/* *****************************************************************************
*	app_EWO_fft.c                                                              *
*   作成日・作成者      ：2016/3/17     Y.Kasahara                             *
********************************************************************************
  ====================================================================
  [削除] void app_EWO_fft( double *f_waveform, int i_nData,
                  double *f_spectrumAmp, double *f_spectrumPhase )
  --------------------------------------------------------------------
  機能：  	波形を FFT し，スペクトルの振幅と位相を返す．
  			値が戻るのは，正の周波数成分のみ．
  			よって，スペクトルの各値が返る配列の大きさは，それぞれ波形
  			データ配列の半分の大きさでよい．
  引数：	double				*f_waveform			FFT 対象の波形（パラメータ）		<=8192
			int					i_nData				FFT データ点数（パラメータ）		<=8192
			double				*f_spectrumAmp		スペクトルの振幅（戻り値）			<=8192
			double				*f_spectrumPhase	スペクトルの位相（戻り値）			<=8192
  戻り値：	なし
  ====================================================================

  ====================================================================
  void app_EWO_rfft( double *f_waveform, int i_nData, double *f_re, double *f_im )
  --------------------------------------------------------------------
  機能：  	波形を FFT し，スペクトルの振幅と位相を返す．
  			値が戻るのは，正の周波数成分のみ．
  			よって，スペクトルの各値が返る配列の大きさは，それぞれ波形
  			データ配列の半分の大きさでよい．
  引数：	double				*f_waveform			FFT 対象の波形（パラメータ）		<=8192
			int					i_nData				FFT データ点数（パラメータ）		<=8192
			double				*f_re				スペクトルの実部（戻り値）			<=8192
			double				*f_im				スペクトルの虚部（戻り値）			<=8192
  戻り値：	なし
  ====================================================================

  ====================================================================
  void	app_EWO_rfft_dual(
			int i_nData,
			double* f_waveform1, double* f_re1, double* f_im1,
			double* f_waveform2, double* f_re2, double* f_im2
			)
  --------------------------------------------------------------------
  機能：  	２つの波形を一度に FFT し，スペクトルの振幅と位相を返す．
  			値が戻るのは，正の周波数成分のみ．
  			よって，スペクトルの各値が返る配列の大きさは，それぞれ波形
  			データ配列の半分の大きさでよい．
  引数：	int					i_nData				FFT データ点数（パラメータ）		<=8192
			double				*f_waveform?		FFT 対象の波形（パラメータ）		<=8192
			double				*f_re?				スペクトルの実部（戻り値）			<=8192
			double				*f_im?				スペクトルの虚部（戻り値）			<=8192
  戻り値：	なし
  ====================================================================

******************************************************************* */

#include	"app_common.h"
#include	"app_EWO.h"

// [in app_EWO_variable.c]
//#define MAX_N_FFT 8192
//double	Gf_EWO_signal[MAX_N_FFT * 2];
//int		Gi_EWO_workarea[(int)app_math_sqrt(MAX_N_FFT) + 2];
//double 	Gf_EWO_sin_table[MAX_N_FFT];

// [in app_EWO.h]
// void app_EWO_fft( double* , int , double* , double* );

// -----------------------------------------------------------------------------------------------------
// --- MACRO: local ------------------------------------------------------------------------------------
void app_EWO_rdft		( int n, int isgn, double *a, int *ip, double *w );
void app_EWO_makewt 	(int nw, int *ip, double *w);
void app_EWO_makect 	(int nc, int *ip, double *c);
void app_EWO_bitrv2 	(int n, int *ip, double *a);
void app_EWO_cftfsub	(int n, double *a, double *w);
void app_EWO_cftbsub	(int n, double *a, double *w);
void app_EWO_rftfsub	(int n, double *a, int nc, double *c);
void app_EWO_rftbsub	(int n, double *a, int nc, double *c);
void app_EWO_cft1st		(int n, double *a, double *w);
void app_EWO_cftmdl		(int n, int l, double *a, double *w);
// -----------------------------------------------------------------------------------------------------

/*
void 	app_EWO_fft( double* f_waveform, int i_nData,
						double* f_spectrumAmp, double* f_spectrumPhase )
{
	double 	f_re, f_im;
	int		i;

	for ( i=0; i<i_nData; i++ ) {
		Gf_EWO_signal[i*2] = f_waveform[i];
		Gf_EWO_signal[i*2 + 1] = 0;
	}

  	Gi_EWO_workarea[0] = 0;
  	app_EWO_rdft( i_nData * 2, 1, Gf_EWO_signal, Gi_EWO_workarea, Gf_EWO_sin_table );

	for ( i=0; i<i_nData / 2; i++ ) {
		f_re = Gf_EWO_signal[i*2];
		f_im = Gf_EWO_signal[i*2+1];
    	f_spectrumAmp[i]   = (double)app_math_sqrt(   f_re * f_re + f_im * f_im ) * 2;
    	f_spectrumPhase[i] = (double)app_math_atan( ( f_re / f_im ) );
  	}
}
*/

void	app_EWO_rfft( double* f_waveform, int i_nData, double* f_re, double* f_im ){
	int		i;

	for ( i=0; i<i_nData; i++ ) {
		Gf_EWO_signal[i*2] = f_waveform[i];
		Gf_EWO_signal[i*2 + 1] = 0;
	}
	
  	Gi_EWO_workarea[0] = 0;
  	app_EWO_rdft( i_nData * 2, 1, Gf_EWO_signal, Gi_EWO_workarea, Gf_EWO_sin_table );
	
	for ( i=0; i<i_nData; i++ ) {
    	f_re[i] = Gf_EWO_signal[i*2];
   	 	f_im[i] = Gf_EWO_signal[i*2 + 1];
	}
}

void	app_EWO_rfft14( double* f_waveform, int i_nData, double* f_re, double* f_im ){
	int		i;

	for ( i=0; i<i_nData; i++ ) {
		G14f_EWO_signal[i*2] = f_waveform[i];
		G14f_EWO_signal[i*2 + 1] = 0;
	}
	
  	Gi_EWO_workarea[0] = 0;
  	app_EWO_rdft( i_nData * 2, 1, G14f_EWO_signal, G14i_EWO_workarea, G14f_EWO_sin_table );
	
	for ( i=0; i<i_nData; i++ ) {
    	f_re[i] = G14f_EWO_signal[i*2];
   	 	f_im[i] = G14f_EWO_signal[i*2 + 1];
	}
}

void	app_EWO_rfft_dual(
			int i_nData,
			double* f_waveform1, double* f_re1, double* f_im1,
			double* f_waveform2, double* f_re2, double* f_im2
			){
	int		i;

	for ( i=0; i<i_nData; i++ ) {
		Gf_EWO_signal[i*2]     = f_waveform1[i];
		Gf_EWO_signal[i*2 + 1] = f_waveform2[i];
	}
	
  	Gi_EWO_workarea[0] = 0;
  	app_EWO_rdft( i_nData * 2, 1, Gf_EWO_signal, Gi_EWO_workarea, Gf_EWO_sin_table );
	
	for ( i=0; i<i_nData; i++ ) {
    	f_re1[i] = ( Gf_EWO_signal[i*2] + Gf_EWO_signal[i_nData * 2 - i*2] ) / 2;
   	 	f_im1[i] = ( Gf_EWO_signal[i*2 + 1] - Gf_EWO_signal[i_nData * 2 - i*2 + 1] ) / 2;
   	 	f_re2[i] = ( Gf_EWO_signal[i*2 + 1] + Gf_EWO_signal[i_nData * 2 - i*2 + 1] ) / 2;
    	f_im2[i] = ( -Gf_EWO_signal[i*2] + Gf_EWO_signal[i_nData * 2 - i*2] ) / 2;
	}
}

void	app_EWO_rfft_dual14(
			int i_nData,
			double* f_waveform1, double* f_re1, double* f_im1,
			double* f_waveform2, double* f_re2, double* f_im2
			){
	int		i;

	for ( i=0; i<i_nData; i++ ) {
		G14f_EWO_signal[i*2]     = f_waveform1[i];
		G14f_EWO_signal[i*2 + 1] = f_waveform2[i];
	}
	
  	G14i_EWO_workarea[0] = 0;
  	app_EWO_rdft( i_nData * 2, 1, G14f_EWO_signal, G14i_EWO_workarea, G14f_EWO_sin_table );
	
	for ( i=0; i<i_nData; i++ ) {
		 //modified by Y. Kasahara(2016.3.16)
    	f_re1[i] = ( G14f_EWO_signal[i*2] + G14f_EWO_signal[i_nData * 2 - i*2] ) / 2;
   	 	f_im1[i] = ( G14f_EWO_signal[i*2 + 1] - G14f_EWO_signal[i_nData * 2 - i*2 + 1] ) / 2;
   	 	f_re2[i] = ( G14f_EWO_signal[i*2 + 1] + G14f_EWO_signal[i_nData * 2 - i*2 + 1] ) / 2;
    	f_im2[i] = ( -G14f_EWO_signal[i*2] + G14f_EWO_signal[i_nData * 2 - i*2] ) / 2;
	}
}

/* ************************************* */

void 	app_EWO_rdft( int n, int isgn, double *a, int *ip, double *w ){
  	int 	nw, nc;
  	double 	xi;
  
  	nw = ip[0];
  	if (n > (nw << 2)) {
    	nw = n >> 2;
    	app_EWO_makewt(nw, ip, w);
  	}
  	nc = ip[1];
  	if (n > (nc << 2)) {
    	nc = n >> 2;
    	app_EWO_makect(nc, ip, w + nw);
  	}
  	if (isgn >= 0) {
    	if (n > 4) {
    		app_EWO_bitrv2(n, ip + 2, a);
      		app_EWO_cftfsub(n, a, w);
      		app_EWO_rftfsub(n, a, nc, w + nw);
    	} else if (n == 4) {
      		app_EWO_cftfsub(n, a, w);
    	}
 	xi = a[0] - a[1];
    a[0] += a[1];
    a[1] = xi;
  } else {
    a[1] = 0.5 * (a[0] - a[1]);
    a[0] -= a[1];
    if (n > 4) {
      app_EWO_rftbsub(n, a, nc, w + nw);
      app_EWO_bitrv2(n, ip + 2, a);
      app_EWO_cftbsub(n, a, w);
    } else if (n == 4) {
      app_EWO_cftfsub(n, a, w);
    }
  }
}



/* -------- initializing routines -------- */
void	app_EWO_makewt(int nw, int *ip, double *w)
{
  void app_EWO_bitrv2(int n, int *ip, double *a);
  int j, nwh;
  double delta, x, y;
  
  ip[0] = nw;
  ip[1] = 1;
  if (nw > 2) {
    nwh = nw >> 1;
    delta = app_math_atan(1.0) / nwh;
    w[0] = 1;
    w[1] = 0;
    w[nwh] = app_math_cos(delta * nwh);
    w[nwh + 1] = w[nwh];
    if (nwh > 2) {
      for (j = 2; j < nwh; j += 2) {
	x = app_math_cos(delta * j);
	y = app_math_sin(delta * j);
	w[j] = x;
	w[j + 1] = y;
	w[nw - j] = y;
	w[nw - j + 1] = x;
      }
      app_EWO_bitrv2(nw, ip + 2, w);
    }
  }
}


void	app_EWO_makect(int nc, int *ip, double *c)
{
  int j, nch;
  double delta;
  
  ip[1] = nc;
  if (nc > 1) {
    nch = nc >> 1;
    delta = app_math_atan(1.0) / nch;
    c[0] = app_math_cos(delta * nch);
    c[nch] = 0.5 * c[0];
    for (j = 1; j < nch; j++) {
      c[j] = 0.5 * app_math_cos(delta * j);
      c[nc - j] = 0.5 * app_math_sin(delta * j);
    }
  }
}


/* -------- child routines -------- */


void	app_EWO_bitrv2(int n, int *ip, double *a)
{
  int j, j1, k, k1, l, m, m2;
  double xr, xi, yr, yi;
  
  ip[0] = 0;
  l = n;
  m = 1;
  while ((m << 3) < l) {
    l >>= 1;
    for (j = 0; j < m; j++) {
      ip[m + j] = ip[j] + l;
    }
    m <<= 1;
  }
  m2 = 2 * m;
  if ((m << 3) == l) {
    for (k = 0; k < m; k++) {
      for (j = 0; j < k; j++) {
	j1 = 2 * j + ip[k];
	k1 = 2 * k + ip[j];
	xr = a[j1];
	xi = a[j1 + 1];
	yr = a[k1];
	yi = a[k1 + 1];
	a[j1] = yr;
	a[j1 + 1] = yi;
	a[k1] = xr;
	a[k1 + 1] = xi;
	j1 += m2;
	k1 += 2 * m2;
	xr = a[j1];
	xi = a[j1 + 1];
	yr = a[k1];
	yi = a[k1 + 1];
	a[j1] = yr;
	a[j1 + 1] = yi;
	a[k1] = xr;
	a[k1 + 1] = xi;
	j1 += m2;
	k1 -= m2;
	xr = a[j1];
	xi = a[j1 + 1];
	yr = a[k1];
	yi = a[k1 + 1];
	a[j1] = yr;
	a[j1 + 1] = yi;
	a[k1] = xr;
	a[k1 + 1] = xi;
	j1 += m2;
	k1 += 2 * m2;
	xr = a[j1];
	xi = a[j1 + 1];
	yr = a[k1];
	yi = a[k1 + 1];
	a[j1] = yr;
	a[j1 + 1] = yi;
	a[k1] = xr;
	a[k1 + 1] = xi;
      }
      j1 = 2 * k + m2 + ip[k];
      k1 = j1 + m2;
      xr = a[j1];
      xi = a[j1 + 1];
      yr = a[k1];
      yi = a[k1 + 1];
      a[j1] = yr;
      a[j1 + 1] = yi;
      a[k1] = xr;
      a[k1 + 1] = xi;
    }
  } else {
    for (k = 1; k < m; k++) {
      for (j = 0; j < k; j++) {
	j1 = 2 * j + ip[k];
	k1 = 2 * k + ip[j];
	xr = a[j1];
	xi = a[j1 + 1];
	yr = a[k1];
	yi = a[k1 + 1];
	a[j1] = yr;
	a[j1 + 1] = yi;
	a[k1] = xr;
	a[k1 + 1] = xi;
	j1 += m2;
	k1 += m2;
	xr = a[j1];
	xi = a[j1 + 1];
	yr = a[k1];
	yi = a[k1 + 1];
	a[j1] = yr;
	a[j1 + 1] = yi;
	a[k1] = xr;
	a[k1 + 1] = xi;
      }
    }
  }
}

void 	app_EWO_cftfsub(int n, double *a, double *w)
{
  void app_EWO_cft1st(int n, double *a, double *w);
  void app_EWO_cftmdl(int n, int l, double *a, double *w);
  int j, j1, j2, j3, l;
  double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
  
  l = 2;
  if (n > 8) {
    app_EWO_cft1st(n, a, w);
    l = 8;
    while ((l << 2) < n) {
      app_EWO_cftmdl(n, l, a, w);
      l <<= 2;
    }
  }
  if ((l << 2) == n) {
    for (j = 0; j < l; j += 2) {
      j1 = j + l;
      j2 = j1 + l;
      j3 = j2 + l;
      x0r = a[j] + a[j1];
      x0i = a[j + 1] + a[j1 + 1];
      x1r = a[j] - a[j1];
      x1i = a[j + 1] - a[j1 + 1];
      x2r = a[j2] + a[j3];
      x2i = a[j2 + 1] + a[j3 + 1];
      x3r = a[j2] - a[j3];
      x3i = a[j2 + 1] - a[j3 + 1];
      a[j] = x0r + x2r;
      a[j + 1] = x0i + x2i;
      a[j2] = x0r - x2r;
      a[j2 + 1] = x0i - x2i;
      a[j1] = x1r - x3i;
      a[j1 + 1] = x1i + x3r;
      a[j3] = x1r + x3i;
      a[j3 + 1] = x1i - x3r;
    }
  } else {
    for (j = 0; j < l; j += 2) {
      j1 = j + l;
      x0r = a[j] - a[j1];
      x0i = a[j + 1] - a[j1 + 1];
      a[j] += a[j1];
      a[j + 1] += a[j1 + 1];
      a[j1] = x0r;
      a[j1 + 1] = x0i;
    }
  }
}


void	app_EWO_cftbsub(int n, double *a, double *w)
{
  int j, j1, j2, j3, l;
  double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
  
  l = 2;
  if (n > 8) {
    app_EWO_cft1st(n, a, w);
    l = 8;
    while ((l << 2) < n) {
      app_EWO_cftmdl(n, l, a, w);
      l <<= 2;
    }
  }
  if ((l << 2) == n) {
    for (j = 0; j < l; j += 2) {
      j1 = j + l;
      j2 = j1 + l;
      j3 = j2 + l;
      x0r = a[j] + a[j1];
      x0i = -a[j + 1] - a[j1 + 1];
      x1r = a[j] - a[j1];
      x1i = -a[j + 1] + a[j1 + 1];
      x2r = a[j2] + a[j3];
      x2i = a[j2 + 1] + a[j3 + 1];
      x3r = a[j2] - a[j3];
      x3i = a[j2 + 1] - a[j3 + 1];
      a[j] = x0r + x2r;
      a[j + 1] = x0i - x2i;
      a[j2] = x0r - x2r;
      a[j2 + 1] = x0i + x2i;
      a[j1] = x1r - x3i;
      a[j1 + 1] = x1i - x3r;
      a[j3] = x1r + x3i;
      a[j3 + 1] = x1i + x3r;
    }
  } else {
    for (j = 0; j < l; j += 2) {
      j1 = j + l;
      x0r = a[j] - a[j1];
      x0i = -a[j + 1] + a[j1 + 1];
      a[j] += a[j1];
      a[j + 1] = -a[j + 1] - a[j1 + 1];
      a[j1] = x0r;
      a[j1 + 1] = x0i;
    }
  }
}


void
app_EWO_cft1st(int n, double *a, double *w)
{
  int j, k1, k2;
  double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
  double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
  
  x0r = a[0] + a[2];
  x0i = a[1] + a[3];
  x1r = a[0] - a[2];
  x1i = a[1] - a[3];
  x2r = a[4] + a[6];
  x2i = a[5] + a[7];
  x3r = a[4] - a[6];
  x3i = a[5] - a[7];
  a[0] = x0r + x2r;
  a[1] = x0i + x2i;
  a[4] = x0r - x2r;
  a[5] = x0i - x2i;
  a[2] = x1r - x3i;
  a[3] = x1i + x3r;
  a[6] = x1r + x3i;
  a[7] = x1i - x3r;
  wk1r = w[2];
  x0r = a[8] + a[10];
  x0i = a[9] + a[11];
  x1r = a[8] - a[10];
  x1i = a[9] - a[11];
  x2r = a[12] + a[14];
  x2i = a[13] + a[15];
  x3r = a[12] - a[14];
  x3i = a[13] - a[15];
  a[8] = x0r + x2r;
  a[9] = x0i + x2i;
  a[12] = x2i - x0i;
  a[13] = x0r - x2r;
  x0r = x1r - x3i;
  x0i = x1i + x3r;
  a[10] = wk1r * (x0r - x0i);
  a[11] = wk1r * (x0r + x0i);
  x0r = x3i + x1r;
  x0i = x3r - x1i;
  a[14] = wk1r * (x0i - x0r);
  a[15] = wk1r * (x0i + x0r);
  k1 = 0;
  for (j = 16; j < n; j += 16) {
    k1 += 2;
    k2 = 2 * k1;
    wk2r = w[k1];
    wk2i = w[k1 + 1];
    wk1r = w[k2];
    wk1i = w[k2 + 1];
    wk3r = wk1r - 2 * wk2i * wk1i;
    wk3i = 2 * wk2i * wk1r - wk1i;
    x0r = a[j] + a[j + 2];
    x0i = a[j + 1] + a[j + 3];
    x1r = a[j] - a[j + 2];
    x1i = a[j + 1] - a[j + 3];
    x2r = a[j + 4] + a[j + 6];
    x2i = a[j + 5] + a[j + 7];
    x3r = a[j + 4] - a[j + 6];
    x3i = a[j + 5] - a[j + 7];
    a[j] = x0r + x2r;
    a[j + 1] = x0i + x2i;
    x0r -= x2r;
    x0i -= x2i;
    a[j + 4] = wk2r * x0r - wk2i * x0i;
    a[j + 5] = wk2r * x0i + wk2i * x0r;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    a[j + 2] = wk1r * x0r - wk1i * x0i;
    a[j + 3] = wk1r * x0i + wk1i * x0r;
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    a[j + 6] = wk3r * x0r - wk3i * x0i;
    a[j + 7] = wk3r * x0i + wk3i * x0r;
    wk1r = w[k2 + 2];
    wk1i = w[k2 + 3];
    wk3r = wk1r - 2 * wk2r * wk1i;
    wk3i = 2 * wk2r * wk1r - wk1i;
    x0r = a[j + 8] + a[j + 10];
    x0i = a[j + 9] + a[j + 11];
    x1r = a[j + 8] - a[j + 10];
    x1i = a[j + 9] - a[j + 11];
    x2r = a[j + 12] + a[j + 14];
    x2i = a[j + 13] + a[j + 15];
    x3r = a[j + 12] - a[j + 14];
    x3i = a[j + 13] - a[j + 15];
    a[j + 8] = x0r + x2r;
    a[j + 9] = x0i + x2i;
    x0r -= x2r;
    x0i -= x2i;
    a[j + 12] = -wk2i * x0r - wk2r * x0i;
    a[j + 13] = -wk2i * x0i + wk2r * x0r;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    a[j + 10] = wk1r * x0r - wk1i * x0i;
    a[j + 11] = wk1r * x0i + wk1i * x0r;
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    a[j + 14] = wk3r * x0r - wk3i * x0i;
    a[j + 15] = wk3r * x0i + wk3i * x0r;
  }
}


void 
app_EWO_cftmdl(int n, int l, double *a, double *w)
{
  int j, j1, j2, j3, k, k1, k2, m, m2;
  double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
  double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
  
  m = l << 2;
  for (j = 0; j < l; j += 2) {
    j1 = j + l;
    j2 = j1 + l;
    j3 = j2 + l;
    x0r = a[j] + a[j1];
    x0i = a[j + 1] + a[j1 + 1];
    x1r = a[j] - a[j1];
    x1i = a[j + 1] - a[j1 + 1];
    x2r = a[j2] + a[j3];
    x2i = a[j2 + 1] + a[j3 + 1];
    x3r = a[j2] - a[j3];
    x3i = a[j2 + 1] - a[j3 + 1];
    a[j] = x0r + x2r;
    a[j + 1] = x0i + x2i;
    a[j2] = x0r - x2r;
    a[j2 + 1] = x0i - x2i;
    a[j1] = x1r - x3i;
    a[j1 + 1] = x1i + x3r;
    a[j3] = x1r + x3i;
    a[j3 + 1] = x1i - x3r;
  }
  wk1r = w[2];
  for (j = m; j < l + m; j += 2) {
    j1 = j + l;
    j2 = j1 + l;
    j3 = j2 + l;
    x0r = a[j] + a[j1];
    x0i = a[j + 1] + a[j1 + 1];
    x1r = a[j] - a[j1];
    x1i = a[j + 1] - a[j1 + 1];
    x2r = a[j2] + a[j3];
    x2i = a[j2 + 1] + a[j3 + 1];
    x3r = a[j2] - a[j3];
    x3i = a[j2 + 1] - a[j3 + 1];
    a[j] = x0r + x2r;
    a[j + 1] = x0i + x2i;
    a[j2] = x2i - x0i;
    a[j2 + 1] = x0r - x2r;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    a[j1] = wk1r * (x0r - x0i);
    a[j1 + 1] = wk1r * (x0r + x0i);
    x0r = x3i + x1r;
    x0i = x3r - x1i;
    a[j3] = wk1r * (x0i - x0r);
    a[j3 + 1] = wk1r * (x0i + x0r);
  }
  k1 = 0;
  m2 = 2 * m;
  for (k = m2; k < n; k += m2) {
    k1 += 2;
    k2 = 2 * k1;
    wk2r = w[k1];
    wk2i = w[k1 + 1];
    wk1r = w[k2];
    wk1i = w[k2 + 1];
    wk3r = wk1r - 2 * wk2i * wk1i;
    wk3i = 2 * wk2i * wk1r - wk1i;
    for (j = k; j < l + k; j += 2) {
      j1 = j + l;
      j2 = j1 + l;
      j3 = j2 + l;
      x0r = a[j] + a[j1];
      x0i = a[j + 1] + a[j1 + 1];
      x1r = a[j] - a[j1];
      x1i = a[j + 1] - a[j1 + 1];
      x2r = a[j2] + a[j3];
      x2i = a[j2 + 1] + a[j3 + 1];
      x3r = a[j2] - a[j3];
      x3i = a[j2 + 1] - a[j3 + 1];
      a[j] = x0r + x2r;
      a[j + 1] = x0i + x2i;
      x0r -= x2r;
      x0i -= x2i;
      a[j2] = wk2r * x0r - wk2i * x0i;
      a[j2 + 1] = wk2r * x0i + wk2i * x0r;
      x0r = x1r - x3i;
      x0i = x1i + x3r;
      a[j1] = wk1r * x0r - wk1i * x0i;
      a[j1 + 1] = wk1r * x0i + wk1i * x0r;
      x0r = x1r + x3i;
      x0i = x1i - x3r;
      a[j3] = wk3r * x0r - wk3i * x0i;
      a[j3 + 1] = wk3r * x0i + wk3i * x0r;
    }
    wk1r = w[k2 + 2];
    wk1i = w[k2 + 3];
    wk3r = wk1r - 2 * wk2r * wk1i;
    wk3i = 2 * wk2r * wk1r - wk1i;
    for (j = k + m; j < l + (k + m); j += 2) {
      j1 = j + l;
      j2 = j1 + l;
      j3 = j2 + l;
      x0r = a[j] + a[j1];
      x0i = a[j + 1] + a[j1 + 1];
      x1r = a[j] - a[j1];
      x1i = a[j + 1] - a[j1 + 1];
      x2r = a[j2] + a[j3];
      x2i = a[j2 + 1] + a[j3 + 1];
      x3r = a[j2] - a[j3];
      x3i = a[j2 + 1] - a[j3 + 1];
      a[j] = x0r + x2r;
      a[j + 1] = x0i + x2i;
      x0r -= x2r;
      x0i -= x2i;
      a[j2] = -wk2i * x0r - wk2r * x0i;
      a[j2 + 1] = -wk2i * x0i + wk2r * x0r;
      x0r = x1r - x3i;
      x0i = x1i + x3r;
      a[j1] = wk1r * x0r - wk1i * x0i;
      a[j1 + 1] = wk1r * x0i + wk1i * x0r;
      x0r = x1r + x3i;
      x0i = x1i - x3r;
      a[j3] = wk3r * x0r - wk3i * x0i;//no 
      a[j3 + 1] = wk3r * x0i + wk3i * x0r;//no
    }
  }
}


void 
app_EWO_rftfsub(int n, double *a, int nc, double *c)
{
  int j, k, kk, ks, m;
  double wkr, wki, xr, xi, yr, yi;
  
  m = n >> 1;
  ks = 2 * nc / m;
  kk = 0;
  for (j = 2; j < m; j += 2) {
    k = n - j;
    kk += ks;
    wkr = 0.5 - c[nc - kk];
    wki = c[kk];
    xr = a[j] - a[k];
    xi = a[j + 1] + a[k + 1];
    yr = wkr * xr - wki * xi;
    yi = wkr * xi + wki * xr;
    a[j] -= yr;
    a[j + 1] -= yi;
    a[k] += yr;
    a[k + 1] -= yi;
  }
}


void	app_EWO_rftbsub(int n, double *a, int nc, double *c)
{
  int j, k, kk, ks, m;
  double wkr, wki, xr, xi, yr, yi;
  
  a[1] = -a[1];
  m = n >> 1;
  ks = 2 * nc / m;
  kk = 0;
  for (j = 2; j < m; j += 2) {
    k = n - j;
    kk += ks;
    wkr = 0.5 - c[nc - kk];
    wki = c[kk];
    xr = a[j] - a[k];
    xi = a[j + 1] + a[k + 1];
    yr = wkr * xr + wki * xi;
    yi = wkr * xi - wki * xr;
    a[j] -= yr;
    a[j + 1] = yi - a[j + 1];
    a[k] += yr;
    a[k + 1] = yi - a[k + 1];
  }
  a[m + 1] = -a[m + 1];
}


void 
app_EWO_dctsub(int n, double *a, int nc, double *c)
{
  int j, k, kk, ks, m;
  double wkr, wki, xr;
  
  m = n >> 1;
  ks = nc / n;
  kk = 0;
  for (j = 1; j < m; j++) {
    k = n - j;
    kk += ks;
    wkr = c[kk] - c[nc - kk];
    wki = c[kk] + c[nc - kk];
    xr = wki * a[j] - wkr * a[k];
    a[j] = wkr * a[j] + wki * a[k];
    a[k] = xr;
  }
  a[m] *= c[0];
}


// ===========================================================================
// app_EWO_Hannig		**** Hanning function: 0.5-0.5 cos(2πx) [x=0-1] ****
//		[INPUT]		double					f_data[]			Original data
//				 	double 					f_work[]			Return   data
//					int 	  				i_num				Num of data
// ===========================================================================
void	app_EWO_Hanning( 	double	f_data[],
						 	double 	f_work[],
							int 	i_num )
{
	int		i;
	double	f_ave, f_tmp;
	
//	f_ave = ( f_data[0] + f_data[i_num-1] ) / 2.0;
	
	f_ave = 0;
	for (i=0; i < i_num; i++) {
/*
		// for test
		f_data[i] = 3000 * app_math_sin( 6.2831852 * (double)i/ ((double)i_num-1.0) * 79 );
*/		f_ave += f_data[i];
	}
	f_ave /= i_num;
	
	for (i=0; i < i_num; i++) {
		f_tmp     =  app_math_cos( 6.2831852 * (double)i/ ((double)i_num-1.0) );
		f_tmp     =  0.5 - (0.5 * f_tmp);
//		f_tmp = 1;
		f_work[i] = (f_data[i] - f_ave) * f_tmp;
	}
}

// ===========================================================================
// app_EWO_Hammig2		**** Hamming function: 0.54-0.46 cos(2πx) [x=0-1] ****
//		[INPUT]		double					f_data[]			Original data
//				 	double 					f_work[]			Return   data
//					int 	  				i_num				Num of data
// ===========================================================================
void	app_EWO_Hamming2( 	double	f_data[],
						 	double 	f_work[],
							int 	i_num )
{
	int		i;
	double	f_ave, f_tmp;
	
//	f_ave = ( f_data[0] + f_data[i_num-1] ) / 2.0; //modified by Y. Kasahara(2016.3.16)
	for (i=0; i < i_num; i++) {
		f_tmp     =  app_math_cos( 6.2831852 * (double)i/ ((double)i_num-1.0) );
		f_tmp     =  0.54 - (0.46 * f_tmp);
//		f_work[i] = (f_data[i] - f_ave) * f_tmp; //modified by Y. Kasahara(2016.3.16)
		f_work[i] = f_data[i] * f_tmp; //modified by Y. Kasahara(2016.3.16)
	}
}


// ===========================================================================
// app_EWO_Hammig		**** Hamming function: 0.54-0.46 cos(2πx) [x=0-1] ****
//		[INPUT]		short					s_data[]			Original data
//				 	double 					f_work[]			Return   data
//					int 	  				i_num				Num of data
// ===========================================================================
void	app_EWO_Hamming( 	short	s_data[],
						 	double 	f_work[],
							int 	i_num )
{
	int		i;
	double	f_ave, f_tmp;
	
//	f_ave = ( (double)s_data[0] + (double)s_data[i_num-1] ) / 2.0; //modified by Y. Kasahara(2016.3.16)
	for (i=0; i < i_num; i++) {
		f_tmp     =  app_math_cos( 6.2831852 * (double)i/ ((double)i_num-1.0) );
		f_tmp     =  0.54 - (0.46 * f_tmp);
//		f_work[i] = ((double)s_data[i] - f_ave) * f_tmp; //modified by Y. Kasahara(2016.3.16)
		f_work[i] = (double)s_data[i] * f_tmp; //modified by Y. Kasahara(2016.3.16)
	}
}



// ===========================================================================
// app_EWO_Blackman		**** Blackman function: 0.42 - 0.5 cos(2πx) + 0.08 cos(4πx) ****
//		[INPUT]		short					s_data[]			Original data
//				 	double 					f_work[]			Return   data
//					int 	  				i_num				Num of data
// ===========================================================================
void	app_EWO_Blackman( 	short	s_data[],
						 	double 	f_work[],
							int 	i_num )
{
	int		i;
	double	f_ave, f_tmp, f_tmp2;
	
//	f_ave = ( (double)s_data[0] + (double)s_data[i_num-1] ) / 2.0; //modified by Y. Kasahara(2016.3.16)
	for (i=0; i < i_num; i++) {
		f_tmp     =  app_math_cos( 6.2831852  * (double)i/ ((double)i_num-1.0) );
		f_tmp2    =  app_math_cos( 12.5663704 * (double)i/ ((double)i_num-1.0) );
		f_tmp     =  0.42 - 0.50 * f_tmp + 0.08 * f_tmp2;
//		f_work[i] = ((double)s_data[i] - f_ave) * f_tmp; //modified by Y. Kasahara(2016.3.16)
		f_work[i] = (double)s_data[i] * f_tmp; //modified by Y. Kasahara(2016.3.16)
	}
}