Re: [microsound] talk about supersonic signals and distortion

["ian stewart" <artsonics@xxxxxxxxxxx>]

No, I agree with Nyquist. Problem is, the Nyquist theorem only claims that 
discrete sampling can reconstruct a continuous waveform when the sampling is 
done over an -infinite- period of time. Finite sampling, especially over 
short periods of time, introduces error, primarily in high frequencies 
approaching the Nyquist frequency.

As for hearing above 20 kHz, hearing has two components: air-conduction 
hearing (upper limit of 15-20 kHz for most) and bone-conduction hearing. 
Both contribute to our perception of sound, and bone conduction hearing 
extends to very high frequencies. There are many studies documenting hearing 
above 20 kHz, and some even report hearing in the MHz range, e.g.:
http://grouper.ieee.org/groups/scc28/sc4/Human%20Perception%20FINAL.pdf

As for 'space' and high frequencies, my comment on phase is mistaken. 
However, there has historically been a problem with preserving phase 
information because of the effects of signal correction (both smoothing 
functions and anti-aliasing filters) to high frequencies, although this has 
been improving.

There are other arguments for higher sampling rates, again that have nothing 
to do with Nyquist.There are audible consequences of ultra-high frequencies- 
e.g. the 1 kHz difference tone (and related harmonics) produced by 30 kHz 
and 29 kHz sines. If these ultra high frequencies were produced by different 
close-miked instruments in an ensemble, recorded at 44.1 kHz, when the 
instruments were later mixed together, these difference tones would not be 
present, since the original frequencies would have been filtered out by the 
low sampling frequency. (the argument is from 
http://www.digitalprosound.com/Htm/SoapBox/soap2_Apogee.htm) Many 
instruments produce frequencies up to at least 30 kHz.

Finally, aliasing (or alias filtering) is still an issue with a number of 
cheap dsp programs and digital recorders, as many of us have no doubt 
discovered. These problems are resolved when all signals are encoded and 
reproduced at higher sampling rates, and as you point out, oversampling 
corrects many of these problems. My point was simply that there are huge 
advantages (regardless of eventual sample rate) in effecting sound 
transformations at higher sampling rates. As one example, using noise shaped 
dithering, one can push most noise over 20 kHz, leaving the most significant 
hearing range untarnished.

best,
Ian

Jan Larsson:
>
That is most certainly wrong.

1. You cannot hear much above 20khz so there is absolutely no reason to
encode anything. 44.1 will let you hear as much of any square wave as a
straight wire or higher sampling frequency. At least if all the research is
to be beleived.

2. No, no, no. Nyquist still holds as far as I know. You are again trying to
reproduce information that would be well above the audible range.

3. Exactly, we cant "hear" above 20khz (give or take a few khz) and that is
exactly why (1) and (2) doesnt matter. Try the mathematics and you'll see.

4. As far as I know only the japanese research referred to by Rupert Neve
has made claims above 20khz. And the researchers said no-one could "hear"
above 20khz or even sense it in practical tests. But they measured brain
activity and they cold see a diff on the measurements.

5. No, not at all. there used to be in the 70s and 80s when filtering was in
the analog domain. All A/D chips in use today (and since at least 10 years)
are all oversampling with digital filtering and they behave exactly the same
(work at the same sampling frequencies, use the same filters) no matter your
destination is 44khz or 192khz.

Your claims would mean that Nyquist was wrong. That would certainly
revolutionize the DSP world!!

Den 03-05-18 19.20, skrev "ian stewart" <artsonics@xxxxxxxxxxx>:

>
>There are several reasons for using frequencies over 20 kHz, and for using
>sample rates over 44.1:
>
>* at -audible- frequencies, e.g. 12 kHz, you can only differentiate a 
>square
>wave from a sine by encoding overtones above 20 kHz. There is almost no
>resolution in high frequencies at CD sampling rate;
>* for an 11 kHz tone, there are only four data points available per cycle,
>and thus only 3 possible phase displacements. this means encoding the
>'space' of high frequencies is virtually impossible;
>* even if we may not 'hear' frequencies over 20 kHz, parts of the bone
>structure respond to them;
>* further, many studies indicate that listeners are able to distinguish
>between recordings containing 'ultra-high' frequencies (over 20 kHz) and
>recordings which do not ;
>* 20 kHz is only a median value for the upper limit of human hearing- I've
>seen speculation that some listeners may be able to hear up to 25 kHz;
>* there are countless other problems with encoding high frequencies at 
>44.1-
>corrective circuits that smooth out high frequency waves because the low
>resolution causes distortion, and anti-aliasing filters that preclude
>reliable frequency data even in the high end of the -audible- range.

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