johnnyV
This means that two super-sonic frequencies that cannot be heard, say 22 kHz and 32 kHz, can create an intermodulation distortion down in the audible range, in this case at the “difference frequency” of 10kHz. This is a real danger whenever super-sonic frequencies are not filtered out.

JohnDubats
Many beat frequencies of inaudibly high frequencies are audible. If you are recording a live orchestra, you'll capture those beats, so you're OK. Many of us record instruments separately, and if we don't capture the inaudible frequencies, the audible beat frequencies are never generated; never heard.

Anderton
 
The only place I disagree a little bit is where he minimizes the number of plug-ins that don't have oversampling. That's true for newer plug-ins, but a lot of older ones (that are still compatible with our computers) don't have oversampling.
 

BobF
In reading both of the above, I did NOT get that justification out of them.

rabeach

BobF
In reading both of the above, I did NOT get that justification out of them.

Bob if you are referring to my post it was not intended to answer or address any post above. I briefly read some of the referenced material and some of the post and just posted my thoughts. Amazing photo by the way.

BobF
This has to be the most discussed topic ever ... well, besides 'Subscription vs Membership'  LOL

rabeach

drewfx1

rabeach
The Shannon-Nyquist sampling theorem, states that a perfectly bandlimited analog signal can be perfectly reconstructed from an infinite sequence of equally spaced uniform samples if the sampling rate exceeds twice the highest frequency of the original signal. Since neither of those entities exist in our reality e.g. a perfect band limited filter or an infinite sequence of equally spaced uniform samples, using the Nyquist-Shannon sampling theorem to justify not using higher sampling frequencies is a bit unreasonable. Empirical data collected on devices being sold today would constitute a reasonable argument. imho

It's perfectly reasonable and you can justify it. You just need to allow additional space of ~10% below the Nyquist frequency for the filter to roll off. 
 
That's the short answer. The full answer in terms of how the pieces fit together in the real world is a bit more involved.
 
But it still all comes down to any issues having to do with the filters being above the frequency range one cares about - in the real world it just ends up being a bit below the Nyquist frequency.

The waveform can only be approximately reconstructed using N samples.  Also interpolation requires a sinc function with the amplitude scaled to the sample value. As the sinc function has infinite impulse response in both positive and negative time directions, it must be approximated for real-world applications. Resulting in interpolation error.
 
My point is that in application it is not a perfectly reconstructed waveform. 
 

rabeach

drewfx1

rabeach

drewfx1

rabeach
The Shannon-Nyquist sampling theorem, states that a perfectly bandlimited analog signal can be perfectly reconstructed from an infinite sequence of equally spaced uniform samples if the sampling rate exceeds twice the highest frequency of the original signal. Since neither of those entities exist in our reality e.g. a perfect band limited filter or an infinite sequence of equally spaced uniform samples, using the Nyquist-Shannon sampling theorem to justify not using higher sampling frequencies is a bit unreasonable. Empirical data collected on devices being sold today would constitute a reasonable argument. imho

It's perfectly reasonable and you can justify it. You just need to allow additional space of ~10% below the Nyquist frequency for the filter to roll off. 
 
That's the short answer. The full answer in terms of how the pieces fit together in the real world is a bit more involved.
 
But it still all comes down to any issues having to do with the filters being above the frequency range one cares about - in the real world it just ends up being a bit below the Nyquist frequency.

The waveform can only be approximately reconstructed using N samples.  Also interpolation requires a sinc function with the amplitude scaled to the sample value. As the sinc function has infinite impulse response in both positive and negative time directions, it must be approximated for real-world applications. Resulting in interpolation error.
 
My point is that in application it is not a perfectly reconstructed waveform. 
 

It doesn't have to be perfect. It only has to be preserve the desired frequency range at a resolution that's better than the bit depth. 
 
In the real world, once a filter reaches a certain length you don't really gain anything by making it longer. And any imperfections in the waveform are lost in the noise for everything except perhaps isolated high level, high frequency content like sine waves. For low frequencies you can get the imperfections below the bit depth just by interpolating with splines, much less an infinitely long filter.
 
 

I never stated that a perfect reconstruction was necessary. Nor did I indicate the interpolation error could be heard. I simply stated a perfect reconstruction does not exist. And invoking a theorem as justification for not sampling at higher frequencies is flawed in my opinion because the math required for the theorem to be held true is not implemented in real-world systems. So whether sampling at a higher frequency is beneficial on the many varied ADC to DAC systems should not be based on a perceived belief that a perfect reconstruction is occurring. That aside sampling at higher frequencies may sound better on some systems and not on others. My aardvark 24/96 was designed by an extremely competent engineer had very stable clocking and filters with extremely low noise and low distortion. It sounded great at 96kHz although I never worked with it at that frequency. My VS-100 sounds great at 44.1kHz (doesn't touch the aardvark though) but I don't care for the sound it has at 96kHz. Stable clocking and filter design are extremely challenging and are not implemented very well in most commercial systems. In my opinion empirical data collected on the varied systems in use trumps the belief that a perfect reconstruction is occurring and all systems will sound the same at 44.1kHz. But if the empirical data is ever collected and says otherwise I will promptly reverse my opinion.
 
Math is just a construct many people experience a sensory variance from using higher sampling frequencies. 
 
There is a Burr Brown white paper that shows the implementation of a linear-phase filter somewhere in between a Butterworth and a Bessel response; It may be outdated by now I came across it in 1994.
 
http://www.ti.com/lit/an/sbaa001/sbaa001.pdf

IfItMovesFunkIt
I don't even record at 96 kHz any more !... I used to but only because my brain was playing the numbers game.. I mean 96 has to be better than 48 because its twice the size right ?
 
But seriously I decided that CD quality is good enough for me.... I'm a 56 year old bass player that records the ocassional song in a bedroom and so the technically inferior CD specification is more than adequate for my purposes

garyhb
Hi All
 
Very interesing discussion. In my reckoning we're rather too fixated on hearing higher frequencies from higher sample rates.
 
Surely the point is that if recording at progressively higher sample rates results in capturing more information then we are progressively hearing more harmonic content and therefore subtle details of the frequency range we are able to perceive.
 
As Bob Katz also points out, the quality of converters has improved over the years so even basic AD/DA conversion results in higher quality captured audio too. Then add in the quality of speakers, room acoustics, mics, personal physiology and critical listening skills...
 
The science is important or course, but in the end, skilled, subjective experience of psychoacoustic phenomenon is down to individual experience...! You pays your money, you takes your choice!!!
 
Harmonics!
 
Best,
 
Gary