Try this:
http://www.lavryengineering.com/documents/Sampling_Theory.pdf
I haven't actually had time to read through the whole thing, but it seems to be pretty comprehensive if you can handle the bit of math involved. There is also a HUGE thread in response to this article here:
http://recforums.prosoundweb.com/index. ... 932c272c77
but there is an awful lot of bullshit to sort through in the thread.
Analog or Digital
22I try to always see this stuff in practical terms, so I know how best to apply it.
Regarding sample rate: How high can we hear?
I have done some tests using a sine generator in the analog domain (hard wired to my speakers; K & H 0300Ds) and in my environment, with my ears, I can hear very faintly at around 20 khz, but I am not sure if that is analog noise I am hearing or the sine wave, as the signal was low and I had to boost the gain.
Regarding bit depth (wordlength): How far into the analog noise floor can we hear?
It is very obvious to me that we can hear into the noise floor, but exactly how far is questionable. 5, 10, 20, 30 dB into the noise floor? My guess is somewhere between 10 and 20 dB into it, and that is proly pushing it!
So applying the answers to these two questions helps us better understand our choice of sample rate and word length.
I personally believe Nyquist's theory is a fact (based on historical and personal application), and that a properly designed converter can adequately capture 20 hz to 20 khz using a sample rate of 44 khz. When I record at 96 khz, I do hear some extra 'air' there, but to say it is better or worse is subjective, most especially using the high end converters.
The main benefit I notice when recording at 96 khz is that plugins sound better, in some cases TONS better. IMO, poor plugins are the number one reason (aside from the choices made) why digital mixes suck, so being able to improve the quality of digital processing is HUGE. Massenburg's EQ for Pro Tools up-samples everything to 96 khz for processing and is the only plugin EQ I have used that sounds just as good processing 44 khz audio, that it does 96 khz audio. Hopefully, more and more devs will catch on to this processing trend (especially as CPUs get more and more powerful).
So let's assume humans can hear music 20 dB into an analog noise floor. The Manley SLAM preamp (which is considered a high end preamp) has a measured dynamic range of about 90 dB (which does include a touch of its noise). The current average high end 24 bit AD converters have a practical dynamic range of about 120 dB. 120 - 90 = 30. So we have roughly 30 dB of 'play' regarding where the preamp's resolution will fit into the converter's resolution. If we pad the 'foot room' of the converter with 20 dB (accounting for humans hearing into the noise floor), that leaves 10 dB of 'head room' at the converter, which can be considered insurance in the event of a wild transient while recording. In most cases, clipping the AD converter is BAD and should be avoided, thus 10 dB headroom above your average peaks can be considered good practice. This is how I record, and I have no regrets as even my most sensitive and transparent preamp (the Buzz MA2.2) is captured well below its noise floor.
There is however, one very good reason for recording hot into digital. The sound of many preamps seems to change as we move through their gain settings. Some of them have a very noticeable sweet-spot with attributes most appealing for the recording situation. In some cases this sweet-spot results in a very hot output in relation to digital, and the converter would need to be re-calibrated if you were to place such a signal into the converter's sweet-spot (20 dB foot room and 10 dB head room). Converters calibrated @ -18dBFS = +4 dBu would allow a preamp to output at +22 dBu before clipping the converter. I find this is an adequate calibration for many of the high end preamps I have used.
Regarding sample rate: How high can we hear?
I have done some tests using a sine generator in the analog domain (hard wired to my speakers; K & H 0300Ds) and in my environment, with my ears, I can hear very faintly at around 20 khz, but I am not sure if that is analog noise I am hearing or the sine wave, as the signal was low and I had to boost the gain.
Regarding bit depth (wordlength): How far into the analog noise floor can we hear?
It is very obvious to me that we can hear into the noise floor, but exactly how far is questionable. 5, 10, 20, 30 dB into the noise floor? My guess is somewhere between 10 and 20 dB into it, and that is proly pushing it!
So applying the answers to these two questions helps us better understand our choice of sample rate and word length.
I personally believe Nyquist's theory is a fact (based on historical and personal application), and that a properly designed converter can adequately capture 20 hz to 20 khz using a sample rate of 44 khz. When I record at 96 khz, I do hear some extra 'air' there, but to say it is better or worse is subjective, most especially using the high end converters.
The main benefit I notice when recording at 96 khz is that plugins sound better, in some cases TONS better. IMO, poor plugins are the number one reason (aside from the choices made) why digital mixes suck, so being able to improve the quality of digital processing is HUGE. Massenburg's EQ for Pro Tools up-samples everything to 96 khz for processing and is the only plugin EQ I have used that sounds just as good processing 44 khz audio, that it does 96 khz audio. Hopefully, more and more devs will catch on to this processing trend (especially as CPUs get more and more powerful).
So let's assume humans can hear music 20 dB into an analog noise floor. The Manley SLAM preamp (which is considered a high end preamp) has a measured dynamic range of about 90 dB (which does include a touch of its noise). The current average high end 24 bit AD converters have a practical dynamic range of about 120 dB. 120 - 90 = 30. So we have roughly 30 dB of 'play' regarding where the preamp's resolution will fit into the converter's resolution. If we pad the 'foot room' of the converter with 20 dB (accounting for humans hearing into the noise floor), that leaves 10 dB of 'head room' at the converter, which can be considered insurance in the event of a wild transient while recording. In most cases, clipping the AD converter is BAD and should be avoided, thus 10 dB headroom above your average peaks can be considered good practice. This is how I record, and I have no regrets as even my most sensitive and transparent preamp (the Buzz MA2.2) is captured well below its noise floor.
There is however, one very good reason for recording hot into digital. The sound of many preamps seems to change as we move through their gain settings. Some of them have a very noticeable sweet-spot with attributes most appealing for the recording situation. In some cases this sweet-spot results in a very hot output in relation to digital, and the converter would need to be re-calibrated if you were to place such a signal into the converter's sweet-spot (20 dB foot room and 10 dB head room). Converters calibrated @ -18dBFS = +4 dBu would allow a preamp to output at +22 dBu before clipping the converter. I find this is an adequate calibration for many of the high end preamps I have used.