[sdiy] [synth-diy] numerically controlled superoscillator without hard sync

[Tom Wiltshire]

Hi Damian,

This is a good idea. I think it came up in a discussion some time ago about the PPG - a famous variable sample rate instrument. We were considering possible ways to do something similar, and this approach was mooted.

It really does have a lot going for it - you could do wave shaping, or phase distortion, or whatever, and as you say, any aliasing products can be forced to remain harmonic. The advantages of this can't really be overstated.

I don't think the reconstruction filter is a massive issue either, since whatever sample rate you're using, you need to make sure it's sufficient for a decent audio quality - so say 48KHz or above. This means you're looking at designing a sharp anti-aliasing filter at around 24KHz - not impossible. Obviously getting a couple more octaves between the top of the audio range and the lowest sample rate would be nice, but that gets more demanding for the VCO.

And that's the problem. The VCO. You've got to run the uP at sufficient speed to get plenty of samples per wave cycle out of it - say 128 as a binary-friendly minimum. You need a certain number of processor instructions to calculate each sample, say 200. So we're looking at 128x200 = 25600 instructions per wave cycle. The PIC (for example) needs a clock at 4x the instruction rate, but let's assume a single clock per instruction. For a full MIDI range, your VCO has to cover 8.176Hz x 25600 = 209,306Hz to
12,543.8 x 25600 = 321,121,280Hz. That's a pretty big ask, unfortunately.

Paul Maddox's Monowave worked on this variable-rate principle (though without a uP doing the synthesis), and he made the job manageable by limiting the highest output frequency to around 4KHz - e.g if you knock a couple of octaves off the top, that helps!

I've thought about this a fair bit, 'cos I'd love it if it worked. So if there's something crucial I'm missing, do please speak up.

Regards,
Tom


On 9 Feb 2014, at 17:08, cheater00 . <cheater00 at gmail.com> wrote:

> Hi,
> 
> thinking about this recently, one could use a high-frequency
> oscillator, and use it as the clock for a microcontroller which
> assuredly outputs a single sample every n clocks. This way you can
> perform VA style synthesis where the time base is derived from an
> analog oscillator that can perform FM and other neat analog tricks. On
> the other hand the uC only has to synthesize at a single frequency. So
> say it's always synthesizing at A440, and you change the pitch by
> changing how fast it executes its algorithm, i.e. by changing the
> clock, i.e. by changing the sampling frequency. This way, externally
> (i.e. at the output of the DAC) the aliases are always precisely at
> the same position in relation to the base frequency of the note being
> played. The aliases become part of the timbre, enriching it. This is
> in contrast to aliasing in a system where the sampling frequency is
> fixed, and the pitch of the note being synthesized is changed in the
> usual way. In this case, which doesn't happen here, the aliases are at
> a different position for every pitch, and therefore the oscillator not
> only plays your desired melody, but also a quieter, undesired melody
> which is completely out of tune and works against your music.
> 
> The variable sample rate oscillator could also contain things like
> filters and other stuff. A whole VA could be implemented, and aliasing
> is not an issue at all.
> 
> The only thing you need to ensure is that your reconstruction filter
> works well with a variable sample rate.
> 
> Cheers,
> D.
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