[PD] 4-point interpolation changes timbre depending on sample rate

[Charles Z Henry]

I read through the code in your d_delay.c for the delread_sinc implementation.
It's a 22-point interpolator--very high quality and it looks like a
good implementation

The Hermite spline is the best 4-point cubic interpolator, but the
point of those polynomial interpolators is just to be cheap, and good
enough for regular usage.  It doesn't require a table, so it also
doesn't need as much cache space

I don't think it's *the* optimal 4-point interpolator.  It's just the
best cubic polynomial 4-point interpolator.  You could re-use your
sinc interpolator code for other shorter interpolation kernels, ones
that are better than cubics but more expensive to calculate.

At least for me, it's still an open mathematical problem that I've
come back to, from time to time.  I started to wonder if I could
expand the error terms in the truncated sinc spectrum in the form of
1/w, 1/w^2, 1/w^3, .... and then cancel them out by polynomial
correctors.  An alternative to windowing the sinc function, this could
be a more precise way to set the rate of attenuation in the stop-band,
while still retaining all the smoothness of the sinc shape.
I get a break from teaching in about 3 weeks.  I'm looking at the math
right now, and I don't think I can solve it quickly (or maybe at all).

How short does your sinc interpolator with Blackman-Harris window need
to be when you start to get the timbre change effect?

Best,
Chuck

On Sun, Apr 25, 2021 at 7:18 PM Max <abonnements at revolwear.com> wrote:
>
> Interesting. I've included that in the test patch.
> It exposes the same samplerate dependent timbre change. So far only the
> Sinc function solves the issue.
>
>
> On 25.04.21 23:15, Sebastian Shader wrote:
> > I have a [vdhs~] object in my library that does hermite spline
> > interpolation for a delay line (like tabread4c~).
> > https://github.com/sebshader/shadylib
> > (also on deken)
> >
> > I had to re-make delread~ as delread4c~ because delread~s delay lines
> > are not exposed in the .h files
> >
> > -seb
> >
> > -----Original Message-----
> > From: Max <abonnements at revolwear.com>
> > To: pd-list at lists.iem.at <pd-list at lists.iem.at>
> > Sent: Sun, Apr 25, 2021 5:45 am
> > Subject: [PD] 4-point interpolation changes timbre depending on sample rate
> >
> > Hi list,
> >
> > the 4-point interpolation in tabread4~ has been a popular topic in the
> > past, going back to at least 2008. [1]
> >
> > A similar issue is in delread4~. In fact a simple resonator changes its
> > timbre quite drastically by just changing the sample rate of the audio
> > interface. Attached is a test patch.
> >
> > The issue becomes audible when choosing an odd delay time and compare
> > the result between an odd and an even sample rate (e.g. 44.1k vs. 48k).
> >
> > This is not good. In fact this is a serious defect. Imagine you want to
> > market a product like a synth plugin (based on libpd) which sounds
> > different depending on if the daw is opened in 44.1 or 48 kHz.
> >
> > Cyrille Henry has coded tabread4c~ with a four-point cubic interpolation
> > in the nusmuk library, but there is no delread4c~ equivalent in nusmuk.
> >
> > Clemens Wegener has coded delreadsinc~ which implements a
> > Whittaker–Shannon interpolation (Sinc function). This implementation
> > does sounds consistent in any sample rate. It also sounds much better at
> > very slow speeds inside a pitch shifter where delread4~ produces serious
> > artefacts. The Sinc function requires a larger padding for the
> > interpolation.
> >
> > There are a couple of questions regarding on how to contribute this to Pd.
> > Vanilla objects are currently:
> >
> > delwrite~ = the sink
> > delread~ = control rate tap
> > delread4~ (vd~) = audio rate tap with a four-point interpolation
> >
> > 1. the code in delwrite~ isn't agnostic towards the interpolation since
> > it already provides the padding for the 4 point interpolation
> >
> > 2. if we add more interpolation methods to delread / tabread, the
> > cleanest way would be to just have one tap object and the interpolation
> > can be changed by a message and argument to it. currently there are
> > implementations for the miller 4pt, cubic 4pt and Sinc.
> >
> > Unfortunately delread4 already carries the 4 from 4-point interpolation
> > in its name, so probably it would be the best to deprecate that and find
> > a new name like varidelay~ or so.
> >
> >
> >
> > [1] Review of tabread4~ threads in the archive
> > https://lists.puredata.info/pipermail/pd-list/2019-06/125391.html
> > <https://lists.puredata.info/pipermail/pd-list/2019-06/125391.html>
> >
> > [2] https://github.com/chairaudio/pure-data/tree/feature/delreadsinc
> > <https://github.com/chairaudio/pure-data/tree/feature/delreadsinc>
> >
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