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