Computer Audio Asylum: RE: Better duck under that desk; by Werner Music servers and other computer based digital audio technologies.

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Posted by Werner (A ) on August 5, 2009 at 23:19:23

In Reply to: RE: Better duck under that desk; posted by Ryelands on August 5, 2009 at 07:59:20:

"Unfortunately, I cannot translate that into the “μsecs” on which Kunchur bases his argument"

The (theoretical) temporal resolution of a 16-bit 44.1kHz sampled system is 22us/2^16 = 346 picoseconds. In practice it is bound to be worse, but still vastly better than 5 microseconds. What this means is that if you have two waveforms that are identical except for a temporal feature of, say, 5us, that the sampled system maintains this temporal feature, even when other aspects of the waveforms, like their bandwidth, are obviously modified when passing through the sampled system. Or even simpler: take a waveform (A), then copy it with a delay of 5 us (B). Then sampled and decode them. What you end up with are two waveforms than are delayed 5us relative to each other.

Or in the specific (but absurd) case of two fast pulses separated by 5us versus one single pulse of the same total energy, the post-sampling waveforms would 1) merge the two pulses (obviously), but 2) still keep a spectral distinction between the two signals as such (so that they can be recognised).

In satellite attitude control this principle allows digital cameras (i.e. spatial sampling) to determine the position of stars with an accuracy that is much much smaller than the image sensor's pixel pitch. That's the one non-audio application I'm quite familiar with. There are others in cellphones and modems, which are after all pretty scary sampled systems, but then I'm not into RF at all...

"This seems optimistic: as I understand it, upper limits are, in practice, significantly lower than 22 KHz because the Nyquist filters are not, by design, “brickwall”."

Digital filters can be arbitrarily brickwall, especially in software sample rate convertors. But that's even not required: in ADC and DAC chips the filter type most often used (for reasons of economy) is the half-band FIR. These have a -6dB point at 22.05kHz for CD. Their response at 21kHz is between 0 and -6dB, so almost level. So yes, CD systems can and do pass 21kHz with quite some ease.

"The poorest, on the other hand, only got to 9.4 KHz and would thus have been struggling a bit with the 8 KHz tone, "

That one 9.4kHz person is indeed something of a sore thumb. I discussed that case already at Hydrogen Audio.

BTW a limit of 9.4k does not imply struggling at 8k. Hearing is pretty much on/off at these elevated frequencies: the cutoff is very abrupt.

"As I read the text, Kunchur demonstrated that all the harmonics of the test tone were inaudible (Table 1 & p 597)."

As pure tones. But fact remains that the subjects did distinguish between the two test signals, and that if the discrimination is not based on level differences of the fundamental, then it *must* be based on something else, which leads to the lowest-order non-linear distortion products of the signals involved, namely the second harmonic of the fundamental, and the first intermodulation between the fundamental and its third. That's all there could be for the ear to work with ...

"If you were to say that Kunchur makes a conceptual leap when he argues that his experiment conclusively proves that 44.1 KHz sampling rates are inadequate, I’d probably agree with you."

Well, that's what I said at the start of this thread.

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