libdspl-2.0/dspl/src/fourier_series.c

/*
* 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 <http://www.gnu.org/licenses/>.
*/


#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "dspl.h"


/*******************************************************************************
Fourier Series Decomposition
*******************************************************************************/
int DSPL_API fourier_series_dec(double* t, double* s, int nt, double period,
                                int nw, double* w, complex_t* y)
{
  int k, m;
  double dw = M_2PI / period;
  complex_t e[2];

  if(!t || !s || !w || !y)
    return ERROR_PTR;
  if(nt<1 || nw < 1)
    return ERROR_SIZE;
  if(period <= 0.0)
    return ERROR_NEGATIVE;

  memset(y, 0 , nw*sizeof(complex_t));

  for(k = 0; k < nw; k++)
  {
    w[k] = (k - nw/2) * dw;
    RE(e[1]) =  s[0] * cos(w[k] * t[0]);
    IM(e[1]) = -s[0] * sin(w[k] * t[0]);
    for(m = 1; m < nt; m++)
    {
      RE(e[0]) = RE(e[1]);
      IM(e[0]) = IM(e[1]);
      RE(e[1]) =   s[m] * cos(w[k] * t[m]);
      IM(e[1]) = - s[m] * sin(w[k] * t[m]);
      RE(y[k]) += 0.5 * (RE(e[0]) + RE(e[1]))*(t[m] - t[m-1]);
      IM(y[k]) += 0.5 * (IM(e[0]) + IM(e[1]))*(t[m] - t[m-1]);
    }
    RE(y[k]) /= period;
    IM(y[k]) /= period;
  }

  if(!(nw%2))
    RE(y[0]) = RE(y[1]) = 0.0;

  return RES_OK;
}



/*******************************************************************************
Fourier Series Decomposition for complex input signal
*******************************************************************************/
int DSPL_API fourier_series_dec_cmplx(double* t, complex_t* s, int nt,
      double period, int nw, double* w, complex_t* y)
{
  int k, m;
  double dw = M_2PI / period;
  complex_t e[2];

  if(!t || !s || !w || !y)
    return ERROR_PTR;
  if(nt<1 || nw < 1)
    return ERROR_SIZE;
  if(period <= 0.0)
    return ERROR_NEGATIVE;

  memset(y, 0 , nw*sizeof(complex_t));

  for(k = 0; k < nw; k++)
  {
    w[k] = (k - nw/2) * dw;
    RE(e[1]) =  RE(s[0]) * cos(w[k] * t[0]) +
    IM(s[0]) * sin(w[k] * t[0]);
    IM(e[1]) = -RE(s[0]) * sin(w[k] * t[0]) +
    IM(s[0]) * cos(w[k] * t[0]);
    for(m = 1; m < nt; m++)
    {
      RE(e[0]) = RE(e[1]);
      IM(e[0]) = IM(e[1]);
      RE(e[1]) =   RE(s[m]) * cos(w[k] * t[m]) +
      IM(s[m]) * sin(w[k] * t[m]);
      IM(e[1]) = -RE(s[m]) * sin(w[k] * t[m]) +
      IM(s[m]) * cos(w[k] * t[m]);
      RE(y[k]) += 0.5 * (RE(e[0]) + RE(e[1]))*(t[m] - t[m-1]);
      IM(y[k]) += 0.5 * (IM(e[0]) + IM(e[1]))*(t[m] - t[m-1]);
    }
    RE(y[k]) /= period;
    IM(y[k]) /= period;
  }

  if(!(nw%2))
    RE(y[0]) = RE(y[1]) = 0.0;

  return RES_OK;
}






/*******************************************************************************
Fourier Transform
*******************************************************************************/
int DSPL_API fourier_integral_cmplx(double* t, complex_t* s, int nt,
      int nw, double* w, complex_t* y)
{
  int k, m;
  complex_t e[2];

  if(!t || !s || !w || !y)
    return ERROR_PTR;
  if(nt<1 || nw < 1)
    return ERROR_SIZE;


  memset(y, 0 , nw*sizeof(complex_t));

  for(k = 0; k < nw; k++)
  {
    RE(e[1]) =  RE(s[0]) * cos(w[k] * t[0]) +
    IM(s[0]) * sin(w[k] * t[0]);
    IM(e[1]) = -RE(s[0]) * sin(w[k] * t[0]) +
    IM(s[0]) * cos(w[k] * t[0]);
    for(m = 1; m < nt; m++)
    {
      RE(e[0]) = RE(e[1]);
      IM(e[0]) = IM(e[1]);
      RE(e[1]) =   RE(s[m]) * cos(w[k] * t[m]) +
      IM(s[m]) * sin(w[k] * t[m]);
      IM(e[1]) = -RE(s[m]) * sin(w[k] * t[m]) +
      IM(s[m]) * cos(w[k] * t[m]);
      RE(y[k]) += 0.5 * (RE(e[0]) + RE(e[1]))*(t[m] - t[m-1]);
      IM(y[k]) += 0.5 * (IM(e[0]) + IM(e[1]))*(t[m] - t[m-1]);
    }
  }

  return RES_OK;
}






/*******************************************************************************
Fourier Series Reconstruction
*******************************************************************************/
int DSPL_API fourier_series_rec(double* w, complex_t* s, int nw,
            double *t, int nt, complex_t* y)
{
  int k, m;
  complex_t e;

  if(!t || !s || !w || !y)
    return ERROR_PTR;
  if(nt<1 || nw < 1)
    return ERROR_SIZE;

  memset(y, 0, nt*sizeof(complex_t));


  for(k = 0; k < nw; k++)
  {
    for(m = 0; m < nt; m++)
    {
      RE(e) =  cos(w[k] * t[m]);
      IM(e) =  sin(w[k] * t[m]);

      RE(y[m]) += CMRE(s[k], e);
      IM(y[m]) += CMIM(s[k], e);
    }
  }
  return RES_OK;
}