[sdiy] BLIT/BLEP virtual analogue synthesis

[cheater cheater]

On Tue, Aug 3, 2010 at 17:41, Olivier Gillet <ol.gillet at gmail.com> wrote:
>> Not if you want sync or any real modulation
>
> True, though 2 BLEP oscillators on an AVR seems a bit out of reach. On
> a 16-bit dsPic, maybe...

Yes, two BLEP oscillators on something that's as fast as a 50 year old
computer is a bit out of reach.

>> The problem here is numerical accuracy
>
> With integration, yes.
>
>> No, but your distortion pedal can and then you can too.
>
> Hmmm, couldn't we use the same argument to dismiss the use of 44.1kHz
> as a sample rate for audio gear, arguing that if the output is passed
> through the right chain of modulators or octave shifters, everything
> above 22kHz could be shifted into the audio range, and must thus be
> preserved?

There's a reason why Protools goes up to 192k and why many people who
use it as a multitrack use maximum sampling rates. Some ADCs go up to
384kHz so that you can replay at 192 without a lot of coloration from
the oversampling filter.

>> Can't you fix that with a multisampled BLEP table?
>
> Correct me if I'm wrong, but at 8kHz you'd still be summing over a few
> tails of bleps to generate a mere sine wave (= the "expected" output
> of a band-limited synthesis of a 8kHz square with sr=44.1kHz)

My knowledge of the BLEP algorithm is not intimate enough to answer
this question off the top of my head, sorry



On Wed, Aug 4, 2010 at 02:45, nicolas <nicolas3141 at yahoo.com.au> wrote:
> I am not such an expert, but my understanding is that you can only trust nyquist with regard to the output you listen to.  But in a synth there are lots of intermediate signals we don't listen to.
>
> For example if that 8kHz sawtooth is beating with an 8.02kHz sawtooth you will clearly hear the beat product in an analogue synth because the higher harmonics are also involved in the beating.  But if those two sawtooths are digital approximations at moderate sample rates, there will be hardly any higher harmonics to beat together and the so resultant beating will be sine-like, which at 20Hz will be hardly audible.
>
> Won't this sort of problem happen throughout the synthesis, giving quite different results from analogue?

the difference will be very audible if this signal you mention is
later put through a clipper




On Wed, Aug 4, 2010 at 04:00, Olivier Gillet <ol.gillet at gmail.com> wrote:
> Isn't band-limiting (low-pass filtering at half the sampling frequency) linear?

yes, but non-linearities are non-linear. Even our ears.

> If so, BL (sawtooth 8kHz + sawtooth 8.02kHz) = BL sawtooth 8kHz + BL
> sawtooth 8.02kHz

Yes, but BL(NL(s8+s8.02)) != NL(BL(s8 + s8.02)) = NL(BL(s8) + BL(s8.02))

Or in short: nonlinear operators are not commutable with linear ones.

> I might be wrong about it, but the sawtooth 8kHz + sawtooth 8.02kHz
> sounds like a 8.01kHz fundamental with a 20 Hz AM rate, a 16.02kHz
> harmonic with a 40 Hz AM rate, a 24.03kHz harmonic with a 60 Hz AM
> rate, etc... and if the bandwidth is smaller than 16kHz (being the
> restriction coming from sr < 32kHz, or the limitations of your ears),
> only the beating fundamental is heard, just like with BL synthesis.
>
> Nonlinear operations that move harmonics down can change the game.
> What obviously comes to my mind is ring modulation. Other examples?
> Don't know how to derive it, but it looks like tanh distortion for
> example only adds higher harmonics.

Pretend that distortion of a signal is just amplitude modulation of
that signal with a specially prepared signal.

> I've played a bit with some code and my first observation was "wow,
> who would want to listen to 8kHz square waves anyway" :)

On Wed, Aug 4, 2010 at 04:11, Olivier Gillet <ol.gillet at gmail.com> wrote:
> I did the test and can hear the beating of two sine waves outside of
> my audible range. Interesting!

That's probably because of non-linearities somewhere in your system.
What's more interesting is that beating of inaudible frequencies can
be seen in (pretty much) perfectly linear systems as well, because of
our ears. The results of this research were ground-breaking.

Cheers,
D.