Interesting Papers re temporal resolution Options

[ncdrawl]

http://www.physics.sc.edu/kunchur/Acoustics-papers.htm

http://www.physics.sc.edu/kunchur/papers/FAQs.pdf

[benski]

I need to do further reading to do a full refutation, but I think I figured out where the problem is right.

Dr Kunchur shows that humans can discern temporal resolution down to 5 microseconds. I mostly agree with this - it's a fundamental part of pitch perception. Where he makes the mistake is assuming that 44,100Hz sampling rate only has a temporal resolution of 22 microseconds. This is patently false. 44100Hz audio has far more temporal resolution than this, due to the antialiasing filter. If you model the impulse response function of the antialiasing function as a sinc wave, small (<20microseconds) delays in an impulse event will correspond to vastly different outputs from the sinc() function. If the input impulse is perfectly aligned, the sinc() output will give 1 followed by an infinite amount of zeroes, but a half-sample (11 microsecond) delay will give 2/PI followed by a series of decaying values. The reconstruction filter will output the original half-sample delayed signal, but in bandlimited form. The half-second delay on the impulse will still be present on the output signal.

This post has been edited by benski: Aug 3 2009, 20:11

[benski]

Also, for his FAQ example of two peaks separated by 5 microseconds, my statement still holds true. The two peaks will "ring" the anti-alias filter in such a way that those two peaks still have an impact into the digital sampling (and on the eventual post-reconstruction-filter output). The waveform will look different and the high frequency spectra will be lost but the "information" of the two separate peaks will remain in the final analog output.

[WernerO]

two peaks separated by 5 microseconds, my statement still holds true. ...The waveform will look different and the high frequency spectra will be lost but the "information" of the two separate peaks will remain in the final analog output.

Er, no. They would be merged into one peak. Do the experiment.

But this of course does not prove that 44.1kHz is insufficient because of the simple
fact that it has not been proven that an audio system can only be audibly transparent
when it keeps 5us impulses separated. That's the error.

It's a bit like stating that airplanes are rubbish because you can't do space missions
with them.

[honestguv]

But this of course does not prove that 44.1kHz is insufficient because of the simple
fact that it has not been proven that an audio system can only be audibly transparent
when it keeps 5us impulses separated. That's the error.

What do these two peaks in the time domain represent? Without a formulation of a comprehensible hypothesis how can one perform a test and claim an error? (Ditto for benski.)

[benski]

But this of course does not prove that 44.1kHz is insufficient because of the simple
fact that it has not been proven that an audio system can only be audibly transparent
when it keeps 5us impulses separated. That's the error.

What do these two peaks in the time domain represent? Without a formulation of a comprehensible hypothesis how can one perform a test and claim an error? (Ditto for benski.)

They are supposed to repesentation two sounds occuring nearly, but not quite, simultaneously, for example two drums where the mallets hit 5 microseconds apart.

The proper way to test would be digitize the sound @ 44.1khz and again at something much higher like 384khz (which has a sampling period smaller than 5 microseconds), and do a blind ABX test with a set of listeners (using the same criteria for choosing listeners as the experiment in question). Most of us at HA know better than to trust a spectrogram. Although my point was simply that the post-experiment statement of the researcher can be easily disproven using Shannon's sampling theorem.

This post has been edited by benski: Aug 3 2009, 22:05

[honestguv]

They are supposed to repesentation two sounds occuring nearly, but not quite, simultaneously, for example two drums where the mallets hit 5 microseconds apart.

The time signals of two drums is not two impulses 5 microseconds apart. An impulse would normally represent something physical and have a known "height" and "width" to use Dr. K.s terminology (or was it vertical and horizontal?). What are the "heights" and "widths" in this case? If they are not known then what can you say about what should be going on in frequency space? Is "energy" conserved which is normally the first check performed when mapping between spaces?

Or are we talking about 2 periodic signals 5 microseconds apart? If so, what are they...

Unless there is a comprehensible statement of a problem one cannot say if it is right or wrong. All one can say is that it is incomprehensible.

The proper way to test would be [...]

Perhaps.