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RE: 44.1 kHz shown scientifically to be inadequate

Posted by Tony Lauck (A) on July 29, 2009 at 10:41:27

In Reply to: RE: 44.1 kHz shown scientifically to be inadequate posted by Ryelands on July 29, 2009 at 09:11:05:

"Can you point me to where he draws ("jumps to”, even) that conclusion?"

I searched his papers and his FAQ for "44.1" and came up with the following paragraphs.

"B. Implications for sound reproduction
The result presented here has relevance for the performance
requirements of audio components and digital encoding
schemes. It is known that the bandwidth requirement
for sonically transparent audio reproduction is higher
than the 20 kHz: in the coding of digital audio it has been
noted (Stuart, 2004) that listeners show a preference for a
96 kHz sampling rate over the CD (digital compact disk)
standard of 44.1 (i.e., a 22 kHz Nyquist frequency). It
is sometimes thought that this may be due to the less
drastically sloped cutoff of the digital filter and the reduced
disturbances introduced in the audible pass band.
The present work shows that the bandwidth requirement
into the ultrasonic range is more fundamental and not just
due to artifacts of digital filtering. It is also commonly
conjectured in the audio literature that the time-domain
response of a system (e.g., temporal smearing caused by
capacitive and other energy-storage mechanisms in cables)
is a key factor in determining the transparency of reproduction
(see, for example, van Maanen, 1993). However a
search of the literature revealed an absence of a controlled
blind experiment comparable to the one conducted here.
The present work thus contributes toward a better fundamental
understanding and provides a quantitative measure
for audio-reproduction standards."

"Digital audio recording: In my papers, statements related to "consumer audio" refer to CD quality, i.e., 16 bits of vertical resolution and a 44.1 kHz sampling rate (when the work for these papers was begun around 2003, 24bit/96kHz and other fancier formats were not in common use in people's homes for music reproduction). 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. Now the CD's lack of temporal resolution for complete fidelity is not systemic of the digital format in general: the problem is relaxed as one goes to higher sampling rates and by the time one gets to 192 kHz, the bandwidth and the ability to reproduce fine temporal details is likely to be adequate. I use the word "likely" rather state definitely for two reasons. In our research we found human temporal resolution to be ~5 microseconds. This is an upper bound: i.e., with even better equipment, younger subjects, more sensitive psychophysical testing protocols, etc., one might find a lower value. The second reason to not give an unambiguous green signal to a particular sampling rate is that the effective bandwidth that can be recorded is less than the Nyquist frequency because of the properties of the anti-aliasing filter, which is never perfect in real life. One more thing I want to add is that one forum poster inquired whether the blurring is an analog effect and not a digital one (“… this isn't a sampling-rate issue, it's a simple question of linear filtering…"). But the two are not separate. While it is true that the smearing may take place in the analog low-pass filter circuitry before the signal reaches the ADC, the low-pass filter cutoff is dictated directly by the sampling rate. The exact amount of smearing and other errors will depend on the slope and other details of the filter, but the big-picture conclusion is still the same."

"As has been noted in the
literature [4], there have also been anecdotal claims by
listeners that an improvement in fidelity can be noticed
for sampling rates in excess of the 44.1 kHz sampling rate
of the digital compact disk (CD) even though the listeners
cannot hear pure tones above the 22 kHz Nyquist
frequency. Such subtle effects may be masked in average
mass-produced commercial audio systems and audiometric
apparatus used in psychoacoustic research, because of
the limited resolution of the equipment—the bottleneck
then arises from the limitations of the apparatus rather
than the ear."

Tony Lauck

"Diversity is the law of nature; no two entities in this universe are uniform." - P.R. Sarkar

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