[sdiy] Digital oscillators [was: Active VCO temp compensation]

[Seb Francis]

Thanks Antti and the others.  This is great information.

Antti Huovilainen wrote:
> Since this question gets asked a lot, I'll list some of the common 
> methods. Roughly from easy to hard. Oversampling here means proper 
> oversampling with high quality lowpass filtering before decimating to 
> target samplerate. Simply averaging N samples will not work.
>
> 1) Trivial saw with oversampling
> Pros: Easy, can do any waveshape, allows simple sync and FM
> Cons: Requires massive (64..256x) oversampling to sound good
>
This is what I had in mind to start with.  I was going to try something 
like 1MHz sampling rate, but you're saying that 3MHz+ is going to be 
needed for a good sound.  What do you mean by 'high quality' lowpass 
filtering? ... Scott talked about a 511 tap FIR filter.  This seems a 
*lot* to implement on a dsPIC (which is what I'm using).

On my 4xD delay when I needed to halve the sampling frequency I used an 
FIR with just 9 taps and was pretty happy with the results.  I actually 
quite liked the sound of the more gentle roll-off.

I guess if one is not too concerned about the very high frequency 
harmonics then the low pass can start at a lower frequency and roll off 
more gently, thus needing less taps.  After all, many much loved analog 
synths have decidedly limited bandwidths.

>
> 5b) BandLimited StEps (BLEP)
> For each oscillator reset, sum a bandlimited step with the trivial 
> saw. The steps are precalculated and stored in a table (can be quite 
> short when interpolation is used between two phases.
>
> Pros: Very good quality. No oversampling required. Can do bandlimited 
> FM, PWM and sync. Probably the only method that can do audio rate PWM 
> and sync.
> Cons: Requires a divide per cycle. Can be complicated: calculating 
> required table entry is not trivial when using sync or pwm.
>

This sounds interesting.  Am I understanding right that it would need a 
separate table for each type of waveform discontinuity - so a pulse, up 
saw, down saw could all use the same table for their transitions, but a 
triangle wave would need a different table of steps?  And presumably 
this can't be applied to something like a sine, or complex waveforms?

In my case I want to have many oscillators, each slightly detuned, so I 
guess the amount of maths is going to add up and there's going to be a 
point where it becomes better to just using simple 
oversampling/filtering/decimating.

Seb