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
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.
 
 

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

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

Good discussion rabeach ... it's all about trade-offs and diminishing returns.
 

I love reading these sorts of threads.
I understand the terms used, enough to follow the discussion and reaching the end realise I don't really understand anyway.
But you know it doesn't really matter because there doesn't seem to be any real consensus when it comes to should I or shouldnt I record in 96khz.

I'll keep recording at 48khz and occasionally go to 96khz when the fancy takes me..

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

The same for me, recording at 48 is just fine for my 63 year old ears.

I tried 96K and 192K.  The higher the sample rate, the more I'm able to discern noise from my cheap cables, mics and lousy technique.  48K is a nice mid ground where all of those shortcomings get blurred together such that they sound like random noise
 
 

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
 

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

 
 
No notation fixes!  has more than twice as many posts.  Cakewalk please take note.
 
(Sorry.  I find this here thread a very interesting read and it has greatly increased my knowledge of the subject)
 

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
 

Gary no, higher sample rates will only increase the bandwidth meaning you will be sampling frequencies that are above human hearing. In most cases there is nothing there to sample. Microphones may or may not reach that high anyway. Most mics cutoff at 22kHz.  
 
44.1 is sufficient to sample 20 Hz to 20 kHz. This is the bandwidth that has musical meaning and usefulness. Further our hearing varies for person to person but a general rule is that most people above the age of 25 can hear to about 15 kHz. The older you get the less highs you can hear. A lot of musicians have very poor hearing due to being exposed to very loud music on a regular basis. Those that play amplified instruments suffer the most.