Band Limited PWM Generator

notes
This is a commented and deobfuscated version of my 1st April fish. It is based on a
tutorial code by Thierry Rochebois. I just translated and added comments.

Regards,

Paul Sernine.
code
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// SelfPMpwm.cpp

// Antialised PWM oscillator

// Based on a tutorial code by Thierry Rochebois (98).
// Itself inspired by US patent 4249447 by Norio Tomisawa (81).
// Comments added/translated by P.Sernine (06).

// This program generates a 44100Hz-raw-PCM-mono-wavefile.
// It is based on Tomisawa's self-phase-modulated sinewave generators.
// Rochebois uses a common phase accumulator to feed two half-Tomisawa-
// oscillators. Each half-Tomisawa-oscillator generates a bandlimited
// sawtooth (band limitation depending on the feedback coeff B).
// These half oscillators are phase offseted according to the desired
// pulse width. They are finally combined to obtain the PW signal.
// Note: the anti-"hunting" filter is a critical feature of a good
// implementation of Tomisawa's method.
#include <math.h>
#include <stdio.h>
const float pi=3.14159265359f;
int main()
{
  float freq,dphi; //!< frequency (Hz) and phase increment(rad/sample)
  float dphif=0;   //!< filtered (anti click) phase increment
  float phi=-pi;   //!< phase
  float Y0=0,Y1=0; //!< feedback memories
  float PW=pi;     //!< pulse width ]0,2pi[
  float B=2.3f;    //!< feedback coef
  FILE *f=fopen("SelfPMpwm.pcm","wb");
  // séquence ('a'=mi=E)
  // you can edit this if you prefer another melody.
  static char seq[]="aiakahiafahadfaiakahiahafahadf"; //!< sequence
  int note=sizeof(seq)-2;  //!< note number in the sequence
  int octave=0;     //!< octave number
  float env,envf=0; //!< envelopped and filtered envelopped
  for(int ns=0;ns<8*(sizeof(seq)-1)*44100/6;ns++)
  {
//waveform control --------------------------------------------------
    //Frequency
    //freq=27.5f*powf(2.0f,8*ns/(8*30*44100.0f/6)); //sweep
    freq=27.5f*powf(2.0f,octave+(seq[note]-'a'-5)/12.0f);
    //freq*=(1.0f+0.01f*sinf(ns*0.0015f));        //vibrato
    dphi=freq*(pi/22050.0f);   // phase increment
    dphif+=0.1f*(dphi-dphif);
    //notes and enveloppe trigger
    if((ns%(44100/6))==0)
    {
      note++;
      if(note>=(sizeof(seq)-1))// sequence loop
      {
        note=0;
        octave++;
      }
      env=1; //env set
      //PW=pi*(0.4+0.5f*(rand()%1000)/1000.0f); //random PW
    }
    env*=0.9998f;              // exp enveloppe
    envf+=0.1f*(env-envf);     // de-clicked enveloppe
    B=1.0f;                    // feedback coefficient
    //try this for a nice bass sound:
    //B*=envf*envf;              // feedback controlled by enveloppe
    B*=2.3f*(1-0.0001f*freq);  // feedback limitation
    if(B<0)
      B=0;

//waveform generation -----------------------------------------------
    //Common phase
    phi+=dphif;                 // phase increment
    if(phi>=pi)
      phi-=2*pi;               // phase wrapping

    // "phase"    half Tomisawa generator 0
    // B*Y0 -> self phase modulation
    float out0=cosf(phi+B*Y0); // half-output 0
    Y0=0.5f*(out0+Y0);         // anti "hunting" filter

    // "phase+PW" half Tomisawa generator 1
    // B*Y1 -> self phase modulation
    // PW   -> phase offset
    float out1=cosf(phi+B*Y1+PW); // half-output 1
    Y1=0.5f*(out1+Y1);            // anti "hunting" filter

    // combination, enveloppe and output
    short s=short(15000.0f*(out0-out1)*envf);
    fwrite(&s,2,1,f);          // file output
  }
  fclose(f);
  return 0;
}

Comments

  • Date: 2006-05-23 09:31:44
  • By: —
Did anyone try this?

How is the antialiasing compared to applying phaserror between two oscs in zerocross, one aliasing
the other not (but pitcherror).

Best Regards,
Arif Ove Karlsen.

The implementation certainly produces aliased waveforms -- they are glaring on a spectrogram
at -60dB and faint at -30dB.  But it is a remarkably efficient algorithm. The aliasing can be
mitigated somewhat by using a smaller feedback coefficient.