I received an email on the 13th from Fritz Fabig, an engineer at B&W that British high end speaker and equipment company. He wrote concerning the MQA posts I wrote and the general area of sampling, timing, and the sinc function. I’m going to admit to being somewhat out of my league with the information he included in his email, but I think there’s merit to his position. I asked him if I could reprint the email and figures and he gave me permission. He did ask that I try to clean up the English…which I have tried to do. Here’s his email:
You wrote a couple of very interesting posts recently. Your post on MQA provoked a discussion about sampling theorem and with the December 12th Stereophile online article about the worlds ‘first’ DXD download store, it’s even more important to educate and inform music enthusiasts about digital technologies correctly, as you do with your site.
The question about human hearing in the time domain leads to the assumption that higher sampling rates than 96k might be useful or even mandatory to provide a level of time accuracy within the digital domain. This is wrong in my opinion.
a) A time shift of for example of 10 microseconds (traveling of sound pressure around the human head) results in a time or phase shift of the signal, which may have a frequency spectrum of normal instruments (up to 40k, if we consider ultrasonics too). To cover this frequency spectrum 96k is sufficient. The time shift between the channels (either our ears or due to spaced mikes) results in a different form of the shell curve at a specific time point, as we have a phase shift between the channels.
b) A lot of people, including many professionals in the audio industry, believe that information between the samples is lost at 96 kHz, which isn’t true. Therefore according to their way of thinking in order to capture these tiny time shifts ultra high sample rates are necessary.
c) In order to get this sorted right and prove that no information between the samples is lost and that these tiny time shifts are captured and reproduced accurately, we have to look at sampling theorem and signal processing on a technical level. Here two useful links about this topic:
Dan Lavry: “Optimal Sampling Rate for Quality Audio” Link
Monty Montgomery from xiph.org: “24/192 Music Download and why the make no sense” Link [NOTE: I’m not in agreement with Monty on some of his contentions]
You are maybe already aware of these papers/videos
d) One important point for proper understanding of the digital concept is the sinc function, seldom mentioned in discussions and papers. We have created a paper to educate our dealers, where we try to convey this rather complex topic in a way, that people with no deep background in mathematics and electrical engineering may understand the essentials. Besides human hearing abilities and frequency range of instruments, the key points in this paper are the transition from time continuous analog to a time discrete digital format and vice versa.
Figure 1 – The digitization process top to bottom and the “Zero Order Hold Spectrum” or Sinc Function.
The key point for us is that the Zero Order Hold Spectrum contains the sync function (theory: sample is multiplied by sinc function . As a next step we see how samples & sinc reconstruct the analog signal with all information including those between the samples and also complex waves (shell curve):
Figure 2 –
Please refer for this also to Dan Lavry’s white papers: Link
e) The sinc pulse is another example, how people can misunderstand a technical term or deliberately abuse it to try to prove their marketing hocus pocus. This new DXD download portal, Promates Music HD Music Store, features a chart with sinc pulses to prove that higher sampling rates are beneficial: here the Link and the chart:
Figure 3 – Pulse or transient response for ADC
The same chart is available on Merging Technologies website, conveying the same nonsense. In order to accurately reconstruct the source signal, it’s essential and mathematically correct that the lower the sampling rate the wider the sinc pulse has to be. If this wouldn’t be the case, the concept wouldn’t work AND the 3 microsecond pulse represents a frequency of 333.3 khz. That’s completely taken out of the context and is absolutely misleading. All this to get $10 extra for a lot of zeroes. Further, the sinc pulse is a mathematical element and there is no direct or proportional relation between pulse width and the ability of a digital system to convey transients and reproduce phase and time shifts. This is only depending on the two parameters S/N Ratio (dynamic) and bandwidth.
Conclusion: It’s obvious that marketing departments can construct graphics and materials that support case when taken out of the context and rearranged to match their story, a story which is unfortunately is pure nonsense.
All the best from Switzerland
B&W Group (Schweiz) GmbH
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