Re: Interpolation on WaveShaperNode?

On Thu, Apr 4, 2013 at 6:57 PM, robert bristow-johnson <
rbj@audioimagination.com> wrote:

> On 4/4/13 7:06 PM, Chris Rogers wrote:
>
>> Another aspect of the WaveShaperNode is anti-aliasing.  In certain cases
>> it would be great to be able to up-sample the signal before applying the
>> shaping, then down-sampling.  This is to avoid the extremely harsh aliasing
>> that can occur in applications such as guitar amp simulations.  Once again
>> we could have an attribute .upsample ("none", "2x", "4x") or something like
>> that.  Then the default value for that would be "none" I think.
>>
>
> just lurking, and i haven't looked at the code at all, but thought i might
> mention a couple of things that might be applicable.
>
> if you can get away from table lookup and implement the waveshaper by use
> of a pure polynomial if finite order, you can get a solid handle on
> aliasing.  a finite-order polynomial is not as general and a general lookup
> table, but for the purposes of distortion (or "warmth" or whatever) in
> audio, it might be closer to what you want anyway.  you can fit polynomials
> to tube curves and the sort pretty well.
>
> the images generated is no higher in frequency than the order of the
> polynomial (let's call that M) times the highest frequency.  if that
> highest frequency is potentially Nyquist, then upsampling by a factor of N
> means that the highest frequency is the *new* Nyquist/N.  that makes the
> highest frequency image (M/N)*Nyquist.  you can allow aliases as long as
> they don't get back into your original baseband which is below the new
> Nyquist/N.  that means
>
>     2*Nyquist - (M/N)*Nyquist > Nyquist/N
>
> or
>
>     2*N - M > 1
>
> or
>
>     M <  2*N - 1
>
> if you upsample by 2x, you can have a 3rd-order polynomial.  if you
> upsample by 4x, you can have a 7th-order polynomial.
>
> then a decent brick-wall LPF with cutoff at Nyquist/N to kill the images
> and aliases.   then downsample by factor of N and you have output.  you
> will get the distortion components you were meant to get (harmonics) and no
> non-harmonic components which are the tell-tales of aliasing and cheezy
> distortion.
>
> you can do this with table lookup if you make sure the table ain't defined
> to wildly (like if it's implementing a Mth-order polynomial), have enough
> points in the table (memory is cheap), and at least linearly interpolate
> between points.  how many points you need (based on what interpolation is
> done between points) in the table is something that i had done some
> analysis about long ago, but i might be able to find notes.  if
> computational burden is no problem, i might suggest implementing this as a
> polynomial and use Horner's rule.
>
> just an idea.


Thanks Robert, this is really valuable information.  I'd still like to
support general shaping curves and bit-crushing applications.  But I'd
really like to get the highest quality sound and best general purpose
approach that is possible, especially for these "warming" applications.

Best Regards,
Chris


>
>
> --
>
> r b-j                  rbj@audioimagination.com
>
> "Imagination is more important than knowledge."
>
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