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All you really need to know is Nyquist's thereom "A bandlimited continuous-time signal can be sampled and perfectly reconstructed from its samples if the wavef

All you really need to know is Nyquist's thereom "A bandlimited continuous-time signal can be sampled and perfectly reconstructed from its samples if the waveform is sampled over twice as fast as it's highest frequency component." This is where the magic 44.1 Khz sampling rate comes from. It is twice the limit of human hearing at 22 Khz. Now I don't really understand why 16-bit or 1-bit makes a difference. Maybe someone can explain that to me.

cillian64 5y ago
Nyquist’s theorem only covers sampling (turning a “continuous” signal (which exists at all points in time) into a “discrete” function (which only exists at certain points in time)). Each of the Nyquist samples is a real-valued number which can take an infinite number of values. To get from Nyquist samples to something we can actually represent digitally we need to do a second step: quantisation. This is where we take the real- valued samples and quantise each to one of a fixed set of values. The bit-depth determines the number of values we can quantise to. The higher the bit depth the more values we can quantise to and so the less error introduced by quantisation. You can think of quantisation error as introducing a noise term which gets added onto your signal. Higher bit depth lets you either reduce the amplitude of quantisation error or increase the range of signals you can represent (this is called dynamic range). Once you get to about 16 bits the quantisation noise is inaudible in even the quietest listening environments while at the same time the dynamic range is high enough to cause instant hearing damage. So, in a similar way to Nyquist telling us that more than 44kHz sample rate is pointless, dynamic range tells us that more than 16 bit depth is pointless (for playback. Things get a little more complicated for recording and editing). Edit: as linked by another commenter, Monty from Xiph explaining it better than me: https://web.archive.org/web/20160304013821/http://people.xiph.org/~xiphmont/demo/neil-young.html https://web.archive.org/web/20160304013821/http://people.xip...
- TedDoesntTalk 5y ago
  Thank you for the excellent explanation. Do you know why CD players went through a phase advertising “1 bit!” after a lengthy time advertising 16-bit? What does or even mean you have a 1-bit depth? (Perhaps marketing)
  - gwbas1c 5y ago
    If you have the time, read through https://www.stereophile.com/content/pdm-pwm-delta-sigma-1-bit-dacs https://www.stereophile.com/content/pdm-pwm-delta-sigma-1-bi... The short answer is that a commodity 1-bit DAC operating highly in excess of 44khz sounds a lot better than the earlier commodity DACs from the 1980s. The above link explains a lot of the problems that those DACs had, like the "zero crossing problem."
- gwbas1c 5y ago
  16-bit audio's quantization error is audible unless there's good dithering and/or noise shaping. Otherwise, the quantization error becomes audible over ~80db. (Normal speech.) Undithered / unshaped 16-bit audio can sound better than a record or cassette, although some people might prefer the sound of analog hiss to the choppiness of rounding.
gwbas1c 5y ago
Some people can go up to 28khz: https://en.wikipedia.org/wiki/Hearing_range#Humans https://en.wikipedia.org/wiki/Hearing_range#Humans > Under ideal laboratory conditions, humans can hear sound as low as 12 Hz[11] and as high as 28 kHz It's just a fraction of an octave over 22khz, but that probably explains why some people swear that 96khz sources sound better than the CD. Related: When I ripped my DVD-A collection, (I like music in surround,) I downsampled everything to 48khz, 16-bit. Later, if I played the original 96khz version, I did notice a slight crispness to the music. It's anecdotal, and I thought it was placebo effect, until I came across the above link.
gwbas1c 5y ago
> Now I don't really understand why 16-bit or 1-bit makes a difference. Maybe someone can explain that to me. Short answer: It's a means to an end. A 1-bit DAC with a DSP is easier to make than a 16-bit DAC with no DSP. Long answer: If you're using dithering, every time you double the sampling rate, the perceived "bits per sample" for everything else doubles. IE: For sounds below 22khz, a 16-bit, 44khz will sound just as good as 15-bit, 88khz, or 14-bit, 176khz. Add some noise shaping, (basically, tuned hiss,) and the perceived bits per sample also go up. Thus, a 1-bit per sample DAC at a super-high sampling rate, coupled with a well-designed DSP, and an analog low-pass filter, will perfectly preserve all of the information in the original 16-bit, 44khz signal. What the DSP does is move all of the distortion into frequencies well above the cutoff of the analog low-pass filter. That's how a 22khz tone comes out as a sine wave instead of a square wave.

cillian64 5y ago

Nyquist’s theorem only covers sampling (turning a “continuous” signal (which exists at all points in time) into a “discrete” function (which only exists at certain points in time)). Each of the Nyquist samples is a real-valued number which can take an infinite number of values. To get from Nyquist samples to something we can actually represent digitally we need to do a second step: quantisation. This is where we take the real- valued samples and quantise each to one of a fixed set of values. The bit-depth determines the number of values we can quantise to. The higher the bit depth the more values we can quantise to and so the less error introduced by quantisation. You can think of quantisation error as introducing a noise term which gets added onto your signal. Higher bit depth lets you either reduce the amplitude of quantisation error or increase the range of signals you can represent (this is called dynamic range). Once you get to about 16 bits the quantisation noise is inaudible in even the quietest listening environments while at the same time the dynamic range is high enough to cause instant hearing damage. So, in a similar way to Nyquist telling us that more than 44kHz sample rate is pointless, dynamic range tells us that more than 16 bit depth is pointless (for playback. Things get a little more complicated for recording and editing). Edit: as linked by another commenter, Monty from Xiph explaining it better than me: https://web.archive.org/web/20160304013821/http://people.xiph.org/~xiphmont/demo/neil-young.html https://web.archive.org/web/20160304013821/http://people.xip...

TedDoesntTalk 5y ago
Thank you for the excellent explanation. Do you know why CD players went through a phase advertising “1 bit!” after a lengthy time advertising 16-bit? What does or even mean you have a 1-bit depth? (Perhaps marketing)
- gwbas1c 5y ago
  If you have the time, read through https://www.stereophile.com/content/pdm-pwm-delta-sigma-1-bit-dacs https://www.stereophile.com/content/pdm-pwm-delta-sigma-1-bi... The short answer is that a commodity 1-bit DAC operating highly in excess of 44khz sounds a lot better than the earlier commodity DACs from the 1980s. The above link explains a lot of the problems that those DACs had, like the "zero crossing problem."
gwbas1c 5y ago
16-bit audio's quantization error is audible unless there's good dithering and/or noise shaping. Otherwise, the quantization error becomes audible over ~80db. (Normal speech.) Undithered / unshaped 16-bit audio can sound better than a record or cassette, although some people might prefer the sound of analog hiss to the choppiness of rounding.

gwbas1c 5y ago

Some people can go up to 28khz: https://en.wikipedia.org/wiki/Hearing_range#Humans https://en.wikipedia.org/wiki/Hearing_range#Humans > Under ideal laboratory conditions, humans can hear sound as low as 12 Hz[11] and as high as 28 kHz It's just a fraction of an octave over 22khz, but that probably explains why some people swear that 96khz sources sound better than the CD. Related: When I ripped my DVD-A collection, (I like music in surround,) I downsampled everything to 48khz, 16-bit. Later, if I played the original 96khz version, I did notice a slight crispness to the music. It's anecdotal, and I thought it was placebo effect, until I came across the above link.

gwbas1c 5y ago

> Now I don't really understand why 16-bit or 1-bit makes a difference. Maybe someone can explain that to me. Short answer: It's a means to an end. A 1-bit DAC with a DSP is easier to make than a 16-bit DAC with no DSP. Long answer: If you're using dithering, every time you double the sampling rate, the perceived "bits per sample" for everything else doubles. IE: For sounds below 22khz, a 16-bit, 44khz will sound just as good as 15-bit, 88khz, or 14-bit, 176khz. Add some noise shaping, (basically, tuned hiss,) and the perceived bits per sample also go up. Thus, a 1-bit per sample DAC at a super-high sampling rate, coupled with a well-designed DSP, and an analog low-pass filter, will perfectly preserve all of the information in the original 16-bit, 44khz signal. What the DSP does is move all of the distortion into frequencies well above the cutoff of the analog low-pass filter. That's how a 22khz tone comes out as a sine wave instead of a square wave.