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

Miller Puckette msp at ucsd.edu
Wed Apr 28 18:14:48 CEST 2021

```On Wed, Apr 28, 2021 at 10:56:58AM -0500, Charles Z Henry wrote:
My 2 cents...

The 4-point interpolation scheme gets radically better if the signal it's
used on is oversampled (error goes down asymptotically by 24 dB for each
doubling of sample rate) - so my own strategy is simply to 4x upsample
to that od designing an upsampling filter, which is much easier than a general
interpolator.

cheers
Miller

> 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~).
> > > (also on deken)
> > >
> > > 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
> > >
> > > 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.
> > >
> > >
> > >
> > > https://urldefense.com/v3/__https://lists.puredata.info/pipermail/pd-list/2019-06/125391.html__;!!Mih3wA!X_0yWoTK9_e2FJ67U92nwUpVsf4J8D52RrtLxDbQec742PCPmHmQsx32PNF8\$
> > > <https://urldefense.com/v3/__https://lists.puredata.info/pipermail/pd-list/2019-06/125391.html__;!!Mih3wA!X_0yWoTK9_e2FJ67U92nwUpVsf4J8D52RrtLxDbQec742PCPmHmQsx32PNF8\$ >
> > >
> > >
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