On 6/29/15 6:43 PM, Sampo Syreeni wrote:
On 2015-06-29, Emanuel Landeholm wrote:
But all waveforms can be antialiased by brick wall filtering, ie.
sine cardinal interpolation.
The point is that you can't represent the continuous time waveforms in
the usual sampled form, and then apply a sinc filter. Which you need
to do in order to synthesize them via a normal D/A converter. Instead
you need to perform the convolution with the sinc in implicit form,
which lands at a nice, regular, equidistantly sampled form.
*and* that has no harmonics above Nyquist before sompling at nice,
regular, equidistantly sampling instances (or extremely reduced
amplitudes of those harmonics exceeding Nyquist).
What we're after here is one of those guaranteed to be bandlimited
implicit forms, only somewhat more general than what the conventional
BLIT/BLEP framework allows.
Certainly not all frameworks can do that, and not for all signals.
but wavetable synthesis *is* a framework that can do that for any
periodic (or quasiperiodic) signal. bandlimited saw, square, PWM,
sync-saw, sync-square, plucked string, piano, sax, horn, FM (where the
carrier or modulation frequencies are all integer multiples of a
common fundamental), whatever. if it's a tone, wavetable synthesis can
do it. bells, tom, tympani and the like are a problem because of
non-harmonic components. wavetable synthesis requires that all partials
are harmonic or close enough to harmonic that you can model the detuning
from harmonic as a change in phase of the specific harmonic.
notes can be conventionally sampled and wavetables can be extracted at
prescribed times in the sample and phase aligned with each other. note
attacks can be mangled a little with wavetable synthesis unless multiple
wavetables are used to represent the initial couple of milliseconds.
there is interpolation or cross-fading between phase-aligned wavetables
to worry about, but there is no overlapping of bandlimited grains or
wavelets or BLI's (or whatever you wanna call them) to worry about.
Closed form discrete summation formulae don't exist for every
waveform. At least at the outset, the BLIT/BLEP-framework seemingly
cannot handle sine-on-sine FM. Vadim's paper is the first I've seen
which handles even arbitrary sync on a sine. And even if what we've
been talking about above does go as far as I (following Vadim)
suggested, exponential segments are still out of the picture for now.
Then, when you fail, you get aliasing, which sounds really bad and
behaves nastily under change of parameters.
So then isn't that the end of the discussion, in *musical* DSP? It
sounds like crap, move along, nothing to hear here.
or, paraphrasing Duke Ellington, if it sounds like crap, it IS crap.
--
r b-j r...@audioimagination.com
Imagination is more important than knowledge.
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