kopia lustrzana https://github.com/Dsplib/libdspl-2.0
196 wiersze
6.9 KiB
C
196 wiersze
6.9 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 idft_cmplx(complex_t* x, int n, complex_t* y)
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\brief Inverse discrete Fourier transform of the complex spectrum.
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The function calculates the \f$ n \f$ -point inverse discrete transform
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Fourier complex spectrum \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$.
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\param [in] x
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Pointer to the vector of the input complex signal spectrum \f$ x (m) \f$,
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\f$ m = 0 \ldots n-1 \f$. \n
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The size of the vector is `[n x 1]`. \n \n
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\param [in] n
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The size of the ODPF \f$ n \f$
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(the size of the vectors of the input spectrum and the result of the ODPF). \n
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\n
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\param [out] y
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Pointer to the complex vector of the ODPF 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 ODPF 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_cmplx` function:
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\include idft_cmplx_test.c
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The result of the program:
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\verbatim
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x [0] = 0.000 + 0.000j, z [0] = 0.000 -0.000
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x [1] = 1.000 + 0.000j, z [1] = 1.000 -0.000
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x [2] = 2.000 + 0.000j, z [2] = 2.000 -0.000
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x [3] = 3.000 + 0.000j, z [3] = 3.000 -0.000
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x [4] = 4.000 + 0.000j, z [4] = 4.000 -0.000
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x [5] = 5.000 + 0.000j, z [5] = 5.000 -0.000
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x [6] = 6.000 + 0.000j, z [6] = 6.000 -0.000
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x [7] = 7.000 + 0.000j, z [7] = 7.000 -0.000
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x [8] = 8.000 + 0.000j, z [8] = 8.000 -0.000
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x [9] = 9.000 + 0.000j, z [9] = 9.000 -0.000
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x [10] = 10.000 + 0.000j, z [10] = 10.000 -0.000
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x [11] = 11.000 + 0.000j, z [11] = 11.000 +0.000
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x [12] = 12.000 + 0.000j, z [12] = 12.000 +0.000
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x [13] = 13.000 + 0.000j, z [13] = 13.000 +0.000
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x [14] = 14.000 + 0.000j, z [14] = 14.000 +0.000
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x [15] = 15.000 + 0.000j, z [15] = 15.000 -0.000
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\endverbatim
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\note
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This function performs the calculation of the DFT using the naive method.
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and requires \f$ n ^ 2 \f$ complex multiplications. \n
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To increase the calculation speed, it is recommended
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use 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 idft_cmplx(complex_t* x, int n, complex_t* y)
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\brief Обратное дискретное преобразование Фурье комплексного спектра.
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Функция рассчитывает \f$ n \f$-точечное обратное дискретное преобразование
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Фурье комплексного спектра \f$ 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$.
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\param[in] x
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Указатель на вектор входного комплексного спектра сигнала \f$x(m)\f$,
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\f$ m = 0 \ldots n-1 \f$. \n
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Размер вектора `[n x 1]`. \n \n
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\param[in] n
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Размер ОДПФ \f$n\f$ (размер векторов входного спектра и результата ОДПФ). \n \n
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\param[out] y
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Указатель на комплексный вектор результата ОДПФ \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 ОДПФ рассчитана успешно. \n
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В противном случае \ref ERROR_CODE_GROUP "код ошибки".
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Пример использования функции `dft_cmplx`:
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\include idft_cmplx_test.c
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Результат работы программы:
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\verbatim
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x[ 0] = 0.000 +0.000j, z[ 0] = 0.000 -0.000
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x[ 1] = 1.000 +0.000j, z[ 1] = 1.000 -0.000
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x[ 2] = 2.000 +0.000j, z[ 2] = 2.000 -0.000
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x[ 3] = 3.000 +0.000j, z[ 3] = 3.000 -0.000
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x[ 4] = 4.000 +0.000j, z[ 4] = 4.000 -0.000
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x[ 5] = 5.000 +0.000j, z[ 5] = 5.000 -0.000
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x[ 6] = 6.000 +0.000j, z[ 6] = 6.000 -0.000
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x[ 7] = 7.000 +0.000j, z[ 7] = 7.000 -0.000
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x[ 8] = 8.000 +0.000j, z[ 8] = 8.000 -0.000
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x[ 9] = 9.000 +0.000j, z[ 9] = 9.000 -0.000
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x[10] = 10.000 +0.000j, z[10] = 10.000 -0.000
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x[11] = 11.000 +0.000j, z[11] = 11.000 +0.000
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x[12] = 12.000 +0.000j, z[12] = 12.000 +0.000
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x[13] = 13.000 +0.000j, z[13] = 13.000 +0.000
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x[14] = 14.000 +0.000j, z[14] = 14.000 +0.000
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x[15] = 15.000 +0.000j, z[15] = 15.000 -0.000
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\endverbatim
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\note
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Данная функция выполняет расчет ОДПФ наивным методом
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и требует \f$ n^2 \f$ комплексных умножений. \n
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Для увеличения скорости расчета рекомендуется
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использовать 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 idft_cmplx(complex_t* 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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complex_t e;
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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(e) = cos(phi);
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IM(e) = sin(phi);
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RE(y[k]) += CMRE(x[m], e);
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IM(y[k]) += CMIM(x[m], e);
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}
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RE(y[k]) /= (double)n;
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IM(y[k]) /= (double)n;
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}
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return RES_OK;
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}
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