Well you definitely want a monotonic, equal-amplitude crossfade, and
probably also time symmetry. So I think raised sinc is right out.

In terms of finer design considerations it depends on the time scale. For
longer crossfades (>100ms), steady-state considerations apply, and you can
design for frequency domain characteristics. I.e., raised cosine, half of
your favorite analysis window, etc.

But for shorter crossfades (particularly 20ms and below), time domain
considerations dominate and you want to minimize the max slope of the
crossfade curve. So a linear crossfade is indicated here.

Of course linear crossfade is also the cheapest option, so you really need
a reason *not* to use it.

Ethan (D)

On Thu, Nov 1, 2018 at 12:18 PM robert bristow-johnson <
r...@audioimagination.com> wrote:

> ---------------------------- Original Message ----------------------------
> Subject: Re: [music-dsp] Antialiased OSC
> From: "Sampo Syreeni" <de...@iki.fi>
> Date: Wed, October 31, 2018 9:35 pm
> To: philb...@mobileer.com
> "A discussion list for music-related DSP" <music-dsp@music.columbia.edu>
> Cc: "robert bristow-johnson" <r...@audioimagination.com>
> --------------------------------------------------------------------------
> > On 2018-08-06, Phil Burk wrote:
> >
> >> I crossfade between two adjacent wavetables.
> >
> > Yes. Now the question is, how to fade between them, optimally.
> >
> > I once again don't have any math to back this up, but intuition says the
> > mixing function ought to be something like a sinc function or a raised
> > cosine, at the lower rate. Because off the inherent bandlimit. And then
> > the ability of such linear phase thingies to be turned into one-off
> > interpolation thingies.
> >
> > Doing it at the lower rate, for the lower wavetable, would seem to be
> > the easiest, while holding to band limitation.
> interpolating between samples of a wavetable and crossfading between
> wavetables are different issues.
> if this wavetable synthesis is for the purpose of synthesizing a
> bandlimited saw, square, triangle, PWM, sync saw, sync square, then you
> adjacent wavetables going up and down the keyboard should be identical
> except on will have more harmonics at the top set to zero.
> i think a linear crossfade, mixing only the two adjacent wavetables, is
> the correct way to do it.
> --
> r b-j                         r...@audioimagination.com
> "Imagination is more important than knowledge."
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