kopia lustrzana https://github.com/Dsplib/libdspl-2.0
1057 wiersze
33 KiB
C
1057 wiersze
33 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 <string.h>
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#include "dspl.h"
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#ifdef DOXYGEN_ENGLISH
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/*! ****************************************************************************
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\ingroup FILTER_CONV_GROUP
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\fn int conv(double* a, int na, double* b, int nb, double* c)
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\brief Real vectors linear convolution.
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Function convolves two real vectors \f$ c = a * b\f$ length `na` and `nb`.
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The output convolution is a vector `c` with length equal to `na + nb - 1`.
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\param[in] a
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Pointer to the first vector `a`. \n
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Vector size is `[na x 1]`. \n \n
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\param[in] na
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Size of the first vector `a`. \n \n
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\param[in] b
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Pointer to the second vector `b`. \n
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Vector size is `[nb x 1]`. \n \n
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\param[in] nb
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Size of the second vector `b`. \n \n
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\param[out] c
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Pointer to the convolution output vector \f$ c = a * b\f$. \n
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Vector size is `[na + nb - 1 x 1]`. \n
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Memory must be allocated. \n \n
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\return `RES_OK` if convolution is calculated successfully. \n
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Else \ref ERROR_CODE_GROUP "code error".
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\note If vectors `a` and `b` are coefficients of two polynomials,
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then convolution of the vectors `a` and `b` returns polynomial product
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coefficients.
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Example:
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\code{.cpp}
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double ar[3] = {1.0, 2.0, 3.0};
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double br[4] = {3.0, -1.0, 2.0, 4.0};
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double cr[6];
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int n;
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conv(ar, 3, br, 4, cr);
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for(n = 0; n < 6; n++)
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printf("cr[%d] = %5.1f\n", n, cr[n]);
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\endcode
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\n
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Output:
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\verbatim
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cr[0] = 3.0
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cr[1] = 5.0
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cr[2] = 9.0
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cr[3] = 5.0
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cr[4] = 14.0
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cr[5] = 12.0
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\endverbatim
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\author Sergey Bakhurin 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 FILTER_CONV_GROUP
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\fn int conv(double* a, int na, double* b, int nb, double* c)
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\brief Линейная свертка двух вещественных векторов
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Функция рассчитывает линейную свертку двух векторов \f$ c = a * b\f$.
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\param[in] a
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Указатель на первый вектор \f$a\f$. \n
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Размер вектора `[na x 1]`. \n \n
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\param[in] na
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Размер первого вектора. \n \n
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\param[in] b
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Указатель на второй вектор \f$b\f$. \n
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Размер вектора `[nb x 1]`. \n \n
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\param[in] nb
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Размер второго вектора. \n \n
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\param[out] c
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Указатель на вектор свертки \f$ c = a * b\f$. \n
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Размер вектора `[na + nb - 1 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 свертка расчитана успешно. \n
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В противном случае \ref ERROR_CODE_GROUP "код ошибки".
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\note
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Если вектора `a` и `b` представляют собой коэффициенты двух полиномов,
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то результат линейной свертки представляет собой коэффициенты произведения
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исходных полиномов.
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Пример использования функции:
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\code{.cpp}
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double ar[3] = {1.0, 2.0, 3.0};
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double br[4] = {3.0, -1.0, 2.0, 4.0};
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double cr[6];
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int n;
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conv(ar, 3, br, 4, cr);
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for(n = 0; n < 6; n++)
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printf("cr[%d] = %5.1f \n ", n, cr[n]);
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\endcode
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\n
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Результат работы:
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\verbatim
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cr[0] = 3.0
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cr[1] = 5.0
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cr[2] = 9.0
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cr[3] = 5.0
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cr[4] = 14.0
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cr[5] = 12.0
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\endverbatim
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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 conv(double* a, int na, double* b, int nb, double* c)
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{
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int k;
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int n;
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double *t;
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size_t bufsize;
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if(!a || !b || !c)
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return ERROR_PTR;
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if(na < 1 || nb < 1)
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return ERROR_SIZE;
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bufsize = (na + nb - 1) * sizeof(double);
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if((a != c) && (b != c))
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t = c;
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else
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t = (double*)malloc(bufsize);
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memset(t, 0, bufsize);
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for(k = 0; k < na; k++)
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for(n = 0; n < nb; n++)
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t[k+n] += a[k]*b[n];
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if(t!=c)
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{
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memcpy(c, t, bufsize);
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free(t);
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}
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return RES_OK;
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}
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#ifdef DOXYGEN_ENGLISH
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/*! ****************************************************************************
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\ingroup FILTER_CONV_GROUP
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\fn int conv_cmplx(complex_t* a, int na, complex_t* b, int nb, complex_t* c)
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\brief Complex vectors linear convolution.
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Function convolves two complex vectors \f$ c = a * b\f$ length `na` and `nb`.
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The output convolution is a vector `c` with length equal to `na + nb - 1`.
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\param[in] a
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Pointer to the first vector `a`. \n
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Vector size is `[na x 1]`. \n \n
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\param[in] na
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Size of the first vector `a`. \n \n
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\param[in] b
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Pointer to the second vector `b`. \n
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Vector size is `[nb x 1]`. \n \n
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\param[in] nb
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Size of the second vector `b`. \n \n
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\param[out] c
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Pointer to the convolution output vector \f$ c = a * b\f$. \n
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Vector size is `[na + nb - 1 x 1]`. \n
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Memory must be allocated. \n \n
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\return `RES_OK` if convolution is calculated successfully. \n
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Else \ref ERROR_CODE_GROUP "code error".
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\note If vectors `a` and `b` are coefficients of two polynomials,
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then convolution of the vectors `a` and `b` returns polynomial product
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coefficients.
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Example:
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\code{.cpp}
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complex_t ac[3] = {{0.0, 1.0}, {1.0, 1.0}, {2.0, 2.0}};
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complex_t bc[4] = {{3.0, 3.0}, {4.0, 4.0}, {5.0, 5.0}, {6.0, 6.0}};
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complex_t cc[6];
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int n;
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conv_cmplx(ac, 3, bc, 4, cc);
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for(n = 0; n < 6; n++)
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printf("cc[%d] = %5.1f%+5.1fj\n", n, RE(cc[n]),IM(cc[n]));
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\endcode
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\n
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Output:
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\verbatim
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cc[0] = -3.0 +3.0j
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cc[1] = -4.0+10.0j
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cc[2] = -5.0+25.0j
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cc[3] = -6.0+32.0j
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cc[4] = 0.0+32.0j
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cc[5] = 0.0+24.0j
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\endverbatim
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\author Sergey Bakhurin 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 FILTER_CONV_GROUP
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\fn int conv_cmplx(complex_t* a, int na, complex_t* b, int nb, complex_t* c)
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\brief Линейная свертка двух комплексных векторов
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Функция рассчитывает линейную свертку двух векторов \f$ c = a * b\f$.
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\param[in] a
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Указатель на первый вектор \f$a\f$. \n
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Размер вектора `[na x 1]`. \n \n
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\param[in] na
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Размер первого вектора. \n \n
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\param[in] b
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Указатель на второй вектор \f$b\f$. \n
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Размер вектора `[nb x 1]`. \n \n
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\param[in] nb
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Размер второго вектора. \n \n
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\param[out] c
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Указатель на вектор свертки \f$ c = a * b\f$. \n
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Размер вектора `[na + nb - 1 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 свертка рассчитана успешно. \n
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В противном случае \ref ERROR_CODE_GROUP "код ошибки".
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\note
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Если векторы `a` и `b` представляют собой коэффициенты двух полиномов,
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то результат линейной свертки представляет собой коэффициенты произведения
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исходных полиномов.
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Пример использования функции:
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\code{.cpp}
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complex_t ac[3] = {{0.0, 1.0}, {1.0, 1.0}, {2.0, 2.0}};
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complex_t bc[4] = {{3.0, 3.0}, {4.0, 4.0}, {5.0, 5.0}, {6.0, 6.0}};
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complex_t cc[6];
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int n;
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conv_cmplx(ac, 3, bc, 4, cc);
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for(n = 0; n < 6; n++)
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printf("cc[%d] = %5.1f%+5.1fj \n ", n, RE(cc[n]),IM(cc[n]));
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\endcode
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\n
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Результат работы:
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\verbatim
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cc[0] = -3.0 +3.0j
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cc[1] = -4.0+10.0j
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cc[2] = -5.0+25.0j
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cc[3] = -6.0+32.0j
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cc[4] = 0.0+32.0j
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cc[5] = 0.0+24.0j
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\endverbatim
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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 conv_cmplx(complex_t* a, int na, complex_t* b,
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int nb, complex_t* c)
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{
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int k;
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int n;
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complex_t *t;
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size_t bufsize;
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if(!a || !b || !c)
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return ERROR_PTR;
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if(na < 1 || nb < 1)
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return ERROR_SIZE;
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bufsize = (na + nb - 1) * sizeof(complex_t);
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if((a != c) && (b != c))
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t = c;
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else
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t = (complex_t*)malloc(bufsize);
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memset(t, 0, bufsize);
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for(k = 0; k < na; k++)
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{
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for(n = 0; n < nb; n++)
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{
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RE(t[k+n]) += CMRE(a[k], b[n]);
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IM(t[k+n]) += CMIM(a[k], b[n]);
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}
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}
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if(t!=c)
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{
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memcpy(c, t, bufsize);
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free(t);
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}
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return RES_OK;
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}
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#ifdef DOXYGEN_ENGLISH
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/*! ****************************************************************************
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\ingroup FILTER_CONV_GROUP
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\fn int conv_fft(double* a, int na, double* b, int nb,
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fft_t* pfft, int nfft, double* c)
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\brief Real vectors fast linear convolution by using fast Fourier
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transform algorithms
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Function convolves two real vectors \f$ c = a * b\f$ length `na` and `nb`
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in the frequency domain by using FFT algorithms. This approach provide
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high-performance convolution which increases with `na` and `nb` increasing.
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The output convolution is a vector `c` with length equal to `na + nb - 1`.
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\param[in] a
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Pointer to the first vector `a`. \n
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Vector size is `[na x 1]`. \n \n
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\param[in] na
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Size of the first vector `a`. \n \n
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\param[in] b
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Pointer to the second vector `b`. \n
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Vector size is `[nb x 1]`. \n \n
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\param[in] nb
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Size of the second vector `b`. \n \n
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\param[in] pfft
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Pointer to the structure `fft_t`. \n
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Function changes `fft_t` structure fields so `fft_t` must
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be clear before program returns. \n \n
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\param[in] nfft
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FFT size. \n
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This parameter set which FFT size will be used
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for overlapped frequency domain convolution. \n
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FFT size must be more of minimal `na` and `nb` value.
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For example if `na = 10`, `nb = 4` then `nfft` parameter must
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be more than 4. \n
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\param[out] c
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Pointer to the convolution output vector \f$ c = a * b\f$. \n
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Vector size is `[na + nb - 1 x 1]`. \n
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Memory must be allocated. \n \n
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\return `RES_OK` if convolution is calculated successfully. \n
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Else \ref ERROR_CODE_GROUP "code error". \n \n
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Example:
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\include conv_fft_test.c
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Program output:
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\verbatim
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conv_fft error: 0x00000000
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conv error: 0x00000000
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c[ 0] = -0.00 d[ 0] = 0.00
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c[ 1] = -0.00 d[ 1] = 0.00
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c[ 2] = 1.00 d[ 2] = 1.00
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c[ 3] = 4.00 d[ 3] = 4.00
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c[ 4] = 10.00 d[ 4] = 10.00
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c[ 5] = 20.00 d[ 5] = 20.00
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c[ 6] = 35.00 d[ 6] = 35.00
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c[ 7] = 56.00 d[ 7] = 56.00
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c[ 8] = 77.00 d[ 8] = 77.00
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c[ 9] = 98.00 d[ 9] = 98.00
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c[ 10] = 119.00 d[ 10] = 119.00
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c[ 11] = 140.00 d[ 11] = 140.00
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c[ 12] = 161.00 d[ 12] = 161.00
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c[ 13] = 182.00 d[ 13] = 182.00
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c[ 14] = 190.00 d[ 14] = 190.00
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c[ 15] = 184.00 d[ 15] = 184.00
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c[ 16] = 163.00 d[ 16] = 163.00
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c[ 17] = 126.00 d[ 17] = 126.00
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c[ 18] = 72.00 d[ 18] = 72.00
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\endverbatim
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\author Sergey Bakhurin www.dsplib.org
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***************************************************************************** */
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#endif
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||
#ifdef DOXYGEN_RUSSIAN
|
||
/*! ****************************************************************************
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\ingroup FILTER_CONV_GROUP
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\fn int conv_fft(double* a, int na, double* b, int nb,
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fft_t* pfft, double* c)
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\brief Линейная свертка двух вещественных векторов с использованием алгоритмов
|
||
быстрого преобразования Фурье
|
||
|
||
Функция рассчитывает линейную свертку двух векторов \f$ c = a * b\f$ используя
|
||
секционную обработку с перекрытием в частотной области. Это позволяет сократить
|
||
вычислительные операции при расчете длинных сверток.
|
||
|
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\param[in] a
|
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Указатель на первый вектор \f$a\f$. \n
|
||
Размер вектора `[na x 1]`. \n \n
|
||
|
||
\param[in] na
|
||
Размер первого вектора. \n \n
|
||
|
||
\param[in] b
|
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Указатель на второй вектор \f$b\f$. \n
|
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Размер вектора `[nb x 1]`. \n \n
|
||
|
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\param[in] nb
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Размер второго вектора. \n \n
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|
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\param[in] pfft
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Указатель на структуру `fft_t` алгоритма
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быстрого преобразования Фурье. \n
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||
Функция изменит состояние полей структуры `fft_t`,
|
||
поэтому структура должна быть очищена перед выходом из
|
||
программы для исключения утечек памяти. \n
|
||
|
||
\param[in] nfft
|
||
Размер алгоритма БПФ который будет использован для расчета
|
||
секционной свертки с перекрытием. \n
|
||
Данный параметр должен быть больше чем минимальное значение
|
||
размеров сворачиваемых векторов. \n
|
||
Например если `na=10`, а `nb=4`, то параметр `nfft` должен быть больше 4. \n
|
||
Библиотека поддерживает алгоритмы БПФ составной длины
|
||
\f$n = n_0 \times n_1 \times n_2 \times \ldots \times n_p \times m\f$,
|
||
где \f$n_i = 2,3,5,7\f$, а \f$m \f$ --- произвольный простой множитель
|
||
не превосходящий 46340 (см. описание функции \ref fft_create).
|
||
Однако, максимальное быстродействие достигается при использовании длин равных
|
||
степени двойки.
|
||
|
||
\param[out] c
|
||
Указатель на вектор свертки \f$ c = a * b\f$. \n
|
||
Размер вектора `[na + nb - 1 x 1]`. \n
|
||
Память должна быть выделена. \n \n
|
||
|
||
\return
|
||
`RES_OK` если свертка рассчитана успешно. \n
|
||
В противном случае \ref ERROR_CODE_GROUP "код ошибки".
|
||
|
||
\note
|
||
Данная функция наиболее эффективна при вычислении длинных сверток.
|
||
|
||
Пример использования функции:
|
||
|
||
\include conv_fft_test.c
|
||
|
||
Результат работы:
|
||
\verbatim
|
||
|
||
conv_fft error: 0x00000000
|
||
conv error: 0x00000000
|
||
c[ 0] = -0.00 d[ 0] = 0.00
|
||
c[ 1] = -0.00 d[ 1] = 0.00
|
||
c[ 2] = 1.00 d[ 2] = 1.00
|
||
c[ 3] = 4.00 d[ 3] = 4.00
|
||
c[ 4] = 10.00 d[ 4] = 10.00
|
||
c[ 5] = 20.00 d[ 5] = 20.00
|
||
c[ 6] = 35.00 d[ 6] = 35.00
|
||
c[ 7] = 56.00 d[ 7] = 56.00
|
||
c[ 8] = 77.00 d[ 8] = 77.00
|
||
c[ 9] = 98.00 d[ 9] = 98.00
|
||
c[ 10] = 119.00 d[ 10] = 119.00
|
||
c[ 11] = 140.00 d[ 11] = 140.00
|
||
c[ 12] = 161.00 d[ 12] = 161.00
|
||
c[ 13] = 182.00 d[ 13] = 182.00
|
||
c[ 14] = 190.00 d[ 14] = 190.00
|
||
c[ 15] = 184.00 d[ 15] = 184.00
|
||
c[ 16] = 163.00 d[ 16] = 163.00
|
||
c[ 17] = 126.00 d[ 17] = 126.00
|
||
c[ 18] = 72.00 d[ 18] = 72.00
|
||
\endverbatim
|
||
|
||
\author Бахурин Сергей. www.dsplib.org
|
||
***************************************************************************** */
|
||
#endif
|
||
int DSPL_API conv_fft(double* a, int na, double* b, int nb,
|
||
fft_t* pfft, int nfft, double* c)
|
||
{
|
||
complex_t *pa = NULL, *pb = NULL, *pc = NULL;
|
||
int err;
|
||
|
||
if(!a || !b || !c || !pfft)
|
||
return ERROR_PTR;
|
||
if(na<1 || nb < 1)
|
||
return ERROR_SIZE;
|
||
if(nfft<2)
|
||
return ERROR_FFT_SIZE;
|
||
|
||
pa = (complex_t*) malloc(na*sizeof(complex_t));
|
||
pb = (complex_t*) malloc(nb*sizeof(complex_t));
|
||
pc = (complex_t*) malloc((na+nb-1)*sizeof(complex_t));
|
||
|
||
re2cmplx(a, na, pa);
|
||
re2cmplx(b, nb, pb);
|
||
|
||
err = conv_fft_cmplx(pa, na, pb, nb, pfft, nfft, pc);
|
||
if(err != RES_OK)
|
||
goto exit_label;
|
||
|
||
err = cmplx2re(pc, na+nb-1, c, NULL);
|
||
|
||
exit_label:
|
||
if(pa) free(pa);
|
||
if(pb) free(pb);
|
||
if(pc) free(pc);
|
||
|
||
return err;
|
||
}
|
||
|
||
|
||
|
||
#ifdef DOXYGEN_ENGLISH
|
||
/*! ****************************************************************************
|
||
\ingroup FILTER_CONV_GROUP
|
||
\fn int conv_fft_cmplx(complex_t* a, int na, complex_t* b, int nb,
|
||
fft_t* pfft, int nfft, complex_t* c)
|
||
\brief Complex vectors fast linear convolution by using fast Fourier
|
||
transform algorithms
|
||
|
||
Function convolves two complex vectors \f$ c = a * b\f$ length `na` and `nb`
|
||
in the frequency domain by using FFT algorithms. This approach provide
|
||
high-performance convolution which increases with `na` and `nb` increasing.
|
||
The output convolution is a vector `c` with length equal to `na + nb - 1`.
|
||
|
||
\param[in] a
|
||
Pointer to the first vector `a`. \n
|
||
Vector size is `[na x 1]`. \n \n
|
||
|
||
\param[in] na
|
||
Size of the first vector `a`. \n \n
|
||
|
||
\param[in] b
|
||
Pointer to the second vector `b`. \n
|
||
Vector size is `[nb x 1]`. \n \n
|
||
|
||
\param[in] nb
|
||
Size of the second vector `b`. \n \n
|
||
|
||
\param[in] pfft
|
||
Pointer to the structure `fft_t`. \n
|
||
Function changes `fft_t` structure fields so `fft_t` must
|
||
be clear before program returns. \n \n
|
||
|
||
\param[in] nfft
|
||
FFT size. \n
|
||
This parameter set which FFT size will be used
|
||
for overlapped frequency domain convolution. \n
|
||
FFT size must be more of minimal `na` and `nb` value.
|
||
For example if `na = 10`, `nb = 4` then `nfft` parameter must
|
||
be more than 4. \n
|
||
|
||
\param[out] c
|
||
Pointer to the convolution output vector \f$ c = a * b\f$. \n
|
||
Vector size is `[na + nb - 1 x 1]`. \n
|
||
Memory must be allocated. \n \n
|
||
|
||
\return `RES_OK` if convolution is calculated successfully. \n
|
||
Else \ref ERROR_CODE_GROUP "code error". \n \n
|
||
|
||
Example:
|
||
\include conv_fft_cmplx_test.c
|
||
|
||
Program output:
|
||
|
||
\verbatim
|
||
c[ 0] = -1.00 -0.00j d[ 0] = -1.00 +0.00j
|
||
c[ 1] = -6.00 +4.00j d[ 1] = -6.00 +4.00j
|
||
c[ 2] = -15.00 +20.00j d[ 2] = -15.00 +20.00j
|
||
c[ 3] = -28.00 +56.00j d[ 3] = -28.00 +56.00j
|
||
c[ 4] = -45.00 +120.00j d[ 4] = -45.00 +120.00j
|
||
c[ 5] = -55.00 +210.00j d[ 5] = -55.00 +210.00j
|
||
c[ 6] = -65.00 +300.00j d[ 6] = -65.00 +300.00j
|
||
c[ 7] = -75.00 +390.00j d[ 7] = -75.00 +390.00j
|
||
c[ 8] = -85.00 +480.00j d[ 8] = -85.00 +480.00j
|
||
c[ 9] = -95.00 +570.00j d[ 9] = -95.00 +570.00j
|
||
c[ 10] = -105.00 +660.00j d[ 10] = -105.00 +660.00j
|
||
c[ 11] = -115.00 +750.00j d[ 11] = -115.00 +750.00j
|
||
c[ 12] = -125.00 +840.00j d[ 12] = -125.00 +840.00j
|
||
c[ 13] = -135.00 +930.00j d[ 13] = -135.00 +930.00j
|
||
c[ 14] = -145.00 +1020.00j d[ 14] = -145.00 +1020.00j
|
||
c[ 15] = -124.00 +1080.00j d[ 15] = -124.00 +1080.00j
|
||
c[ 16] = -99.00 +1016.00j d[ 16] = -99.00 +1016.00j
|
||
c[ 17] = -70.00 +820.00j d[ 17] = -70.00 +820.00j
|
||
c[ 18] = -37.00 +484.00j d[ 18] = -37.00 +484.00j
|
||
\endverbatim
|
||
|
||
\author Sergey Bakhurin www.dsplib.org
|
||
***************************************************************************** */
|
||
#endif
|
||
#ifdef DOXYGEN_RUSSIAN
|
||
/*! ****************************************************************************
|
||
\ingroup FILTER_CONV_GROUP
|
||
\fn int conv_fft_cmplx(complex_t* a, int na, complex_t* b, int nb,
|
||
fft_t* pfft, complex_t* c)
|
||
\brief Линейная свертка двух комплексных векторов с использованием алгоритмов
|
||
быстрого преобразования Фурье
|
||
|
||
Функция рассчитывает линейную свертку двух векторов \f$ c = a * b\f$ используя
|
||
секционную обработку с перекрытием в частотной области. Это позволяет сократить
|
||
вычислительные операции при расчете длинных сверток.
|
||
|
||
\param[in] a
|
||
Указатель на первый вектор \f$a\f$. \n
|
||
Размер вектора `[na x 1]`. \n \n
|
||
|
||
\param[in] na
|
||
Размер первого вектора. \n \n
|
||
|
||
\param[in] b
|
||
Указатель на второй вектор \f$b\f$. \n
|
||
Размер вектора `[nb x 1]`. \n \n
|
||
|
||
\param[in] nb
|
||
Размер второго вектора. \n \n
|
||
|
||
\param[in] pfft
|
||
Указатель на структуру `fft_t` алгоритма
|
||
быстрого преобразования Фурье. \n
|
||
Функция изменит состояние полей структуры `fft_t`,
|
||
поэтому структура должна быть очищена перед выходом из
|
||
программы для исключения утечек памяти. \n
|
||
|
||
\param[in] nfft
|
||
Размер алгоритма БПФ который будет использован для расчета
|
||
секционной свертки с перекрытием. \n
|
||
Данный параметр должен быть больше чем минимальное значение
|
||
размеров сворачиваемых векторов. \n
|
||
Например если `na=10`, а `nb=4`, то параметр `nfft` должен быть больше 4. \n
|
||
Библиотека поддерживает алгоритмы БПФ составной длины
|
||
\f$n = n_0 \times n_1 \times n_2 \times \ldots \times n_p \times m\f$,
|
||
где \f$n_i = 2,3,5,7\f$, а \f$m \f$ --- произвольный простой множитель
|
||
не превосходящий 46340 (см. описание функции \ref fft_create).
|
||
Однако, максимальное быстродействие достигается при использовании длин равных
|
||
степени двойки.
|
||
|
||
\param[out] c
|
||
Указатель на вектор свертки \f$ c = a * b\f$. \n
|
||
Размер вектора `[na + nb - 1 x 1]`. \n
|
||
Память должна быть выделена. \n \n
|
||
|
||
\return
|
||
`RES_OK` если свертка рассчитана успешно. \n
|
||
В противном случае \ref ERROR_CODE_GROUP "код ошибки".
|
||
|
||
\note
|
||
Данная функция наиболее эффективна при вычислении длинных сверток.
|
||
|
||
Пример использования функции:
|
||
|
||
\include conv_fft_cmplx_test.c
|
||
|
||
Результат работы:
|
||
\verbatim
|
||
c[ 0] = -1.00 -0.00j d[ 0] = -1.00 +0.00j
|
||
c[ 1] = -6.00 +4.00j d[ 1] = -6.00 +4.00j
|
||
c[ 2] = -15.00 +20.00j d[ 2] = -15.00 +20.00j
|
||
c[ 3] = -28.00 +56.00j d[ 3] = -28.00 +56.00j
|
||
c[ 4] = -45.00 +120.00j d[ 4] = -45.00 +120.00j
|
||
c[ 5] = -55.00 +210.00j d[ 5] = -55.00 +210.00j
|
||
c[ 6] = -65.00 +300.00j d[ 6] = -65.00 +300.00j
|
||
c[ 7] = -75.00 +390.00j d[ 7] = -75.00 +390.00j
|
||
c[ 8] = -85.00 +480.00j d[ 8] = -85.00 +480.00j
|
||
c[ 9] = -95.00 +570.00j d[ 9] = -95.00 +570.00j
|
||
c[ 10] = -105.00 +660.00j d[ 10] = -105.00 +660.00j
|
||
c[ 11] = -115.00 +750.00j d[ 11] = -115.00 +750.00j
|
||
c[ 12] = -125.00 +840.00j d[ 12] = -125.00 +840.00j
|
||
c[ 13] = -135.00 +930.00j d[ 13] = -135.00 +930.00j
|
||
c[ 14] = -145.00 +1020.00j d[ 14] = -145.00 +1020.00j
|
||
c[ 15] = -124.00 +1080.00j d[ 15] = -124.00 +1080.00j
|
||
c[ 16] = -99.00 +1016.00j d[ 16] = -99.00 +1016.00j
|
||
c[ 17] = -70.00 +820.00j d[ 17] = -70.00 +820.00j
|
||
c[ 18] = -37.00 +484.00j d[ 18] = -37.00 +484.00j
|
||
\endverbatim
|
||
|
||
\author Бахурин Сергей. www.dsplib.org
|
||
***************************************************************************** */
|
||
#endif
|
||
int DSPL_API conv_fft_cmplx(complex_t* a, int na, complex_t* b, int nb,
|
||
fft_t* pfft, int nfft, complex_t* c)
|
||
{
|
||
|
||
int La, Lb, Lc, Nz, n, p0, p1, ind, err;
|
||
complex_t *pa, *pb;
|
||
complex_t *pt, *pA, *pB, *pC;
|
||
|
||
if(!a || !b || !c)
|
||
return ERROR_PTR;
|
||
if(na < 1 || nb < 1)
|
||
return ERROR_SIZE;
|
||
|
||
if(na >= nb)
|
||
{
|
||
La = na;
|
||
Lb = nb;
|
||
pa = a;
|
||
pb = b;
|
||
}
|
||
else
|
||
{
|
||
La = nb;
|
||
pa = b;
|
||
Lb = na;
|
||
pb = a;
|
||
}
|
||
|
||
Lc = La + Lb - 1;
|
||
Nz = nfft - Lb;
|
||
|
||
if(Nz <= 0)
|
||
return ERROR_FFT_SIZE;
|
||
|
||
pt = (complex_t*)malloc(nfft*sizeof(complex_t));
|
||
pB = (complex_t*)malloc(nfft*sizeof(complex_t));
|
||
pA = (complex_t*)malloc(nfft*sizeof(complex_t));
|
||
pC = (complex_t*)malloc(nfft*sizeof(complex_t));
|
||
|
||
memset(pt, 0, nfft*sizeof(complex_t));
|
||
memcpy(pt+Nz, pb, Lb*sizeof(complex_t));
|
||
|
||
err = fft_cmplx(pt, nfft, pfft, pB);
|
||
if(err != RES_OK)
|
||
goto exit_label;
|
||
|
||
p0 = -Lb;
|
||
p1 = p0 + nfft;
|
||
ind = 0;
|
||
while(ind < Lc)
|
||
{
|
||
if(p0 >=0)
|
||
{
|
||
if(p1 < La)
|
||
err = fft_cmplx(pa + p0, nfft, pfft, pA);
|
||
else
|
||
{
|
||
memset(pt, 0, nfft*sizeof(complex_t));
|
||
memcpy(pt, pa+p0, (nfft+La-p1)*sizeof(complex_t));
|
||
err = fft_cmplx(pt, nfft, pfft, pA);
|
||
}
|
||
}
|
||
else
|
||
{
|
||
memset(pt, 0, nfft*sizeof(complex_t));
|
||
if(p1 < La)
|
||
memcpy(pt - p0, pa, (nfft+p0)*sizeof(complex_t));
|
||
else
|
||
memcpy(pt - p0, pa, La * sizeof(complex_t));
|
||
err = fft_cmplx(pt, nfft, pfft, pA);
|
||
}
|
||
|
||
if(err != RES_OK)
|
||
goto exit_label;
|
||
|
||
for(n = 0; n < nfft; n++)
|
||
{
|
||
RE(pC[n]) = CMRE(pA[n], pB[n]);
|
||
IM(pC[n]) = CMIM(pA[n], pB[n]);
|
||
}
|
||
|
||
|
||
if(ind+nfft < Lc)
|
||
err = ifft_cmplx(pC, nfft, pfft, c+ind);
|
||
else
|
||
{
|
||
err = ifft_cmplx(pC, nfft, pfft, pt);
|
||
memcpy(c+ind, pt, (Lc-ind)*sizeof(complex_t));
|
||
}
|
||
if(err != RES_OK)
|
||
goto exit_label;
|
||
|
||
p0 += Nz;
|
||
p1 += Nz;
|
||
ind += Nz;
|
||
}
|
||
|
||
exit_label:
|
||
if(pt) free(pt);
|
||
if(pB) free(pB);
|
||
if(pA) free(pA);
|
||
if(pC) free(pC);
|
||
|
||
return err;
|
||
}
|
||
|
||
|
||
#ifdef DOXYGEN_ENGLISH
|
||
/*! ****************************************************************************
|
||
\ingroup FILTER_CONV_GROUP
|
||
\fn int filter_iir(double* b, double* a, int ord, double* x, int n, double* y)
|
||
\brief Real IIR filtration
|
||
|
||
Function calculates real IIR filter output for real signal. The real filter
|
||
contains real coefficients of the transfer function \f$H(z)\f$
|
||
numerator and denominator:
|
||
\f[
|
||
H(z) = \frac{\sum_{n = 0}^{N} b_n z^{-n}}
|
||
{1+{\frac{1}{a_0}}\sum_{m = 1}^{M} a_m z^{-n}},
|
||
\f]
|
||
here \f$a_0\f$ cannot be equals zeros, \f$N=M=\f$`ord`.
|
||
|
||
\param[in] b
|
||
Pointer to the vector \f$b\f$ of IIR filter
|
||
transfer function numerator coefficients. \n
|
||
Vector size is `[ord + 1 x 1]`. \n \n
|
||
|
||
\param[in] a
|
||
Pointer to the vector \f$a\f$ of IIR filter
|
||
transfer function denominator coefficients. \n
|
||
Vector size is `[ord + 1 x 1]`. \n
|
||
This pointer can be `NULL` if filter is FIR. \n \n
|
||
|
||
\param[in] ord
|
||
Filter order. Number of the transfer function
|
||
numerator and denominator coefficients
|
||
(length of vectors `b` and `a`) is `ord + 1`. \n \n
|
||
|
||
\param[in] x
|
||
Pointer to the input signal vector. \n
|
||
Vector size is `[n x 1]`. \n \n
|
||
|
||
\param[in] n
|
||
Size of the input signal vector `x`. \n \n
|
||
|
||
\param[out] y
|
||
Pointer to the IIR filter output vector. \n
|
||
Vector size is `[n x 1]`. \n
|
||
Memory must be allocated. \n \n
|
||
|
||
\return
|
||
`RES_OK` if filter output is calculated successfully. \n
|
||
Else \ref ERROR_CODE_GROUP "code error". \n
|
||
|
||
Example:
|
||
|
||
\include filter_iir_test.c
|
||
|
||
Input signal is
|
||
\f$s(t) = \sin(2\pi \cdot 0.05 t) + n(t)\f$, here \f$n(t)\f$ white Gaussian
|
||
noise with zero mean value and unit standard deviation. \n
|
||
|
||
Input signal is filtered by elliptic LPF order 6 and output signal and data
|
||
saves in the txt-files
|
||
|
||
\verbatim
|
||
dat/s.txt - input signal + noise
|
||
dat/sf.txt - filter output.
|
||
\endverbatim
|
||
|
||
Plots:
|
||
|
||
\image html filter_iir_test.png
|
||
|
||
GNUPLOT script for make plots is:
|
||
\include filter_iir.plt
|
||
|
||
\author Sergey Bakhurin www.dsplib.org
|
||
***************************************************************************** */
|
||
#endif
|
||
#ifdef DOXYGEN_RUSSIAN
|
||
/*! ****************************************************************************
|
||
\ingroup FILTER_CONV_GROUP
|
||
\fn int filter_iir(double* b, double* a, int ord, double* x, int n, double* y)
|
||
\brief Фильтрация вещественного сигнала вещественным БИХ-фильтром
|
||
|
||
Функция рассчитывает выход фильтра заданного выражением
|
||
\f[
|
||
H(z) = \frac{\sum_{n = 0}^{N} b_n z^{-n}}
|
||
{1+{\frac{1}{a_0}}\sum_{m = 1}^{M} a_m z^{-m}},
|
||
\f]
|
||
где \f$a_0\f$ не может быть 0, \f$N=M=\f$`ord`.
|
||
|
||
\param[in] b
|
||
Указатель на вектор коэффициентов числителя
|
||
передаточной функции \f$H(z)\f$ БИХ-фильтра. \n
|
||
Размер вектора `[ord + 1 x 1]`. \n \n
|
||
|
||
\param[in] a
|
||
Указатель на вектор коэффициентов знаменателя
|
||
передаточной функции \f$H(z)\f$ БИХ-фильтра. \n
|
||
Размер вектора `[ord + 1 x 1]`. \n
|
||
Этот указатель может быть `NULL`, тогда фильтрация производится
|
||
без использования рекурсивной части
|
||
(вектор коэффициентов `b` задает КИХ-фильтр). \n \n
|
||
|
||
\param[in] ord
|
||
Порядок фильтра. Количество коэффициентов числителя и знаменателя
|
||
передаточной функции \f$H(z)\f$ БИХ-фильтра равно `ord + 1`. \n \n
|
||
|
||
\param[in] x
|
||
Указатель на вектор отсчетов входного сигнала. \n
|
||
Размер вектора `[n x 1]`. \n \n
|
||
|
||
\param[in] n
|
||
Длина входного сигнала. \n \n
|
||
|
||
\param[out] y
|
||
Указатель на вектор выходных отсчетов фильтра. \n
|
||
Размер вектора `[n x 1]`. \n
|
||
Память должна быть выделена заранее. \n \n
|
||
|
||
\return
|
||
`RES_OK` Если фильтрация произведена успешно. \n
|
||
В противном случае \ref ERROR_CODE_GROUP "код ошибки". \n
|
||
|
||
Пример использования функции `filter_iir`:
|
||
|
||
\include filter_iir_test.c
|
||
|
||
На входе цифрового фильтра задан сигнал
|
||
\f$s(t) = \sin(2\pi \cdot 0.05 t) + n(t)\f$, где \f$n(t)\f$ белый гауссовский
|
||
шум, с нулевым средним и единичной дисперсией. \n
|
||
Фильтр представляет собой эллиптический ФНЧ 6 порядка.
|
||
Входной сигнал фильтруется данным фильтром, и результат сохраняется в файлы:
|
||
|
||
\verbatim
|
||
dat/s.txt - исходный зашумленный сигнал
|
||
dat/sf.txt - сигнал на выходе фильтра.
|
||
\endverbatim
|
||
|
||
По полученным данным производится построение графиков:
|
||
|
||
\image html filter_iir_test.png
|
||
|
||
\author Бахурин Сергей www.dsplib.org
|
||
***************************************************************************** */
|
||
#endif
|
||
int DSPL_API filter_iir(double* b, double* a, int ord,
|
||
double* x, int n, double* y)
|
||
{
|
||
double *buf = NULL;
|
||
double *an = NULL;
|
||
double *bn = NULL;
|
||
double u;
|
||
int k;
|
||
int m;
|
||
int count;
|
||
|
||
if(!b || !x || !y)
|
||
return ERROR_PTR;
|
||
|
||
if(ord < 1 || n < 1)
|
||
return ERROR_SIZE;
|
||
|
||
if(a && a[0]==0.0)
|
||
return ERROR_FILTER_A0;
|
||
|
||
count = ord + 1;
|
||
buf = (double*) malloc(count*sizeof(double));
|
||
an = (double*) malloc(count*sizeof(double));
|
||
|
||
memset(buf, 0, count*sizeof(double));
|
||
|
||
if(!a)
|
||
{
|
||
memset(an, 0, count*sizeof(double));
|
||
bn = b;
|
||
}
|
||
else
|
||
{
|
||
bn = (double*) malloc(count*sizeof(double));
|
||
for(k = 0; k < count; k++)
|
||
{
|
||
an[k] = a[k] / a[0];
|
||
bn[k] = b[k] / a[0];
|
||
}
|
||
}
|
||
|
||
for(k = 0; k < n; k++)
|
||
{
|
||
for(m = ord; m > 0; m--)
|
||
buf[m] = buf[m-1];
|
||
u = 0.0;
|
||
for(m = ord; m > 0; m--)
|
||
u += buf[m]*an[m];
|
||
|
||
buf[0] = x[k] - u;
|
||
y[k] = 0.0;
|
||
for(m = 0; m < count; m++)
|
||
y[k] += buf[m] * bn[m];
|
||
}
|
||
|
||
if(buf)
|
||
free(buf);
|
||
if(an)
|
||
free(an);
|
||
if(bn && (bn != b))
|
||
free(bn);
|
||
return RES_OK;
|
||
}
|
||
|