/*
* Copyright (c) 2015-2019 Sergey Bakhurin
* Digital Signal Processing Library [http://dsplib.org]
*
* This file is part of libdspl-2.0.
*
* 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 3 of the License, or
* (at your option) any later version.
*
* DSPL 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 Lesser General Public License
* along with Foobar. If not, see .
*/
#include
#include
#include "dspl.h"
#ifdef DOXYGEN_ENGLISH
/*! ****************************************************************************
\ingroup DFT_GROUP
\fn int dft(double* x, int n, complex_t* y)
\brief Discrete Fourier transform of a real signal.
The function calculates the \f$ n \f$ -point discrete Fourier transform
real signal \f$ x (m) \f$, \f$ m = 0 \ldots n-1 \f$. \n
\f[
Y (k) = \sum_ {m = 0} ^ {n-1} x (m)
\exp \left (-j \frac {2 \pi} {n} m k \right),
\f]
where \f$ k = 0 \ldots n-1 \f$.
\param [in] x
Pointer to the vector of the real input signal \f$ x (m) \f$,
\f$ m = 0 \ldots n-1 \f$. \n
The size of the vector is `[n x 1]`. \n \n
\param [in] n
The size of the DFT \f$ n \f$
(the size of the vectors of the input signal and the result of the DFT). \n \n
\param [out] y
Pointer to the complex vector of the DFT result \f$ Y (k) \f$,
\f$ k = 0 \ldots n-1 \f$.
The size of the vector is `[n x 1]`. \n
Memory must be allocated. \n \n
\return
`RES_OK` if the DFT is calculated successfully. \n
Otherwise, \ref ERROR_CODE_GROUP "error code".
An example of using the `dft` function:
\include dft_test.c
The result of the program:
\verbatim
y [0] = 120.000 0.000
y [1] = -8.000 40.219
y [2] = -8.000 19.314
y [3] = -8.000 11.973
y [4] = -8.000 8.000
y [5] = -8.000 5.345
y [6] = -8.000 3.314
y [7] = -8.000 1.591
y [8] = -8.000 0.000
y [9] = -8.000 -1.591
y [10] = -8.000 -3.314
y [11] = -8.000 -5.345
y [12] = -8.000 -8.000
y [13] = -8.000 -11.973
y [14] = -8.000 -19.314
y [15] = -8.000 -40.219
\endverbatim
\note
This function performs the DFT calculation using the naive method and
requires \f$ n ^ 2 \f$ complex multiplications. \n
To increase the calculation speed, it is recommended to use
fast Fourier transform algorithms.
\author Bakhurin Sergey www.dsplib.org
**************************************************************************** */
#endif
#ifdef DOXYGEN_RUSSIAN
/*! ****************************************************************************
\ingroup DFT_GROUP
\fn int dft(double* x, int n, complex_t* y)
\brief Дискретное преобразование Фурье вещественного сигнала.
Функция рассчитывает \f$ n \f$-точечное дискретное преобразование Фурье
вещественного сигнала \f$ x(m) \f$, \f$ m = 0 \ldots n-1 \f$. \n
\f[
Y(k) = \sum_{m = 0}^{n-1} x(m)
\exp \left( -j \frac{2\pi}{n} m k \right),
\f]
где \f$ k = 0 \ldots n-1 \f$.
\param[in] x
Указатель на вектор вещественного входного сигнала \f$x(m)\f$,
\f$ m = 0 \ldots n-1 \f$. \n
Размер вектора `[n x 1]`. \n \n
\param[in] n
Размер ДПФ \f$n\f$ (размер векторов входного сигнала и результата ДПФ). \n \n
\param[out] y
Указатель на комплексный вектор результата ДПФ \f$Y(k)\f$,
\f$ k = 0 \ldots n-1 \f$.
Размер вектора `[n x 1]`. \n
Память должна быть выделена. \n \n
\return
`RES_OK` если ДПФ рассчитана успешно. \n
В противном случае \ref ERROR_CODE_GROUP "код ошибки".
Пример использования функции `dft`:
\include dft_test.c
Результат работы программы:
\verbatim
y[ 0] = 120.000 0.000
y[ 1] = -8.000 40.219
y[ 2] = -8.000 19.314
y[ 3] = -8.000 11.973
y[ 4] = -8.000 8.000
y[ 5] = -8.000 5.345
y[ 6] = -8.000 3.314
y[ 7] = -8.000 1.591
y[ 8] = -8.000 0.000
y[ 9] = -8.000 -1.591
y[10] = -8.000 -3.314
y[11] = -8.000 -5.345
y[12] = -8.000 -8.000
y[13] = -8.000 -11.973
y[14] = -8.000 -19.314
y[15] = -8.000 -40.219
\endverbatim
\note
Данная функция выполняет расчет ДПФ наивным методом и требует \f$ n^2 \f$
комплексных умножений. \n
Для увеличения скорости расчета рекомендуется использовать
алгоритмы быстрого преобразования Фурье.
\author Бахурин Сергей www.dsplib.org
***************************************************************************** */
#endif
int DSPL_API dft(double* x, int n, complex_t* y)
{
int k;
int m;
double divn;
double phi;
if(!x || !y)
return ERROR_PTR;
if(n<1)
return ERROR_SIZE;
divn = 1.0 / (double)n;
for(k = 0; k < n; k++)
{
RE(y[k]) = IM(y[k]) = 0.0;
for(m = 0; m < n; m++)
{
phi = -M_2PI * divn * (double)k * (double)m;
RE(y[k]) += x[m] * cos(phi);
IM(y[k]) += x[m] * sin(phi);
}
}
return RES_OK;
}