[PD] tabread4~ "broken" interpolation algorithm - was Re:, Max Smoother Audio than Pd?

[Matteo Sisti Sette]

 > So to me
 > it still remains unclear in what aspect [tabread4~] is superior
 > to [tabread4c~], from both a theoretical and from an empirical
 > perspective.

The answer may be here:

http://www.aes.org/e-lib/browse.cfm?elib=8151

Btw does anybody have access to that article?

"The analysis reveals an interesting performance trade-off between 
signal-to-noise ratio and passband flatness."

So since it seems quite obvious that discontinuities (tabread4) generate 
more high-frequency noise (and assuming that is the most relevant source 
of noise), the only aspect where tabread4 can be superior may be 
"passband flatness". Indeed, intuitively it seems plausible: passband 
flatness means that the low-frequency part of the signal is more close 
to the "original" (the ideal perfectly interpolated signal); and I do 
expect that an interpolator that doesn't try to match first derivatives 
is less likely to do crazy oscillations.

It would be interesting to see a zoom-in of the low frequency part of 
Charles Henry's graph (the ripples in the flat zone).

However, even in presence of a tradeoff that makes some sense (i.e. each 
of the two choices has advantages and disadvantages), it seems to me 
that for audio applications the generated high-frequency noise due to 
discontinuities should be _hugely_ worse than the passband-non-flatness.

I'd really like to see and hear an example of a case where this isn't 
true, that is, where tabread4 gives better results than tabread4c.

This other article seems to contain an answer:

http://www.akademiai.com/content/r0192mk0908k31k3/
http://www.akademiai.com/content/r0192mk0908k31k3/fulltext.pdf?page=1

"The aim of this paper is to give a positive answer for a
problem [...]:
Do there exist a system of nodes and function class for which the 
Lagrange process is better than the Hermite-Fej6r one?"

If anybody has access and can share it that would be great.

Now regarding Matt's words:

 > I have read that the Lagrange interpolators have better stopband
 > attenuation and Hermites have flatter passband response, but I'm not
 > sure this is true

Is it possible that it is exactly viceversa?

By the way thanks again Matt (and everybody else who contributed to this 
thread) for the didactic effort and the links.

-- 
Matteo Sisti Sette
matteosistisette at gmail.com
http://www.matteosistisette.com