Bandlimited waveforms…

  • Author or source: Paul Kellet
  • Created: 2002-01-17 00:56:04
notes
(Quoted from Paul's mail)
Below is another waveform generation method based on a train of sinc functions (actually
an alternating loop along a sinc between t=0 and t=period/2).

The code integrates the pulse train with a dc offset to get a sawtooth, but other shapes
can be made in the usual ways... Note that 'dc' and 'leak' may need to be adjusted for
very high or low frequencies.

I don't know how original it is (I ought to read more) but it is of usable quality,
particularly at low frequencies. There's some scope for optimisation by using a table for
sinc, or maybe a a truncated/windowed sinc?

I think it should be possible to minimise the aliasing by fine tuning 'dp' to slightly
less than 1 so the sincs join together neatly, but I haven't found the best way to do it.
Any comments gratefully received.
code
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float p=0.0f;      //current position
float dp=1.0f;     //change in postion per sample
float pmax;        //maximum position
float x;           //position in sinc function
float leak=0.995f; //leaky integrator
float dc;          //dc offset
float saw;         //output


//set frequency...

  pmax = 0.5f * getSampleRate() / freqHz;
  dc = -0.498f/pmax;


//for each sample...

  p += dp;
  if(p < 0.0f)
  {
    p = -p;
    dp = -dp;
  }
  else if(p > pmax)
  {
    p = pmax + pmax - p;
    dp = -dp;
  }

  x= pi * p;
  if(x < 0.00001f)
     x=0.00001f; //don't divide by 0

  saw = leak*saw + dc + (float)sin(x)/(x);

Comments

Hi,
Has anyone managed to implement this in a VST?
If anyone could mail me and talk me through it I'd be very grateful.  Yes, I'm a total newbie and yes, I'm after a quick-fix solution...we all have to start somewhere, eh?

As it stands, where I should be getting a sawtooth I'm getting a full-on and inaudible signal...!

Even a small clue would be nice.
Cheers,
A

this sounds quite nice, maybe going to use it an LV 2 plugin
  • Date: 2016-01-17 13:24:11
  • By: pvdmeer [atorsomething] gmail [point] com
this is really amazing, and easily hacked into a lut-based algo. i'll try windowing it too, but it already looks like aliasing is well within acceptable levels.