卷积及其快速算法的C++实现

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头文件:

/*
 * Copyright (c) 2008-2011 Zhang Ming (M. Zhang), [email protected]
 *
 * This program is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License as published by the
 * Free Software Foundation, either version 2 or any later version.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 *
 * 1. Redistributions of source code must retain the above copyright notice,
 *    this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * This program 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. A copy of the GNU General Public License is available at:
 * http://www.fsf.org/licensing/licenses
 */


/*****************************************************************************
 *                                 convolution.h
 *
 * Linear convolution and polynomial multiplication.
 *
 * The convolution routine "conv" is implemented by it's definition in time
 * domain. If the sequence to be convoluted are long, you should use the
 * fast convolution algorithm "fastConv", which is implemented in frequency
 * domain by usin FFT.
 *
 * Zhang Ming, 2010-01, Xi'an Jiaotong University.
 *****************************************************************************/


#ifndef CONVOLUTION_H
#define CONVOLUTION_H


#include 
#include 
#include 


namespace splab
{

    template Vector conv( const Vector&,
                                               const Vector& );
    template Vector convolution( const Vector&,
                                                      const Vector& );

    template Vector fastConv( const Vector&,
                                                   const Vector& );


    #include 

}
// namespace splab


#endif
// CONVOLUTION_H

实现文件:

/*
 * Copyright (c) 2008-2011 Zhang Ming (M. Zhang), [email protected]
 *
 * This program is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License as published by the
 * Free Software Foundation, either version 2 or any later version.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 *
 * 1. Redistributions of source code must retain the above copyright notice,
 *    this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * This program 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. A copy of the GNU General Public License is available at:
 * http://www.fsf.org/licensing/licenses
 */


/*****************************************************************************
 *                             convolution-impl.h
 *
 * Implementation for linear convolution.
 *
 * Zhang Ming, 2010-01, Xi'an Jiaotong University.
 *****************************************************************************/


/**
 * convolution and ploynonal multiplication.
 */
template 
Vector conv( const Vector &signal, const Vector &filter )
{
    if( signal.dim() < filter.dim() )
        return convolution( filter, signal );
    else
        return convolution( signal, filter );
}

template 
Vector convolution( const Vector &signal, const Vector &filter )
{
    int sigLength = signal.dim();
    int filLength = filter.dim();
    assert( sigLength >= filLength );

    int length = sigLength + filLength - 1;
    Vector x(length);

    for( int i=1; i<=length; ++i )
    {
        x(i) = 0;
        if( i < filLength )
            for( int j=1; j<=i; ++j )
                x(i) += filter(j) * signal(i-j+1);
        else if( i <= sigLength )
            for( int j=1; j<=filLength; ++j )
                x(i) += filter(j) * signal(i-j+1);
        else
            for( int j=i-sigLength+1; j<=filLength; ++j )
                x(i) += filter(j) * signal(i-j+1);
    }
    return x;
}


/**
 * Fast convolution by FFT.
 */
template
Vector fastConv( const Vector &xn, const Vector &yn )
{
    int M = xn.dim(),
        N = yn.dim();

    Vector xnPadded = wextend( xn, N-1, "right", "zpd" ),
                 ynPadded = wextend( yn, M-1, "right", "zpd" );
    return ifftc2r( fft(xnPadded) * fft(ynPadded) );

//    Vector< complex > Zk = fft(xnPadded) * fft(ynPadded);
//    return ifftc2r(Zk);

//    return ifftc2r( fft(wextend(xn,N-1,"right","zpd")) * fft(wextend(yn,M-1,"right","zpd")) );
}

测试代码:

/*****************************************************************************
 *                              convolution.cpp
 *
 * Convolution testing.
 *
 * Zhang Ming, 2010-01, Xi'an Jiaotong University.
 *****************************************************************************/


#define BOUNDS_CHECK

#include 
#include 


using namespace std;
using namespace splab;


typedef double  Type;
const   int     M = 3;
const   int     N = 5;


int main()
{
    Vector xn( M ), yn( N );
    Vector zn;

    for( int i=0; i

运行结果:

xn:  size: 3 by 1
0
1
2

yn:  size: 5 by 1
-2
-1
0
1
2

convolution of xn and yn:   size: 7 by 1
0
-2
-5
-2
1
4
4

fast convolution of xn and yn:   size: 7 by 1
-2.53765e-016
-2
-5
-2
1
4
4


Process returned 0 (0x0)   execution time : 0.078 s
Press any key to continue.

转载于:https://my.oschina.net/zmjerry/blog/3671

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