Why are more bits/ higher sampling rate better?

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I'm wondering if anyone has a good explanation as to why we need more than 16 bits and 44.1 KHz sampling.

16-bits = 65,536 discreet levels = 96dB worth of dynamic range.

Most albums don't use nearly that much dynamic range. Why do we need more dynamic range if we aren't using all that we have now?

According to the Nyquist theorem, 44.1 KHz sampling rate should be sufficient to capture > 20KHz of frequency range. I know my 40 year-old ears can't reach up to 20 KHz, I doubt most people's ears can.

So why do we need to sample at a higher frequency?

I'm not arguing that higher bit rates aren't better, I'm sure there wouldn't be 24 bit / 96 KHz formats out there if somebody couldn't tell the difference. I'm just curious why. Where does the theory fall short?
 
The steep anti-aliasing filters in PCM coding create artefacts that reach far below the Nyquist frequency. This is the reason why higher sample rate gives an audible improvement.
The SACD has no filter ringing problem, but high sample rate is necessary to get a reasonable signal to noise ratio. The high bandwidth is a side effect.
 
16 bits is not 96 dB dynamic range. This were true if the music at -96 dB level could be represented on 1 bit (the LSB), but then this is no music just jumping between two levels. Similarly, a signal of -60 dB is represented on 6 bits only. 6 bits has 64 discrete steps, imagine what happens to the music with such poor resolution. Also most recordings never reach near 0 dB level, and I assume the average could be around -30 to -40 dB.
The steep analog filter after the DAC has very large phase shift much below the cutoff frequency, that may also be audible.
 
Nyquist only really applies to frequency reproduction.

As you get closer to the nyquist freq you lose amplitude and phase information. Really from about nyquist/4 you're starting to lose this information.

As for up and oversampling, as the source is 16bit 44.1k you've lost the information already and it can't be recovered.
 
BlackCatSound said:
Nyquist only really applies to frequency reproduction.

As you get closer to the nyquist freq you lose amplitude and phase information. Really from about nyquist/4 you're starting to lose this information.

As for up and oversampling, as the source is 16bit 44.1k you've lost the information already and it can't be recovered.

No. The definition of sampling theorem is basically that for any frequency under fs/2 you have all of the information necessary to exactly reproduce the signal (emphasis mine):

Exact reconstruction of a continuous-time baseband signal from its samples is possible if the signal is bandlimited and the sampling frequency is greater than twice the signal bandwidth.

Practical considerations (and quantization) aside, the frequency and phase response is perfect until you get to fs/2.
 
error401 said:


Practical considerations (and quantization) aside, the frequency and phase response is perfect until you get to fs/2.


If this sine (f=fs/2) is sampled in the given phase (see slashes) you get nothing. If it is sampled 90° shifted you get the full amplitude in the right phase. For any other phase you get neither the correct phase nor the correct amplitude.
I`m no expert, correct me if I`m wrong.
 

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el`Ol said:



If this sine (f=fs/2) is sampled in the given phase (see slashes) you get nothing. If it is sampled 90° shifted you get the full amplitude in the right phase. For any other phase you get neither the correct phase nor the correct amplitude.
I`m no expert, correct me if I`m wrong.
This sine has a frequency of exactly fs/2. Nyquist-Shannon states that the signal bandwidth must be below fs/2 for exact reproduction.

It's not the most intuitive theorem, but the fundamental idea is that for a signal bandwidth under fs/2, there is only one possible interpolation between two samples. If the input signal is bandlimited to a bandwidth of less than fs/2, that means that the entire signal can be exactly reproduced, since the interpolated signal exactly defines the input signal.
 
el`Ol said:
Doesn`t this only work for sines of very long duration and very high order interpolation?
Nope, my understanding is that it works for any signal with frequency less than fs/2, but you're correct that the interpolation is where the practical deviates from the ideal. This is one of the main reasons that higher sample rates are better - they allow less aggressive filters with better passband characteristics to be used.

I'm not a practical expert on this either, but the theory is quite clear - with a sampling frequency greater than twice the signal bandwidth, the signal can be reproduced exactly. As far as I understand, modern DAC technology comes quite close to realizing this, to the limits of the quantization depth used.
 
with a sampling frequency greater than twice the signal bandwidth, the signal can be reproduced exactly.

That's exactly right. No interpolation needed. And with proper dither (not at all difficult), there's no resolution loss at a finite number of bits, just a degradation of S/N.

As a practical matter, one needs to take into account the phase response of the antialiasing and anti-imaging filters to reconstruct phase perfectly. But again, that's an easy thing to do.
 
frugal-phile™
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error401 said:
No. The definition of sampling theorem is basically that for any frequency under fs/2 you have all of the information necessary to exactly reproduce the signal (emphasis mine):

But only if the signal is periodic & there is absolutely no signal above the Nyquist, Both of which are violated when you are sampling music.

Syncronystically, i was taking a senior level statistics course on sampling theory when Sony's white paper on CD hit... my 1st comment after reading it was that they would need to get the samplint frequency at least 4x as high before it had any hope of comparing to analog. Current technology is starting to prove that correct, althou i have to say that i am surprised that they are getting 16/44 to sound as good as it can with 1st rate kit.

An externally hosted image should be here but it was not working when we last tested it.


http://www.t-linespeakers.org/oddsends/mrFourier.html

dave
 
Here are some sines I made with audacity. Admittedly its just done 'join the dots'.

First is 5k, then 10k and finally 20k. ie not nice fractions of 44.1k.

Nyquist works if you're trying to fit a single sine wave to the data points. Not something you do in real life.
 

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But only if the signal is periodic & there is absolutely no signal above the Nyquist, Both of which are violated when you are sampling music.

I'm tempted to just say "Four!" since I've knocked that objection down enough times that I may as well use shorthand. ALL signals of finite length can be made periodic with no error as long as you accept the basic physical principle of the Universe that events in the future do not affect those in the past; time flows in one direction for macroscopic phenomena.
 
Nyquist works if you're trying to fit a single sine wave to the data points.

It works, period (bad pun). Anything with a frequency sufficiently close to the Nyquist frequency will be a sine wave once it's passed through a low pass filter since the harmonics fall above the Nyquist frequency. Multiple sine waves of varying phases near the Nyquist fequency are no problem and no exception to the theorem.

A really good reference is Mischa Schwartz's superb "Information Transmission, Modulation, and Noise" which covers this stuff thoroughly and rigorously in Chapter 2.

BTW, your plots do not take into account the second requirement: anti-imaging on the output.
 
frugal-phile™
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SY said:
I'm tempted to just say "Four!" since I've knocked that objection down enough times that I may as well use shorthand. ALL signals of finite length can be made periodic with no error as long as you accept the basic physical principle of the Universe that events in the future do not affect those in the past; time flows in one direction for macroscopic phenomena.

That doesn't address the band-limited requirement. I'll have to have a look at your other arguement because i've a feeling there is a gotcha you are missing.

dave
 
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