Computer Audio Asylum: RE: 44.1 kHz shown scientifically to be inadequate by Werner Music servers and other computer based digital audio technologies.

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Posted by Werner (A ) on July 29, 2009 at 13:04:49

In Reply to: RE: 44.1 kHz shown scientifically to be inadequate posted by Tony Lauck on July 29, 2009 at 10:41:27:

"For CD, the sampling period is 1/44100 ~ 23 microseconds and the Nyquist frequency fN for this is 22.05 kHz. Frequencies above fN must be removed by anti-alias/low-pass filtering to avoid aliasing. While oversampling and other techniques may be used at one stage or another, the final 44.1 kHz sampled digital data should have no content above fN. If there are two sharp peaks in sound pressure separated by 5 microseconds (which was the threshold upper bound determined in our experiments), they will merge together and the essential feature (the
presence of two distinct peaks rather than one blurry blob) is destroyed. There is no ambiguity about this and no number of vertical bits or DSP can fix this. Hence the temporal resolution of the CD is inadequate for delivering the essence of the acoustic signal (2 distinct peaks). However this lack of temporal resolution regarding the acoustic signal transmission should not be confused with the coding resolution of the digitizer, which is given by 23 microseconds/2^16 = 346 picoseconds. This latter quantity has no direct bearing on the system's ability to separate and keep distinct two nearby peaks and hence to preserve the details of musical sounds."

That quote came from the FAQ Prof.Kunchur wrote as a reply to the questions and comments he got on the three published papers. It contains some interesting things. Let's go through them.

"While oversampling and other techniques may be used at one stage or another"

Oversampling techniques *must* be used in order to get correct reconstruction. This is not optional, and this should not be dismissed.

"the final 44.1 kHz sampled digital data should have no content above fN."

That data cannot have content above fN. Once sampled, Fn is 'infinity' (or rather, the edge of the circle) and there is nothing outside/above it.

Methinks the two above quotes are rather unscientific in their formulation.

"If there are two sharp peaks in sound pressure separated by 5 microseconds (which was the threshold upper bound determined in our experiments), they will merge together "

That two such peaks would merge together with 44.1kHz sampling (or rather, as a result of the anti-aliasing filtering prior to the deed
of sampling) is obvious. We don't need any scientific publications for that.

"(which was the threshold upper bound determined in our experiments)"

Er. NO.

The experiments were about a 5us delay in one source of a continuous, periodic 7kHz signal, and another about a 5us time constant in a first-order low-pass filter, gain for a continuous and periodic signal. There were no experiments involving 'sharp peaks separated by 5us'. The auditory relevance of 44.1kHz not resolving two such peaks was not proven at all. That proof was not even on the agenda.

So

"Hence the temporal resolution of the CD is inadequate for delivering the essence of the acoustic signal (2 distinct peaks)."

is a very questionable claim (the jump), at least under the experimental evidence published in the three papers.

"this lack of temporal resolution regarding the acoustic signal transmission should not be confused with the coding resolution of the digitizer, which is given by 23 microseconds/2^16 = 346 picoseconds. "

It is a fact of nature that the spatio/temporal resulotion(*) of a correctly
band-limited sampled system far exceeds the actual spatio/temporal sample period. Many advanced systems operate according to this principle. In the awful wars JJ quoted cellphones, digital TV, and modems. I add the optical attitude control systems of spacecraft to the list. The last time I checked most satellites presently in orbit knew more or less where they were, so it must be working...

(* Meaning the accuracy with which the position of a signal event on a time or spacial axis can be determined.)

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Kimber Kable

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