---------------------------- Original Message ----------------------------

Subject: Re: [music-dsp] Antialiased OSC

From: "Ross Bencina" <rossb-li...@audiomulch.com>

Date: Sat, August 4, 2018 2:12 am

To: "A discussion list for music-related DSP" <music-dsp@music.columbia.edu>


> Hi Kevin,


> Wavetables are for synthesizing ANY band-limited *periodic* signal.



> If all you need to do is synthesize bandlimited periodic signals, I

> don't see many benefits to BLEP methods over wavetable synthesis.
i might suggest prepending "quasi-" to "periodic".� notes don't have to be 
perfectly periodic, just *mostly* periodic.� one cycle in this quasi-periodic 
waveform should look just like its
adjacent cycles on the left or right.� but it wouldn't necessarily look like a 
cycle 1 second away.

> (1) With wavetable switching, frequency modulation will cause high

> frequency harmonics to fade in and out as the wavetables are crossfaded

> -- a kind of amplitude modulation on the high-order harmonics. The

> strength of the effect will depend on the amount of high-frequency

> content in the waveform, and the number of wavetables (per octave, say):

> Less wavetables per-octave will cause lower frequency harmonics to be

> affected, more wavetables per-octave will lessen the effect on low-order

> harmonics, but will cause the rate of amplitude modulation to increase.

> To some extent you can push this AM effect to higher frequencies by

> allowing some aliasing (say above 18kHz). You could eliminate the AM

> effect entirely with 2x oversampling.
two things:� 1.� the AM effect should *not* affect the lower harmonics that are 
not potential aliases.� as you cross-fade, those harmonics are identical in 
amplitude and phase in the beginning and ending wavetables.� it's only the
highest harmonics that start to fade out (before they alias) as the pitch 
2. it's possible to show that if you have a sample rate of 48 kHz (so 24 kHz is 
the "folding frequency") and two wavetables per octave you can make all this 
nasty harmonic aliasing (and variation in
amplitude) happen above 19.88 kHz.
at the bottom of the half-octave split, the fundamental is f0.� the Nth 
harmonic is right at 19.88 kHz so N = (19.88 kHz)/f0 and there are no other 
harmonics above it.� at the top of the split the fundamental is 2^(1/2)*f0 and 
the Nth harmonic is
at�2^(1/2)*(19.88 kHz) = 28.11 kHz, if there was no fold over.� but since there 
is, this top harmonic folds over to 48 kHz -�28.11 kHz = 19.89 kHz.� admittedly 
that's a little tight to start fading it out and fading in the waveform that 
has fundamental at 2^(1/2)*f0 and top
harmonic of 19.88 kHz, but you can back off a little and maybe just do this all 
above 19 kHz and put a brickwall LPF at 19 kHz.� i know i (at age 62) won't be 
missing any harmonics above 19 kHz.� below 19 kHz, every harmonic is harmonic 
(unaliased) and unchanging in
another thing you can do is make your splits be smaller than 6 semitone spacing.
and, of course, if the sample rate is 96 kHz, no one will be hearing any 
aliasing nor loss of harmonics below even 24 kHz.� but at 96 kHz, maybe you can 
get away with "naive"
sawtooths and square and maybe even naive hard-sync.� maybe not.

r b-j� � � � � � � � � � � � �r...@audioimagination.com

"Imagination is more important than knowledge."

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