# Bandlimited waveforms…¶

**Author or source:**Paul Kellet**Created:**2002-01-17 00:56:04

```
(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.
```

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 | ```
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¶

**Date**: 2004-09-23 00:07:02**By**: es.ollehc@evawenis

```
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
```

**Date**: 2012-01-01 23:17:35**By**: ku.oc.oohay@ekolbdiurd

```
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.
```