ngspice/src/frontend/com_fft.c

/**********
Copyright 2008 Holger Vogt.  All rights reserved.
Author:   2008 Holger Vogt
**********/

/*
 * Code to do fast fourier transform on data.
 */

#define GREEN /* select fast Green's fft */

#include "ngspice/ngspice.h"
#include "ngspice/ftedefs.h"
#include "ngspice/dvec.h"
#include "ngspice/sim.h"

#include "com_fft.h"
#include "variable.h"
#include "parse.h"
#include "../misc/misc_time.h"
#include "ngspice/fftext.h"

static void fftext(double*, double*, long int, long int, int);

void
com_fft(wordlist *wl)
{
    ngcomplex_t **fdvec;
    double  **tdvec;
    double  *freq, *win, *time;
    double  delta_t, span;
    int     fpts, i, j, tlen, ngood;
    struct dvec  *f, *vlist, *lv = NULL, *vec;
    struct pnode *names, *first_name;

#ifdef GREEN
    int mm;
#endif

    double *reald, *imagd;
    int size, sign, order;
    double scale, sigma;

    if (!plot_cur || !plot_cur->pl_scale) {
        fprintf(cp_err, "Error: no vectors loaded.\n");
        return;
    }
    if (!isreal(plot_cur->pl_scale) ||
        ((plot_cur->pl_scale)->v_type != SV_TIME)) {
        fprintf(cp_err, "Error: fft needs real time scale\n");
        return;
    }

    tlen = (plot_cur->pl_scale)->v_length;
    time = (plot_cur->pl_scale)->v_realdata;
    span = time[tlen-1] - time[0];
    delta_t = span/(tlen - 1);

#ifdef GREEN
    // size of input vector is power of two and larger than spice vector
    size = 1;
    mm = 0;
    while (size < tlen) {
        size <<= 1;
        mm++;
    }
#else
    /* size of input vector is power of two and larger than spice vector */
    size = 1;
    while (size < tlen)
        size *= 2;
#endif
    /* output vector has length of size/2 */
    fpts = size/2;

    /* window functions - should have an average of one */
    win = TMALLOC(double, tlen);
    {
       char   window[BSIZE_SP];
       double maxt = time[tlen-1];
       if (!cp_getvar("specwindow", CP_STRING, window))
           strcpy(window,"blackman");
       if (eq(window, "none"))
          for(i=0; i<tlen; i++) {
             win[i] = 1.0;
          }
       else if (eq(window, "rectangular"))
          for(i=0; i<tlen; i++) {
             if (maxt-time[i] > span) {
                win[i] = 0.0;
             } else {
                win[i] = 1.0;
             }
          }
       else if (eq(window, "triangle") || eq(window, "bartlet") || eq(window, "bartlett"))
          for(i=0; i<tlen; i++) {
             if (maxt-time[i] > span) {
                win[i] = 0.0;
             } else {
                win[i] = 2.0 - fabs(2+4*(time[i]-maxt)/span);
             }
          }
       else if (eq(window, "hann") || eq(window, "hanning") || eq(window, "cosine"))
          for(i=0; i<tlen; i++) {
             if (maxt-time[i] > span) {
                win[i] = 0.0;
             } else {
                win[i] = 1.0 - cos(2*M_PI*(time[i]-maxt)/span);
             }
          }
       else if (eq(window, "hamming"))
          for(i=0; i<tlen; i++) {
             if (maxt-time[i] > span) {
                win[i] = 0.0;
             } else {
                win[i] = 1.0 - 0.46/0.54*cos(2*M_PI*(time[i]-maxt)/span);
             }
          }
       else if (eq(window, "blackman"))
          for(i=0; i<tlen; i++) {
             if (maxt-time[i] > span) {
                win[i] = 0;
             } else {
                win[i]  = 1.0;
                win[i] -= 0.50/0.42*cos(2*M_PI*(time[i]-maxt)/span);
                win[i] += 0.08/0.42*cos(4*M_PI*(time[i]-maxt)/span);
             }
          }
       else if (eq(window, "flattop"))
          for(i=0; i<tlen; i++) {
             if (maxt-time[i] > span) {
                win[i] = 0;
             } else {
                win[i]  = 1.0;
                win[i] -= 1.93*cos(2*M_PI*(time[i]-maxt)/span);
                win[i] += 1.29*cos(4*M_PI*(time[i]-maxt)/span);
                win[i] -= 0.388*cos(6*M_PI*(time[i]-maxt)/span);
                win[i] += 0.032*cos(8*M_PI*(time[i]-maxt)/span);
             }
          }
       else if (eq(window, "gaussian")) {
          if (!cp_getvar("specwindoworder", CP_NUM, &order)) order = 2;
          if (order < 2) order = 2;
          sigma=1.0/order;
          scale=0.83/sigma;
          for(i=0; i<tlen; i++) {
             if (maxt-time[i] > span) {
                win[i] = 0;
             } else {
                win[i] = scale*exp(-0.5*pow((time[i]-maxt/2)/(sigma*maxt/2),2));
             }
          }
       } else {
          fprintf(cp_err, "Warning: unknown window type %s\n", window);
          tfree(win);
          return;
       }
    }

    names = ft_getpnames(wl, TRUE);
    first_name = names;
    vlist = NULL;
    ngood = 0;
    while (names) {
        vec = ft_evaluate(names);
        names = names->pn_next;
        while (vec) {
            if (vec->v_length != tlen) {
                fprintf(cp_err, "Error: lengths of %s vectors don't match: %d, %d\n",
                        vec->v_name, vec->v_length, tlen);
                vec = vec->v_link2;
                continue;
            }
            if (!isreal(vec)) {
                fprintf(cp_err, "Error: %s isn't real!\n",
                        vec->v_name);
                vec = vec->v_link2;
                continue;
            }
            if (vec->v_type == SV_TIME) {
                vec = vec->v_link2;
                continue;
            }
            if (!vlist)
                vlist = vec;
            else
                lv->v_link2 = vec;
            lv = vec;
            vec = vec->v_link2;
            ngood++;
        }
    }
    free_pnode_o(first_name);
    if (!ngood) {
       tfree(win);
       return;
    }

    plot_cur = plot_alloc("spectrum");
    plot_cur->pl_next = plot_list;
    plot_list = plot_cur;
    plot_cur->pl_title = copy((plot_cur->pl_next)->pl_title);
    plot_cur->pl_name = copy("Spectrum");
    plot_cur->pl_date = copy(datestring( ));

    freq = TMALLOC(double, fpts);
    f = alloc(struct dvec);
    ZERO(f, struct dvec);
    f->v_name = copy("frequency");
    f->v_type = SV_FREQUENCY;
    f->v_flags = (VF_REAL | VF_PERMANENT | VF_PRINT);
    f->v_length = fpts;
    f->v_realdata = freq;
    vec_new(f);

    for (i = 0; i<fpts; i++) freq[i] = i*1.0/span*tlen/size;


    tdvec = TMALLOC(double  *, ngood);
    fdvec = TMALLOC(ngcomplex_t *, ngood);
    for (i = 0, vec = vlist; i<ngood; i++) {
       tdvec[i] = vec->v_realdata; /* real input data */
       fdvec[i] = TMALLOC(ngcomplex_t, fpts); /* complex output data */
       f = alloc(struct dvec);
       ZERO(f, struct dvec);
       f->v_name = vec_basename(vec);
       f->v_type = SV_NOTYPE;
       f->v_flags = (VF_COMPLEX | VF_PERMANENT);
       f->v_length = fpts;
       f->v_compdata = fdvec[i];
       vec_new(f);
       vec = vec->v_link2;
    }

    sign = 1;

    printf("FFT: Time span: %g s, input length: %d, zero padding: %d\n", span, size, size-tlen);
    printf("FFT: Freq. resolution: %g Hz, output length: %d\n", 1.0/span*tlen/size, fpts);

    reald = TMALLOC(double, size);
    imagd = TMALLOC(double, size);
    for (i = 0; i<ngood; i++) {
        for (j = 0; j < tlen; j++){
            reald[j] = tdvec[i][j]*win[j];
            imagd[j] = 0.0;
        }
        for (j = tlen; j < size; j++){
            reald[j] = 0.0;
            imagd[j] = 0.0;
        }
#ifdef GREEN
        // Green's FFT 
        fftInit(mm);
        rffts(reald, mm, 1);
        fftFree();
        scale = size;
/* Re(x[0]), Re(x[N/2]), Re(x[1]), Im(x[1]), Re(x[2]), Im(x[2]), ... Re(x[N/2-1]), Im(x[N/2-1]). */
        for (j=0;j<fpts;j++){
            fdvec[i][j].cx_real = reald[2*j]/scale;
            fdvec[i][j].cx_imag = reald[2*j+1]/scale;
        }
        fdvec[i][0].cx_imag = 0;
#else
        fftext(reald, imagd, size, tlen, sign);
        scale = 0.66;

        for (j=0;j<fpts;j++){
            fdvec[i][j].cx_real = reald[j]/scale;
            fdvec[i][j].cx_imag = imagd[j]/scale;
        }
#endif
    }
    tfree(reald);
    tfree(imagd);

    tfree(tdvec);
    tfree(fdvec);
    tfree(win);
}

void
com_psd(wordlist *wl)
{
    ngcomplex_t **fdvec;
    double  **tdvec;
    double  *freq, *win, *time, *ave;
    double  delta_t, span, noipower;
    int     mm;
    unsigned long size, ngood, fpts, i, j, tlen, jj, smooth, hsmooth;
    char    *s;
    struct dvec  *f, *vlist, *lv = NULL, *vec;
    struct pnode *names, *first_name;

    double *reald, *imagd;
    int sign, isreal;
    double scaling, sum;
    int order;
    double scale, sigma;

    if (!plot_cur || !plot_cur->pl_scale) {
        fprintf(cp_err, "Error: no vectors loaded.\n");
        return;
    }
    if (!isreal(plot_cur->pl_scale) || 
        ((plot_cur->pl_scale)->v_type != SV_TIME)) {
        fprintf(cp_err, "Error: fft needs real time scale\n");
        return;
    }
		
    tlen = (plot_cur->pl_scale)->v_length;
    time = (plot_cur->pl_scale)->v_realdata;
    span = time[tlen-1] - time[0];
    delta_t = span/(tlen - 1);
    
    // get filter length from parameter input
    s = wl->wl_word;
    ave = ft_numparse(&s, FALSE);
    if (!ave || (*ave < 1.0)) {
    	fprintf(cp_out, "Number of averaged data points:  %d\n", 1);
        smooth = 1;
    }
    else smooth = (int)(*ave);    
    wl = wl->wl_next;    
    
    // size of input vector is power of two and larger than spice vector
    size = 1;
    mm = 0;
    while (size < tlen) {
        size <<= 1;
        mm++;
    }

    // output vector has length of size/2
    fpts = size>>1;    

    // window function   
    win = TMALLOC(double, tlen);
    {
       char   window[BSIZE_SP];
       double maxt = time[tlen-1];
       if (!cp_getvar("specwindow", CP_STRING, window)) 
           strcpy(window,"blackman");
       if (eq(window, "none"))
          for(i=0; i<tlen; i++) {
             win[i] = 1;
          }
       else if (eq(window, "rectangular"))
           for(i=0; i<tlen; i++) {
             if (maxt-time[i] > span) {
                win[i] = 0;
             } else {
                win[i] = 1;
             }
          }
       else if (eq(window, "hanning") || eq(window, "cosine"))
          for(i=0; i<tlen; i++) {
             if (maxt-time[i] > span) {
                win[i] = 0;
             } else {
                win[i] = 1 - cos(2*M_PI*(time[i]-maxt)/span);
             }
          }
       else if (eq(window, "hamming"))
          for(i=0; i<tlen; i++) {
             if (maxt-time[i] > span) {
                win[i] = 0;
             } else {
                win[i] = 1 - 0.92/1.08*cos(2*M_PI*(time[i]-maxt)/span);
             }
          }
       else if (eq(window, "triangle") || eq(window, "bartlet"))
          for(i=0; i<tlen; i++) {
             if (maxt-time[i] > span) {
                win[i] = 0;
             } else {
                win[i] = 2 - fabs(2+4*(time[i]-maxt)/span);
             }
          }
       else if (eq(window, "blackman")) {
          int order;
          if (!cp_getvar("specwindoworder", CP_NUM, &order)) order = 2;
          if (order < 2) order = 2;  /* only order 2 supported here */
          for(i=0; i<tlen; i++) {
             if (maxt-time[i] > span) {
                win[i] = 0;
             } else {
                win[i]  = 1;
                win[i] -= 0.50/0.42*cos(2*M_PI*(time[i]-maxt)/span);
                win[i] += 0.08/0.42*cos(4*M_PI*(time[i]-maxt)/span);
             }
          }
       } else if (eq(window, "gaussian")) {
          if (!cp_getvar("specwindoworder", CP_NUM, &order)) order = 2;
          if (order < 2) order = 2;
          sigma=1.0/order;
          scale=0.83/sigma;
          for(i=0; i<tlen; i++) {
             if (maxt-time[i] > span) {
                win[i] = 0;
             } else {
                win[i] = scale*exp(-0.5*pow((time[i]-maxt/2)/(sigma*maxt/2),2));
             }
          }
/*          int order;
          double scale;
          extern double erfc(double);
          if (!cp_getvar("specwindoworder", CP_NUM, &order)) order = 2;
          if (order < 2) order = 2;
          scale = pow(2*M_PI/order,0.5)*(0.5-erfc(pow(order,0.5)));
          for(i=0; i<tlen; i++) {
             if (maxt-time[i] > span) {
                win[i] = 0;
             } else {
                win[i] = exp(-0.5*order*(1-2*(maxt-time[i])/span)
                                       *(1-2*(maxt-time[i])/span))/scale;
             }
          }
*/
      } else {
          fprintf(cp_err, "Warning: unknown window type %s\n", window);
          tfree(win);
          return;
       }
    }

    names = ft_getpnames(wl, TRUE);
    first_name = names;
    vlist = NULL;
    ngood = 0;
    while (names) {
        vec = ft_evaluate(names);
        names = names->pn_next;
        while (vec) {
            if (vec->v_length != (int)tlen) {
                fprintf(cp_err, "Error: lengths of %s vectors don't match: %d, %lu\n",
                        vec->v_name, vec->v_length, tlen);
                vec = vec->v_link2;
                continue;
            }
            if (!isreal(vec)) {
                fprintf(cp_err, "Error: %s isn't real!\n", 
                        vec->v_name);
                vec = vec->v_link2;
                continue;
            }
            if (vec->v_type == SV_TIME) {
                vec = vec->v_link2;
                continue;
            }
            if (!vlist)
                vlist = vec;
            else
                lv->v_link2 = vec;
            lv = vec;
            vec = vec->v_link2;
            ngood++;
        }
    }
    free_pnode_o(first_name);
    if (!ngood) {
       return;
    }
 
    plot_cur = plot_alloc("spectrum");
    plot_cur->pl_next = plot_list;
    plot_list = plot_cur;
    plot_cur->pl_title = copy((plot_cur->pl_next)->pl_title);
    plot_cur->pl_name = copy("PSD");
    plot_cur->pl_date = copy(datestring( ));

    freq = TMALLOC(double, fpts + 1);
    f = alloc(struct dvec);
    ZERO(f, struct dvec);
    f->v_name = copy("frequency");
    f->v_type = SV_FREQUENCY;
    f->v_flags = (VF_REAL | VF_PERMANENT | VF_PRINT);
    f->v_length = fpts;
    f->v_realdata = freq;
    vec_new(f);

    for (i = 0; i <= fpts; i++) freq[i] = i*1./span*tlen/size;

    tdvec = TMALLOC(double*, ngood);
    fdvec = TMALLOC(ngcomplex_t*, ngood);
    for (i = 0, vec = vlist; i<ngood; i++) {
       tdvec[i] = vec->v_realdata; /* real input data */
       fdvec[i] = TMALLOC(ngcomplex_t, fpts + 1); /* complex output data */
       f = alloc(struct dvec);
       ZERO(f, struct dvec);
       f->v_name = vec_basename(vec);
       f->v_type = SV_NOTYPE; //vec->v_type;
       f->v_flags = (VF_COMPLEX | VF_PERMANENT);
       f->v_length = fpts + 1;
       f->v_compdata = fdvec[i];
       vec_new(f);
       vec = vec->v_link2;
    }

    printf("PSD: Time span: %g s, input length: %lu, zero padding: %lu\n", span, size, size-tlen);
    printf("PSD: Freq. resolution: %g Hz, output length: %lu\n", 1.0/span*tlen/size, fpts);

    sign = 1;
    isreal = 1;
    
    reald = TMALLOC(double, size);
    imagd = TMALLOC(double, size);
        
//        scale = 0.66;

    for (i = 0; i<ngood; i++) {
        double intres;
        for (j = 0; j < tlen; j++){
    	   reald[j] = (tdvec[i][j]*win[j]);
           imagd[j] = 0.;
        }            
        for (j = tlen; j < size; j++){
    	   reald[j] = 0.;
           imagd[j] = 0.;
        }  
                 
        // Green's FFT 
        fftInit(mm);
        rffts(reald, mm, 1);
        fftFree();
        scaling = size;

/* Re(x[0]), Re(x[N/2]), Re(x[1]), Im(x[1]), Re(x[2]), Im(x[2]), ... Re(x[N/2-1]), Im(x[N/2-1]). */
        intres = (double)size * (double)size;
        noipower = fdvec[i][0].cx_real = reald[0]*reald[0]/intres;
        fdvec[i][fpts].cx_real = reald[1]*reald[1]/intres;
        noipower += fdvec[i][fpts-1].cx_real;    
        for (j=1; j < fpts; j++){
           jj = j<<1;
           fdvec[i][j].cx_real = 2.* (reald[jj]*reald[jj] + reald[jj + 1]*reald[jj + 1])/intres;
           fdvec[i][j].cx_imag = 0;
           noipower += fdvec[i][j].cx_real;
        if (!finite(noipower))
            break;
        }

        printf("Total noise power up to Nyquist frequency %5.3e Hz:\n%e V^2 (or A^2), \nnoise voltage or current %e V (or A)\n",
            freq[fpts],noipower, sqrt(noipower));
         
        /* smoothing with rectangular window of width "smooth",
           plotting V/sqrt(Hz) or I/sqrt(Hz) */
        if (smooth < 1)
            continue;

        hsmooth = smooth>>1;
        for (j=0; j<hsmooth; j++){
           sum = 0.;
           for (jj = 0; jj < hsmooth + j; jj++)
              sum += fdvec[i][jj].cx_real;
           sum /= (hsmooth + j);        
           reald[j] = (sqrt(sum)/scaling);
        }
        for (j=hsmooth; j<fpts-hsmooth; j++){
           sum = 0.;
           for (jj = 0; jj < smooth; jj++)
              sum += fdvec[i][j-hsmooth+jj].cx_real;
           sum /= smooth;        
           reald[j] = (sqrt(sum)/scaling);
        }
        for (j=fpts-hsmooth; j<fpts; j++){
           sum = 0.;
           for (jj = 0; jj < smooth; jj++)
              sum += fdvec[i][j-hsmooth+jj].cx_real;
           sum /= (fpts - j + hsmooth - 1);        
           reald[j] = (sqrt(sum)/scaling);
        }        
        for (j=0; j<fpts; j++)
           fdvec[i][j].cx_real = reald[j];
    }
        
    free(reald);
    free(imagd);
    
    tfree(tdvec);
    tfree(fdvec);
}




static void fftext(double* x, double* y, long int n, long int nn, int dir)
{
/*
   http://local.wasp.uwa.edu.au/~pbourke/other/dft/
   download 22.05.08
   Used with permission from the author Paul Bourke
*/

/*
   This computes an in-place complex-to-complex FFT
   x and y are the real and imaginary arrays
   n is the number of points, has to be to the power of 2
   nn is the number of points w/o zero padded values
   dir =  1 gives forward transform
   dir = -1 gives reverse transform
*/

   long i,i1,j,k,i2,l,l1,l2;
   double c1,c2,tx,ty,t1,t2,u1,u2,z;
   int m=0, mm=1;

   /* get the exponent to the base of 2 from the number of points */
   while (mm < n) {
       mm *= 2;
       m++;
   }

   /* Do the bit reversal */
   i2 = n >> 1;
   j = 0;
   for (i=0;i<n-1;i++) {
      if (i < j) {
         tx = x[i];
         ty = y[i];
         x[i] = x[j];
         y[i] = y[j];
         x[j] = tx;
         y[j] = ty;
      }
      k = i2;
      while (k <= j) {
         j -= k;
         k >>= 1;
      }
      j += k;
   }

   /* Compute the FFT */
   c1 = -1.0;
   c2 = 0.0;
   l2 = 1;
   for (l=0;l<m;l++) {
      l1 = l2;
      l2 <<= 1;
      u1 = 1.0;
      u2 = 0.0;
      for (j=0;j<l1;j++) {
         for (i=j;i<n;i+=l2) {
            i1 = i + l1;
            t1 = u1 * x[i1] - u2 * y[i1];
            t2 = u1 * y[i1] + u2 * x[i1];
            x[i1] = x[i] - t1;
            y[i1] = y[i] - t2;
            x[i] += t1;
            y[i] += t2;
         }
         z =  u1 * c1 - u2 * c2;
         u2 = u1 * c2 + u2 * c1;
         u1 = z;
      }
      c2 = sqrt((1.0 - c1) / 2.0);
      if (dir == 1)
         c2 = -c2;
      c1 = sqrt((1.0 + c1) / 2.0);
   }

   /* Scaling for forward transform */
   if (dir == 1) {
      double scale = 1.0 / nn;
      for (i=0;i<n;i++) {
         x[i] *= scale; /* don't consider zero padded values */
         y[i] *= scale;
      }
   }
}