You can still take a heuristic approach. You probably have some idea of the
max modulation rate, right? I would just indiscriminately apply a low-pass
filter at Nyquist/fastest rate of change (forgive my fast and loose math
here). You can also relax that a little bit by taking a perceptual criteria
(say -60dB or so assuming you're going to end up making the aliased
components). You can further relax your constraints if you know anything
about the frequency content of your samples. For example, if they're
constructed to have a certain number of partials with a known rolloff than
your highest frequency content may already be at, say -20dB. If your
highest partial were my completely arbitrarily chosen -20dB and it didn't
come very close to Nyquist and it shifted into a range where you know it's
going to be completely masked at some level, you might get away with a
pretty gentle (relatively) roll-off instead of the usual brick-wall
criteria (cue comments from oversampling-philes).

Knowing the frequency content may be a generous assumption depending on
your application. Wavetables can be pretty well categorized, but if there's
any user-provided or otherwise genetic samples it may not be very useful to
you. Still, it's probably safe to assume that you don't have a 0dBFS
partial right below Nyquist, and I'm guessing that your modulated delay
line is probably not being applied to percussive samples.

Actually now that I say that, I wouldn't be surprised if there's some
papers about perceptual alias-free resampling of wavetables by Dattoro or
Pirkle, or one of the other authors who like synthesis. Anybody on the list
know some papers on the subject?


On Fri, Jun 1, 2018, 12:04 Kevin Chi <> wrote:

> Thanks for your ideas, I'll look into those!
> It's actually just a digital delay effect or a sample playback system,
> where I have a playhead that have to read samples from a buffer, but the
> playhead
> position can be modulated, so the output will be pitching up/down
> depending on the
> actual direction. It's realtime resampling of the original material
> where if the playhead is
> moving faster than the original sample rate, then the higher frequencies
> will be folding back
> at Nyquist. So before sampling I should apply an antialias filter to
> prevent it, but as the rate of
> the playback is always modulated, there is not an exact frequency where
> I should apply the
> lowpass filter, it's changing constantly.
> This is what I meant by comparing to resampling.
> --
> Kevin
> > Hello Kevin
> >
> > I am not convinced that your application totally compares to a
> > continously changed sampling rate, but anyway:
> >
> > The maths stays the same, so you will have to respect Nyquist and take
> > the artifacts of your AA filter as well as your signal processing into
> > account. This means you might use a sampling rate significantly higher
> > than the highest frequency to be represented correctly and this is the
> > edge frequency of the stop band of your AA-filter.
> >
> > For a wave form generator in an industrial device, having similar
> > demands, we are using something like DSD internally and perform a
> > continous downsampling / filtering. According to the fully digital
> > representation no further aliasing occurs. There is only the alias from
> > the primary sampling process, held low because of the high input rate.
> >
> > What you can / must do is an internal upsampling, since I expect to
> > operate with normal 192kHz/24Bit input (?)
> >
> > Regarding your concerns: It is a difference if you playback the stream
> > with a multiple of the sampling frequency, especially with the same
> > frequency, performing modulation mathematically or if you perform a
> > slight variation of the output frequency, such as with an analog PLL
> > with modulation taking the values from a FIFO. In the first case, there
> > is a convolution with the filter behaviour of you processing, in the
> > second case, there is also a spreading, according to the individual
> > ratio to the new sampling frequency.
> >
> >   From the view of a musical application, case 2 is preferred, because
> > any harmonics included in the stream , such as the wave table, can be
> > preprocess, easier controlled and are a "musical" harmonic. In one of my
> > synths I operate this way, that all primary frequencies come from a PLL
> > buffered 2 stage DDS accesssing the wave table with 100% each so there
> > are no gaps and jumps in the wave table as with classical DDS.
> >
> > j
> >
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