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

Thu Apr 29 18:59:03 CEST 2021

I think this is a bit too application-specific to put in Pd vanilla...  but
anyway, I don't understand why you can't just run the entire waveguide
at 4x sample rate - am I missing something?

cheers
M

On Thu, Apr 29, 2021 at 02:06:11PM +0200, Max wrote:
> Hi Miller,
> 
> I think the oversampling workaround is great for cases like slow playback of
> a sound file, but I'm not sure how this would work in a waveguide, ans
> particularly our situation where we have different timbre depending on if
> the number of samples in the delay line is odd or even. Since we vary the
> delay time in ms it's kind of a gamble and inconsistent depending on
> samplerate.
> 
> Do you think delreadsinc~ could have a chance to be merged into vanilla and
> if so how?
> 
> I've outlined some ideas here:
> https://urldefense.com/v3/__https://github.com/pure-data/pure-data/issues/1305__;!!Mih3wA!XMhJYxjhME5toHvcGQaK14n4LmNU0RlX-iYx637isdS8y31b1M1Q3joyLE6z$
> 
> 
> Max
> 
> 
> 
> On 28.04.21 18:14, Miller Puckette via Pd-list wrote:
> > 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
> > everything I send through tabread4~ or delread4~.  This moves the "problem"
> > to that of designing an upsampling filter, which is much easier than a general
> > interpolator.
> > 
> > cheers
> > Miller
> > 
> > > 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://urldefense.com/v3/__https://github.com/sebshader/shadylib__;!!Mih3wA!X_0yWoTK9_e2FJ67U92nwUpVsf4J8D52RrtLxDbQec742PCPmHmQs5HJnxR0$
> > > > > (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://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$ >
> > > > > 
> > > > > [2] https://urldefense.com/v3/__https://github.com/chairaudio/pure-data/tree/feature/delreadsinc__;!!Mih3wA!X_0yWoTK9_e2FJ67U92nwUpVsf4J8D52RrtLxDbQec742PCPmHmQs9PZY2Zx$
> > > > > <https://urldefense.com/v3/__https://github.com/chairaudio/pure-data/tree/feature/delreadsinc__;!!Mih3wA!X_0yWoTK9_e2FJ67U92nwUpVsf4J8D52RrtLxDbQec742PCPmHmQs9PZY2Zx$ >
> > > > > 
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