
}
REAL(data,stride,k % n) = z_real;
IMAG(data,stride,k % n) = z_imag;
/* fourier transform, fft[j] = z * exp(-2 pi i j k / n) */
for (j = 0; j < n; j++)
{
const double arg = -2 * M_PI * ((double) ((j * k) % n)) / ((double) n);
const BASE w_real = (BASE)cos (arg);
const BASE w_imag = (BASE)sin (arg);
REAL(fft,stride,j) = w_real * z_real - w_imag * z_imag;
IMAG(fft,stride,j) = w_real * z_imag + w_imag * z_real;
}
return 0;
}
int
FUNCTION(fft_signal,complex_constant) (const size_t n,
const size_t stride,
const BASE z_real,
const BASE z_imag,
BASE data[],
BASE fft[])
{
size_t j;
if (n == 0)
{
GSL_ERROR ("length n must be positive integer", GSL_EDOM);
}
/* constant, data[j] = z */
for (j = 0; j < n; j++)
{
REAL(data,stride,j) = z_real;
IMAG(data,stride,j) = z_imag;
}
/* fourier transform, fft[j] = n z delta_{j0} */
for (j = 0; j < n; j++)
{
REAL(fft,stride,j) = 0.0;
IMAG(fft,stride,j) = 0.0;
}
REAL(fft,stride,0) = ((BASE) n) * z_real;
IMAG(fft,stride,0) = ((BASE) n) * z_imag;
return 0;
}
int
FUNCTION(fft_signal,complex_exp) (const int k,
const size_t n,
const size_t stride,
const BASE z_real,
const BASE z_imag,
BASE data[],
BASE fft[])
{
size_t j;
if (n == 0)
{
GSL_ERROR ("length n must be positive integer", GSL_EDOM);
}
/* exponential, data[j] = z * exp(2 pi i j k) */
for (j = 0; j < n; j++)
{
const double arg = 2 * M_PI * ((double) ((j * k) % n)) / ((double) n);
const BASE w_real = (BASE)cos (arg);
const BASE w_imag = (BASE)sin (arg);
REAL(data,stride,j) = w_real * z_real - w_imag * z_imag;
IMAG(data,stride,j) = w_real * z_imag + w_imag * z_real;
}
/* fourier transform, fft[j] = z * delta{(j - k),0} */
for (j = 0; j < n; j++)
{
REAL(fft,stride,j) = 0.0;
IMAG(fft,stride,j) = 0.0;
}
{
int freq;
if (k <= 0)
{
freq = (n-k) % n ;
}
else
{
freq = (k % n);
};
REAL(fft,stride,freq) = ((BASE) n) * z_real;
IMAG(fft,stride,freq) = ((BASE) n) * z_imag;
}
return 0;
}
int
FUNCTION(fft_signal,complex_exppair) (const int k1,
const int k2,
const size_t n,
const size_t stride,
const BASE z1_real,
const BASE z1_imag,
const BASE z2_real,
const BASE z2_imag,
BASE data[],
BASE fft[])
{
size_t j;
if (n == 0)
{
GSL_ERROR ("length n must be positive integer", GSL_EDOM);
}
/* exponential, data[j] = z1 * exp(2 pi i j k1) + z2 * exp(2 pi i j k2) */
for (j = 0; j < n; j++)
{
const double arg1 = 2 * M_PI * ((double) ((j * k1) % n)) / ((double) n);
const BASE w1_real = (BASE)cos (arg1);
const BASE w1_imag = (BASE)sin (arg1);
const double arg2 = 2 * M_PI * ((double) ((j * k2) % n)) / ((double) n);
const BASE w2_real = (BASE)cos (arg2);
const BASE w2_imag = (BASE)sin (arg2);
REAL(data,stride,j) = w1_real * z1_real - w1_imag * z1_imag;
IMAG(data,stride,j) = w1_real * z1_imag + w1_imag * z1_real;
REAL(data,stride,j) += w2_real * z2_real - w2_imag * z2_imag;
IMAG(data,stride,j) += w2_real * z2_imag + w2_imag * z2_real;
}
/* fourier transform, fft[j] = z1 * delta{(j - k1),0} + z2 *
delta{(j - k2,0)} */
for (j = 0; j < n; j++)
{
REAL(fft,stride,j) = 0.0;
IMAG(fft,stride,j) = 0.0;
}
{
int freq1, freq2;
if (k1 <= 0)
{
freq1 = (n - k1) % n;
}
else
{
freq1 = (k1 % n);
};
if (k2 <= 0)
{
freq2 = (n - k2) % n;
}
else
{
freq2 = (k2 % n);
};
REAL(fft,stride,freq1) += ((BASE) n) * z1_real;
IMAG(fft,stride,freq1) += ((BASE) n) * z1_imag;
REAL(fft,stride,freq2) += ((BASE) n) * z2_real;
IMAG(fft,stride,freq2) += ((BASE) n) * z2_imag;
}
return 0;
}
int
FUNCTION(fft_signal,complex_noise) (const size_t n,
const size_t stride,
BASE data[],
BASE fft[])
{
size_t i;
int status;
if (n == 0)
{
GSL_ERROR ("length n must be positive integer", GSL_EDOM);
}
for (i = 0; i < n; i++)
{
REAL(data,stride,i) = (BASE)urand();
IMAG(data,stride,i) = (BASE)urand();
}
/* compute the dft */
status = FUNCTION(gsl_dft_complex,forward) (data, stride, n, fft);
return status;
}
int
FUNCTION(fft_signal,real_noise) (const size_t n,
const size_t stride,
BASE data[],
BASE fft[])
{
size_t i;
int status;
if (n == 0)
{
GSL_ERROR ("length n must be positive integer", GSL_EDOM);
}
for (i = 0; i < n; i++)
{
REAL(data,stride,i) = (BASE)urand();
IMAG(data,stride,i) = 0.0;
}
/* compute the dft */
status = FUNCTION(gsl_dft_complex,forward) (data, stride, n, fft);
return status;
}