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.