[sdiy] Stupid Lookup Table Tricks - BLEPs when you can't divide (and can barely multiply)

[O Gillet]

There is an alternate firmware for Shruthi / Ambika that uses
PolyBlep. The reciprocal computation code has a better resolution,
using the identity 1 / 0.5x = 2x. Code here:
https://github.com/bjoeri/ambika/blob/master/voicecard/oscillator.cc#L56

The original Shruthi / Ambika code uses band-limited wavetables, as
described by Richie ; with some crossfading from one octave to the
other.
On Thu, Jun 28, 2018 at 1:05 PM <rburnett at richieburnett.co.uk> wrote:
>
> Neat!  The quality is not bad but there is still quite a bit of audible
> aliasing even with the corrections enabled.
>
> I think the problem is that your LUT of reciprocal values really needs a
> lot more resolution.  It returns the same value for large ranges of
> input index.  This heavily quantizes the positioning of the polyBLEP
> corrections and ultimately limits their effectiveness for the
> anti-aliasing.
>
> You're only seeing about 20dB reduction in aliasing, and should be able
> to do much better than this in practice.  But I think the implementation
> is being limited by the resolution of the reciprocal lookup.
>
> The neat thing about polyBLEP is that the correction curves are simple
> functions, so you would ideally calculate these on a more capable
> platform, instead of using a pre-calculated lookup table.  Then you are
> only limited to the numerical precision of the calculations and not the
> number of entries in a LUT.  But I understand your motivations for doing
> it this way to see if it can be made to work :-)
>
> FWIW, if you just want to generate anti-aliased sawtooths and pulse
> waveforms on a low-end 8-bit platform without oscillator-sync, then the
> best option is probably just to use wavetables.  You store a whole load
> of sawtooth renderings generated by additive synthesis with
> progressively less harmonics in a lookup table.  Every time you go up by
> one octave in pitch you switch to the next waveform from the table.
> Square an pulse can be generated by taking the difference of two
> phase-shifted sawtooths.
>
> -Richie,
>
>
> On 2018-06-28 01:14, Gordonjcp wrote:
> > Why would you pick an avr8 to do bandlimited oscillators?
> >
> > Because folk say it won't work, that's why!
> >
> > https://github.com/ErroneousBosh/slttblep
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