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