Generator

  • Author or source: Paul Sernine
  • Type: antialiased sawtooth
  • Created: 2006-02-23 22:38:56
notes
This code generates a swept antialiasing sawtooth in a raw 16bit pcm file.
It is based on the quad differentiation of a 5th order polynomial. The polynomial
harmonics (and aliased harmonics) decay at 5*6 dB per oct. The differenciators correct the
spectrum and waveform, while aliased harmonics are still attenuated.
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/* clair.c         Examen Partiel 2b
   T.Rochebois
   02/03/98
*/
#include <stdio.h>
#include <math.h>
main()
{
  double phase=0,dphase,freq,compensation;
  double aw0=0,aw1=0,ax0=0,ax1=0,ay0=0,ay1=0,az0=0,az1=0,sortie;
  short aout;
  int sr=44100;       //sample rate (Hz)
  double f_debut=55.0;//start freq (Hz)
  double f_fin=sr/6.0;//end freq (Hz)
  double octaves=log(f_fin/f_debut)/log(2.0);
  double duree=50.0;  //duration (s)
  int i;
  FILE* f;
  f=fopen("saw.pcm","wb");
  for(i=0;i<duree*sr;i++)
  {
    //exponential frequency sweep
    //Can be replaced by anything you like.
    freq=f_debut*pow(2.0,octaves*i/(duree*sr));
    dphase=freq*(2.0/sr);     //normalised phase increment
    phase+=dphase;            //phase incrementation
    if(phase>1.0) phase-=2.0; //phase wrapping (-1,+1)

    //polynomial calculation (extensive continuity at -1 +1)
    //        7       1  3    1   5
    //P(x) = --- x - -- x  + --- x
    //       360     36      120
    aw0=phase*(7.0/360.0 + phase*phase*(-1/36.0 + phase*phase*(1/120.0)));
    // quad differentiation (first order high pass filters)
    ax0=aw1-aw0; ay0=ax1-ax0; az0=ay1-ay0; sortie=az1-az0;
    //compensation of the attenuation of the quad differentiator
    //this can be calculated at "control rate" and linearly
    //interpolated at sample rate.
    compensation=1.0/(dphase*dphase*dphase*dphase);
    // compensation and output
    aout=(short)(15000.0*compensation*sortie);
    fwrite(&aout,1,2,f);
    //old memories of differentiators
    aw1=aw0; ax1=ax0; ay1=ay0; az1=az0;
  }
  fclose(f);
}

Comments

More infos and discussions in the KVR thread:
http://www.kvraudio.com/forum/viewtopic.php?t=123498

nice but i prefer the fishy algo, it generates less alias.
bonaveture rosignol