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Is it possible to train yourself to be able to hear higher frequencies
Ken G
post Oct 31 2013, 02:12
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Not having connected to this website for years, I was amused to come on this string. I suggest readers should look up Audio Engineering Society preprint 1449, from the IRT way back in 1979 when there was discussion of what sample rates should be used in digital audio recording. Over-simplifying slightly, the conclusion was that while some people could distinguish bandwidth limitation to 15 kHz from no limitation (or at least a higher one), the difference was very minor and was not considered a degradation, that is, if listeners could tell the limited version from the unlimited, they weren't sure which was which. This of course reinforced the decision 20+ years earlier to employ 38 kHz as the carrier frequency for FM stereo, offering 15 kHz bandwidth without the need for very complex anti-imaging filters.

Incidentally, there is apparently an exception. Some people with severe asthma from childhood can hear higher frequencies, and might therefore be more aware of a 15 kHz limitation compared with the live sound.

Ken G

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2tec
post Oct 31 2013, 02:26
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"... Most of these brain areas are part of the cortical motor system, but there were also structural changes in the auditory system and in the corpus callosum. This is the first longitudinal study demonstrating brain plasticity in children in the context of learning a musical instrument." ~ http://f1000.com/prime/reports/b/1/78
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greynol
post Oct 31 2013, 04:16
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QUOTE (Ken G @ Oct 30 2013, 18:12) *
Not having connected to this website for years, I was amused to come on this string.

We'd love it if you'd visit more frequently, Mr. G.


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Arnold B. Kruege...
post Oct 31 2013, 12:59
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QUOTE (kdo @ Oct 30 2013, 17:18) *
QUOTE (Arnold B. Krueger @ Oct 30 2013, 20:42) *
Infinite spectrum implies infinite energy...

That's just wrong.


Since when is being practical wrong?

Admittedly an exception is indeed infinitesimal (negligibly small) energy density at higher frequencies.

But negligibly small is negligible, and from a practical standpoint negligible is indeed negligible. I just consciously neglected it! ;-)

Sue me for being practical.
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pdq
post Oct 31 2013, 13:07
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Unless negligibly small means zero, infinite frequency DOES mean infinite energy, since infinity times anything other than zero equals infinity.

And if the amplitude at infinity is zero then the frequency range is not infinite.
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greynol
post Oct 31 2013, 14:56
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Gabriel's horn, perhaps?

This post has been edited by greynol: Oct 31 2013, 14:57


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Martel
post Oct 31 2013, 19:25
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I could be wrong (sorry, I haven't seen math for many years since I left the university), but I think there are functions which are non-zero all the way to infinity yet their integral/sum is a finite number.

Integral from 1 to infinity of 1/x^2 is 1.
Sum of 1/n from 2 to infinity is 1.

Create a signal which has spectral distribution like above (and is e.g. a finite constant at the beginning) and you have an infinitely wide frequency signal with finite energy.

This post has been edited by Martel: Oct 31 2013, 19:29


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pdq
post Nov 1 2013, 02:05
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The amplitude can be non-zero as frequency approaches infinity, it just can't be non-zero AT infinity.

Infinite frequency would mean that the signal would have to equal every possible value over the range of the amplitude simultaneously. The only way this is possible is if the amplitude is zero, so there is only one possible value.
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Martel
post Nov 1 2013, 09:05
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You cannot evaluate anything AT infinity (infinity is not a number), you can evaluate a limit of a function as it approaches infinity. For any single point (x value), you can always find a greater x for which f(x)=1/x^2 will be non-zero.
For me, this is pretty much infinite. smile.gif

Whether this function (or any other function with similar sum/integral properties) can be transformed back to the time domain (with a reasonable result) is another matter, I agree.

This post has been edited by Martel: Nov 1 2013, 09:12


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Woodinville
post Nov 1 2013, 23:23
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QUOTE (pdq @ Oct 31 2013, 18:05) *
The amplitude can be non-zero as frequency approaches infinity, it just can't be non-zero AT infinity.

Infinite frequency would mean that the signal would have to equal every possible value over the range of the amplitude simultaneously. The only way this is possible is if the amplitude is zero, so there is only one possible value.


Having content at infinite frequency is a very interesting issue. Since photos are what actually sends stuff down wires, it would seem that that last photo for the highest frequency might exceed the mass-energy of the universe, eh?


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Martel
post Nov 2 2013, 10:33
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In other words - don't try this at home! smile.gif


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