Last time I looked Nyquist was not an "assumption" but a correct piece of mathematics. 2x is the bare absolute minimum. Sample slower than that and you cannot reproduce the signal; sample at least that fast and you can reproduce it - but whether you do reproduce it depends on your filter designs.shanx said:
I suspect some of the confusion and 'Nyquist denial' often seen on here comes from the fact that merely joining the dots of a sampled signal looks 'correct' but actually is seriously incorrect as it includes all the images as well as the orginal signal. The reconstruction filter gets rid of the images and what is left is the original signal as it left the anti-aliasing filter (possibly attenuated by a sinc function).
'Faster than necessary' sampling rate merely makes filter design easier.
Yes, Nyquist is very much stating the 2x as bare absolute minimum and is harder to get a true reproduction around that point, depending on filtering. With CD being the storage playback media, it was pretty close to that edge at 20kHz audio limit. If you were recording source material on ADAT, you had 44.1 kHz or 48 kHz option and it was fine.20 to 24 bit is fine too. DAW can do 24 and 32 bit pretty standard now so if given a choice why not master at 96kHz rate? At least from the master you can ''down sample'' to whatever clock rate is required for media playback. I'd be kinda disappointed if somebody mastered material at 32kHz rate even if I couldn't hear much of anything above16 kHz. I don't think the sound engineer would still be working at the studio, either.
The problem with mastering at 32kHz is that some people (mainly youngsters) can hear above 16kHz, and lots of people think they can. I doubt if anyone can hear up to 48kHz, so 96kHz is not necessary - but will do little harm apart from doubling file sizes.
For recording my understanding is that there is no need to go above 24 bits at 48kHz. For distribution 16 bits is fine.
For recording my understanding is that there is no need to go above 24 bits at 48kHz. For distribution 16 bits is fine.
How much 20kHz is there in music?
On bit depth pictures can be 8, 12, or 14bit depth, how noticeable this is depends on your print size and resolution of your sensor, it is very hard to tell any of them apart when printed....does 24 bit music sound better or has it been proven to sound better...
I would love to try some higher bit rate stuff but have never got around to it so I am curious here....
On bit depth pictures can be 8, 12, or 14bit depth, how noticeable this is depends on your print size and resolution of your sensor, it is very hard to tell any of them apart when printed....does 24 bit music sound better or has it been proven to sound better...
I would love to try some higher bit rate stuff but have never got around to it so I am curious here....
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Yes, percussive sounds is where it's at ... there are a few high bit rate samples around as demo's, and every time I've looked at them to see where the above 20kHz energy is, it's always a "bang!!!" moment in the sound. Musically, it's completely irrelevant - unless you're obsessed with the precise spectrum of a whack on an object then I don't think you're missing anything, 
...
...From a recording point of view 20 to 24 bit compared to 16 is a big advantage. It has more to do with dynamic range of musical instruments, and how much resolution you get for the overall headroom. Same of playback. Like the 8 bit visual picture, as soon as you scale it up you start to see the pixelation. If you have 24 bit audio on record and playback, the whisper is as detailed as the saxophone blast, without having to use peak compression. At 32 bit, I really can't hear a difference compared to 24..but that is me.. When recording, some peak compression is required to keep digital distortion at bay, but if your threshold is 24 bit full scale, it's still huge dynamic range which is not compressed. A 20 bit conversion has potentially 8 times the peak voltage range as a 16 bit conversion (if ADC resolution same as 16).
The bits in a picture correspond to grey scales generally, or colours if 24-bit. That's the grey level or color of each pixel.
The pixel resolution corresponds to the sample rate in audio. Except, of course, it's 2D.
But, but... what of aliasing freq folding?
Actually, the problem remains frequency folding, or heterodyne aliasing.
The “worst case” (but easiest to visualize) is when sampling rate is exactly 2× frequency. Remember (for those of you know might not know it…) 1 Hz = two peaks per second. One positive, one negative. If it is a classical text-book picture, the wave starts at zero (volts, pressure, etc), rises to +1 unit of (V, P, etc), drops back to zero at the midpoint, goes negative to –1 unit, then back to zero.
The “worst case” is this: if the digital sampler catches this perfect wave at exactly T = 0, then the digital representation is also of zero. N[0] = 0. If the sampling rate is 2 Hz (2× 1 Hz) then it will take a sample exactly at the midpoint. N[1] = 0. And then it'll catch the thing at the beginning of the next cycle, N[2] = 0. And so on.
Point is, N will always be exactly zero. There's no way from that digital stream, no matter what assortment of filters you conjure up, to reproduce the 1 Hz actual analog wave. Just can't be done.
_______
OK, now think about the heterodyning case.
F = 0.95 Hz, and sample rate = 2 Hz. (i.e. F is below SR/2). Problem is that the resulting sample stream is a far cry from something that'd hint either an analog or digital filter into believing that a pure-sinusoid was to be reconstructed and reproduced.
0.00
0.16
–0.31
0.45
–0.59
0.71
–0.81
0.89
–0.95
0.99
–1.00
0.99
–0.95
0.89
–0.81
0.71
–0.59
0.45
–0.31
0.16
0.00
–0.16
0.31
–0.45
0.59
–0.71
0.81
–0.89
0.95
–0.99
1.00
That there is your classic heterodyning chirp signal.
By the grace of "the gods", it turns out there are very few unwavering frequencies of audio high enough to get significantly close to the heterodyning sampling case. And - they waver a lot - which while it exacerbates the problem in a sense (introducing wolf beat frequencies), it also smooshes over the issue to, by making periods of noticeable heterodyning blessedly short.
Hence, 44.1 kHz sampling was found in practice to be a decent compromise between occasional non-musical inaccuracy and the maximum capacity of itty-bitty bits on the CD disk medium. With the added real world limitations of there only being cheap infrared laser diodes, and not visible-wavelength ones. If one was going to make a CD player cheaply, one had to get the laser cost down to something competitive.
Compromises, compromises. The truth is that just as 44.1 kHz is “just enough” to get up to perhaps 16 kHz or so without appreciable heterodyning, going all the way up to 96 kHz is very good … and 192 kHz is just fu-cakes, and rather unnecessary. Its not like there are many recordings at 192 kHz that are real. Most are just digitally reconstructed super samplings of other lower-frequency recordings. With tons of fancy digital deconvolution algorithm application to 'suss out whether the chirps are heterodyne caused, or possibly from an original and now masked signal.
GoatGuy
DF₉₆;4133978 said:
Actually, the problem remains frequency folding, or heterodyne aliasing.
The “worst case” (but easiest to visualize) is when sampling rate is exactly 2× frequency. Remember (for those of you know might not know it…) 1 Hz = two peaks per second. One positive, one negative. If it is a classical text-book picture, the wave starts at zero (volts, pressure, etc), rises to +1 unit of (V, P, etc), drops back to zero at the midpoint, goes negative to –1 unit, then back to zero.
The “worst case” is this: if the digital sampler catches this perfect wave at exactly T = 0, then the digital representation is also of zero. N[0] = 0. If the sampling rate is 2 Hz (2× 1 Hz) then it will take a sample exactly at the midpoint. N[1] = 0. And then it'll catch the thing at the beginning of the next cycle, N[2] = 0. And so on.
Point is, N will always be exactly zero. There's no way from that digital stream, no matter what assortment of filters you conjure up, to reproduce the 1 Hz actual analog wave. Just can't be done.
_______
OK, now think about the heterodyning case.
F = 0.95 Hz, and sample rate = 2 Hz. (i.e. F is below SR/2). Problem is that the resulting sample stream is a far cry from something that'd hint either an analog or digital filter into believing that a pure-sinusoid was to be reconstructed and reproduced.
0.00
0.16
–0.31
0.45
–0.59
0.71
–0.81
0.89
–0.95
0.99
–1.00
0.99
–0.95
0.89
–0.81
0.71
–0.59
0.45
–0.31
0.16
0.00
–0.16
0.31
–0.45
0.59
–0.71
0.81
–0.89
0.95
–0.99
1.00
That there is your classic heterodyning chirp signal.
By the grace of "the gods", it turns out there are very few unwavering frequencies of audio high enough to get significantly close to the heterodyning sampling case. And - they waver a lot - which while it exacerbates the problem in a sense (introducing wolf beat frequencies), it also smooshes over the issue to, by making periods of noticeable heterodyning blessedly short.
Hence, 44.1 kHz sampling was found in practice to be a decent compromise between occasional non-musical inaccuracy and the maximum capacity of itty-bitty bits on the CD disk medium. With the added real world limitations of there only being cheap infrared laser diodes, and not visible-wavelength ones. If one was going to make a CD player cheaply, one had to get the laser cost down to something competitive.
Compromises, compromises. The truth is that just as 44.1 kHz is “just enough” to get up to perhaps 16 kHz or so without appreciable heterodyning, going all the way up to 96 kHz is very good … and 192 kHz is just fu-cakes, and rather unnecessary. Its not like there are many recordings at 192 kHz that are real. Most are just digitally reconstructed super samplings of other lower-frequency recordings. With tons of fancy digital deconvolution algorithm application to 'suss out whether the chirps are heterodyne caused, or possibly from an original and now masked signal.
GoatGuy
Sorry, I should have said that 2x is just not quite enough. Anything over 2x is enough. So sample a 22kHz sinewave at 44.1kHz and use a sufficiently good reconstruction filter and you get a perfect 22kHz sine wave back again.
This is because the signal before the reconstruction filter consists almost entirely of 22.0kHz and 22.1kHz at almost equal amplitude. 22.0 is what we want; 22.1 is the first image which the filter will remove. Granted you need a very good filter, but Nyquist is about what is possible - not what is easy.
Someone is bound to ask "What about a short burst of 22kHz? If the phase is wrong then you will get lots of near-zero samples as Goatguy says.". The answer is that a 22kHz burst will have lots of frequency components above 22kHz which the anti-aliasing filter will remove so what you end up sampling is not a 22kHz burst but something a bit different. Remember, all digital audio claims to be able to reproduce is the output from the anti-aliasing filter, not its input.
This is because the signal before the reconstruction filter consists almost entirely of 22.0kHz and 22.1kHz at almost equal amplitude. 22.0 is what we want; 22.1 is the first image which the filter will remove. Granted you need a very good filter, but Nyquist is about what is possible - not what is easy.
Someone is bound to ask "What about a short burst of 22kHz? If the phase is wrong then you will get lots of near-zero samples as Goatguy says.". The answer is that a 22kHz burst will have lots of frequency components above 22kHz which the anti-aliasing filter will remove so what you end up sampling is not a 22kHz burst but something a bit different. Remember, all digital audio claims to be able to reproduce is the output from the anti-aliasing filter, not its input.
Low bit depth gives colour pastelisation (I think I have the correct word), distinct bands where a colour changes to another, blue sky is the main culprit
Thank you, pastelisation is now a new word in my vocabulary..I accept that as being correct. When saying I didn't trust Nyquist, I do not "disbelieve it", as said before it is a minimum requirement. If we want to trust that an antialias filter rejecting to 0.1 hz accuracy is more practically buildable than sampling double that minimum? If we master at 96 Khz 24 bit, and give leeway to the layback media and equipment (lower res is fine for some). At 96k 24 resolution, the recorded playbeck versus original signal is indistinguishable to my ears on the same system. And probably not measurable, if you measured it at the playback speaker either.
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