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Band Limited PWM Generator

Type : PWM generator
References : Posted by paul_sernine75 AT hotmail DOT fr

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.


Paul Sernine.

Code :
// 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.
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 --------------------------------------------------
//freq=27.5f*powf(2.0f,8*ns/(8*30*44100.0f/6)); //sweep
//freq*=(1.0f+0.01f*sinf(ns*0.0015f)); //vibrato
dphi=freq*(pi/22050.0f); // phase increment
//notes and enveloppe trigger
if(note>=(sizeof(seq)-1))// sequence loop
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

//waveform generation -----------------------------------------------
//Common phase
phi+=dphif; // phase increment
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
return 0;


Added on : 23/05/06 by ---
Comment :
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.

Added on : 04/02/10 by penrose[ AT ]alumni[ DOT ]princeton[ DOT ]edu
Comment :

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.

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