[leeperry]

Quote:

Originally Posted by slytown /img/forum/go_quote.gif We can't hear the difference between 24 and 16 but I remember hearing that we can feel the difference. Is that right?

It might give more room for dynamic contrast. Actually reproduction volume is irrelevant. If they play something at 96db, and then crescendo to 120...you're not going to hear any difference with 16 bits. Lets say your system is set at a max volume of 80db. Well, at 16 bit it would crescendo from 80 to 80. But at 24 bit it could go from like 53 to 66 or so.

or not?

 

[TStewart422]

Quote:

Originally Posted by xnor /img/forum/go_quote.gif what a Moment of Glory

A ZILLION cool points for you for that one! Love the Scorps!

 

[grokit]

 
Quote:

W00t! Thank you for that indepth explanation.. NOW I KNOW MORE!

QFT, glad I was able to see through the SACD BS a long time ago, iTunes all the way for me 

 
(bumpity bump for a great thread and a fantastic OP!)

 

[chesebert]

Nyquist sampling theorem is just that a theorem.
 
1. In practice, to avoid aliasing, most signals are ran through a LPF to cut off any frequency above Fmax (in this case 20khz)
 
2. However, in order to sample the 20khz signal, the sampling frequency has to be increased above the 2*Fmax (or Fs the sampling frequency) to avoid getting zero results.
 
3. now, come the fun part, D/A conversion.  D/A can be perfect if it follows pure Nyquist reconstruction formula.  I don't believe a filter is needed if the actual Nyquist reconstruction formula can be used.  So since everyone uses some type of filter, I presume no one has figuered out how to actually use the damn formula.
 
Here is the formula for your amusement:  Xa(t) = Summation [Xa * (n/(2B)) ( (sine2piB (t-n/2B))/ (2piB (t-n/2B))], from negative infinity to infinity.
 
On to quantization errors:
 
Theoretically, quantization of analog sigansl always results in a loss of information.  This is result of the ambiguity introduced by quantization.  Quantization is an irreversibel or noninvertible process (many to one mapping). In a fixed dynamic range, increasing the level of quantization will reduce the quantization steps, thereby reducing the quantization error. (always remember its a many to one mapping, more levels means less error).  This has nothing to do with dynamic range which is really the difference between the highest and lowest value in the signal.
 
So in conclusion: Nyquist works on paper, the reconstruction formula works on paper, but nothing is perfect in the real world and higher sampling frequency and higher quantization level means less crap to worry about later on (easier and more accurate non-perfect reconstruction and minimizaing of quantization errors). Or you can just use your own ear to hear if there is a difference and leave all the 'objective' discussions to the engineers.
 
If you are interested in this D/A monbojumbo, take Digital Signal Processing at your local engineering college.  I had fun when I took it a long time ago, and the labs are usually great (like designing your own D/A chip using FPGA).

 

[Isak]

 
Disclaimer: I have read the thread until about page 10 since it seemed to deteriorate at that point and did not seem to answer the question I’m going to ask now – which might even be a stupid question.
I’m not going to discuss whether or not we cannot perceive anything outside the frequencies that can be recreated at a 44.1 khz sample rate, a 96 khz, 192 or whatever.
 
My question is whether or not rates above 44.1 khz will provide greater detail within the spectrum we can hear even though we cannot hear the ‘new’ frequenzies that they can reproduce.
Let me give an example that at least makes me understand my question better (not being condescending here, just trying to keep things within my own limited knowledge!) Suppose we are only able of hearing frequencies from 1-4 herz (I’m quite aware that we cannot hear those but it makes the example much easier). In that case you would only need to sample what would effectively produce a high note of 4 hz, which is a sample rate of 8 hz, right? If that is the case wouldn’t you only be able to reproduce 4 tones (1, 2, 3 and 4 hz) on such a recording? And if this is true would it not be the case that while you would not be able to hear, say, a 7 hz tone on a 16 hz recording, you’d still be able to hear the 2.5 hz tone, and hence benefit from the doubling?
 
Or does our inability to hear things beyond 1-4 hz also mean that we’re unable to distinguish tonal differences at less than 1 hz? 

 

[chesebert]

see above post.
 
The short of it is, in theory, 44khz is really all you need.  But in practice since Nyquist reconstruction formula is never used to do the interpolation between the samples, you end up getting a stepped/approximate/half-assed interpolation of signal between each sample.  The most basic one is the zero-order-hold D/A, which results in the stepped response many magazines like to print.  Then stepped signal is "smoothed" out by a LPF (yeah..like that's a really accurate representation of the analog signal). I believe we have moved beyond that, but still making crap up by not using the formula.
 
oh if you can believe this, at 96khz sampling frequency, D/A has less crap to make up in between samples.  And a trivia, the Nyquist guy died in the 70s and we still can't make his formula work in the real world. But who really cares? All you really need is higher sampling frequency to solve most of the problems described.
 
So essentially the commercial audio DACs now days are just making crap up (cough..intelligent sample reconstruction) between the samples, as I don't believe they actually implement the Nyquist reconstruction formula.
 
I would like to stress that a perfect reconstruction of the analog signal is possible, but only by following the Nyquist reconstruction formula. (It really works on paper).  It's quite amazing to see the math all work out perfectly no matter how complex the starting analog signal is.
 
Quote:

 
My question is whether or not rates above 44.1 khz will provide greater detail within the spectrum we can hear even though we cannot hear the ‘new’ frequenzies that they can reproduce.

 

[kwkarth]

A couple of reasons we do not want to limit sample rate to the Nyquist freq. for the limits of human hearing...
 

1. The higher the sampling freq. the less deleterious effects of brick wall filters on the passband, including aliasing, etc.

 

1. Upper harmonics of fundamentals do lend "air" and aliveness to a recording

 

1. Because upper harmonics are generally greatly diminished in amplitude from the fundamental, low level resolution and detail is also critical for the preservation of an accurate recording so not only is sampling frequency important, but bit depth as well so that low levels can be faithfully maintained and not lost in the dither.

 

[Pio2001]

Quote:

Originally Posted by chesebert /img/forum/go_quote.gif
 
So since everyone uses some type of filter, I presume no one has figuered out how to actually use the damn formula.
 
Here is the formula for your amusement:  Xa(t) = Summation [Xa * (n/(2B)) ( (sine2piB (t-n/2B))/ (2piB (t-n/2B))], from negative infinity to infinity.

You presume wrong. The filter is there to implement the very formula. 
 
Actually, the perfect implementation is what is called a brickwall filter, or Sinc filter. The sinc function is defined by sinc(t) = sin(t) / t). But these are not used in audio because they lead to unwanted artifacts. They introduce ringing at the Nyquist frequency. That's the normal behaviour of perfect sampling. First you lowpass your original, which introduce a lot of ringing, then you sample, then you reconstruct your original lowpassed signal with all its ringing.
 
Using a lowpass filter with an cosinus attenuation profile, as viewed in the frequency domain, is much cleaner. If you can generate lowpass filters by yourself, compare a given sample lowpassed at 10 kHz with a perfect sinc filter, then with a cosine filter starting at 9500 Hz and ending at 10500 Hz.
 
Quote:

Originally Posted by chesebert 

On to quantization errors:
 
Theoretically, quantization of analog sigansl always results in a loss of information.

 
Right. It introduce noise at -96 dB if you quantize with 16 bits, at -144 dB if you quantize at 24 bits etc.

 
Quote:

 
My question is whether or not rates above 44.1 khz will provide greater detail within the spectrum we can hear even though we cannot hear the ‘new’ frequenzies that they can reproduce.
 

 
Yes, by using the additional bandwidth to add noise shaped dither, you can increase the resolution in you working bandwidth. It is the same thing as increasing the number of bits.
 
Quote:

 
sample rate of 8 hz, right? If that is the case wouldn’t you only be able to reproduce 4 tones (1, 2, 3 and 4 hz) on such a recording?

Not at all. You can reproduce any frequency below 4 Hz with a sampling rate of 8 Hz. 3.255664 Hz is perfectly possible, for example.
 
Quote:

Originally Posted by chesebert /img/forum/go_quote.gif
 
The most basic one is the zero-order-hold D/A, which results in the stepped response many magazines like to print.  Then stepped signal is "smoothed" out by a LPF (yeah..like that's a really accurate representation of the analog signal). I believe we have moved beyond that, but still making crap up by not using the formula.

No ! The signal is oversampled first, which allow to apply the Nyquist formula with good accuracy.
 
Only very high end DACs directly lowpass the zero-order hold. That indeed leads to crappy results (-2 dB of treble in the audible range). That's a coloration that they either believe is "more musical", either deliberately introduce to distinguish them from their competitors.
 
Quote:

Originally Posted by chesebert 
 
oh if you can believe this, at 96khz sampling frequency, D/A has less crap to make up in between samples. 

 
There is more crap between the samples ! All the ultrasonic noise, parasites from computer displays etc is recorded and fed into the amplifier during playback.
 
Quote:

The higher the sampling freq. the less deleterious effects of brick wall filters on the passband, including aliasing, etc.

 
There is no deleterious effects of brick wall filters in the audible range at 44.1 kHz.
 
Quote:

1. Upper harmonics of fundamentals do lend "air" and aliveness to a recording

 
No, they don't. They're inaudible.
 
Quote:

1. Because upper harmonics are generally greatly diminished in amplitude from the fundamental, low level resolution and detail is also critical for the preservation of an accurate recording so not only is sampling frequency important, but bit depth as well so that low levels can be faithfully maintained and not lost in the dither.

 
16 bits are enough in all practical situations for this purpose.
 

 

[grokit]

Quote:

16 bits are enough in all practical situations for this purpose.

While I don't completely understand all of the details of this ongoing debate as reflected in this thread, I do get the jist of it, and what you are saying makes sense to me. It also makes me trust my own conclusions, that the most important thing is the quality of the source recording and mastering, regardless of the bit rate and sampling frequency used for playback. Anyways I do appreciate all of the thoughtful posts lately, it's very interesting subject but sometimes it just makes me want to play a record!

 

[chesebert]

I didn't know the brickwall (that is, the brick wall is a frequency-domain brickwall) was even implmeneted.  It has an impulse reponse that extends for all time. 
 
input signal -> perfect D/A -> impulse response -> brick wall -> perfect analog signal.
 
let's see which one of these steps can't be implemented. . . all of it.
 
One disclaimer: I haven't touched this DSP stuff in many many years, so my knowledge may be dated and certain things I can't remember that well.  in order words, I may not know what I am talking about
Quote:

You presume wrong. The filter is there to implement the very formula. 
 
Actually, the perfect implementation is what is called a brickwall filter, or Sinc filter. The sinc function is defined by sinc(t) = sin(t) / t). But these are not used in audio because they lead to unwanted artifacts. They introduce ringing at the Nyquist frequency. That's the normal behaviour of perfect sampling. First you lowpass your original, which introduce a lot of ringing, then you sample, then you reconstruct your original lowpassed signal with all its ringing.
 

 

 

[JaZZ]

 

You presume wrong. The filter is there to implement the very formula. Actually, the perfect implementation is what is called a brickwall filter, or Sinc filter. The sinc function is defined by sinc(t) = sin(t) / t). But these are not used in audio because they lead to unwanted artifacts. They introduce ringing at the Nyquist frequency. That's the normal behaviour of perfect sampling. First you lowpass your original, which introduce a lot of ringing, then you sample, then you reconstruct your original lowpassed signal with all its ringing.

 
Why exactly are you concerned about a ringing at 22,050 Hz? In my understanding it would theoretically be better to accept it, as 22 kHz are known to be inaudible. Theoretically a steep filter with massive ringing barely affects transient response at audible frequencies, in contrast to your favored smoother filter with reduced ringing which moreover may affect amplitude response.
 
Well, at least according to the established audio doctrine. In reality the ringing is most likely audible nonetheless, as the different filter settings on my Corda Symphony with different characteristic and intensity of the ringing show (note that some of them have identical amplitude response!). Which makes me think that – at least in view of finite perfection of the used electronics components – an abrupt and steep low-pass filter so close to the audio band is critical for sensitive and experienced ears. Actually I have passably made friends with the CD format since the HD 800 era, and due to an imcompatibility of my hearing with speaker-based recordings listened through headphones I'm forced to use crossfeed. The CD format is perfect for my own implementation, so it has become my audio standard since quite a while. But lately I have compared some double-discs again with the same recording once on DVD-A, once on CD (DGG), and the result is clear, although not night and day: Despite the plausibility of the Nyquist theorem and the reasonings of its proponents, in practice recordings with higher frequency bandwidth sound better to my ears.

 

No, they don't. They're inaudible.

No, not necessarily. Maybe (!) if they're in the ultrasonic range, but his statement didn't implicate that. I'm fairly convinced that preserved overtone transient accuracy/sharpness is the key to a non-digital sound (to avoid the term «analogue»). Whereas low-rez digital tends to smear them.
.

 

[kwkarth]

Quote:

Originally Posted by Pio2001 /img/forum/go_quote.gif
 
You presume wrong. The filter is there to implement the very formula. 
 
Actually, the perfect implementation is what is called a brickwall filter, or Sinc filter. The sinc function is defined by sinc(t) = sin(t) / t). But these are not used in audio because they lead to unwanted artifacts. They introduce ringing at the Nyquist frequency. That's the normal behaviour of perfect sampling. First you lowpass your original, which introduce a lot of ringing, then you sample, then you reconstruct your original lowpassed signal with all its ringing.
 
Using a lowpass filter with an cosinus attenuation profile, as viewed in the frequency domain, is much cleaner. If you can generate lowpass filters by yourself, compare a given sample lowpassed at 10 kHz with a perfect sinc filter, then with a cosine filter starting at 9500 Hz and ending at 10500 Hz.
 
Right. It introduce noise at -96 dB if you quantize with 16 bits, at -144 dB if you quantize at 24 bits etc.
 
Yes, by using the additional bandwidth to add noise shaped dither, you can increase the resolution in you working bandwidth. It is the same thing as increasing the number of bits.
 
Not at all. You can reproduce any frequency below 4 Hz with a sampling rate of 8 Hz. 3.255664 Hz is perfectly possible, for example.
 
No ! The signal is oversampled first, which allow to apply the Nyquist formula with good accuracy.
 
Only very high end DACs directly lowpass the zero-order hold. That indeed leads to crappy results (-2 dB of treble in the audible range). That's a coloration that they either believe is "more musical", either deliberately introduce to distinguish them from their competitors.
 
There is more crap between the samples ! All the ultrasonic noise, parasites from computer displays etc is recorded and fed into the amplifier during playback.
 
16 bits are enough in all practical situations for this purpose.

Well, I guess we've been told.
 

 

[grokit]

There's an "established audio doctrine"?
 
That seems debatable; as far as I can tell there are many oppositional viewpoints that are extremely well-argued, without any apparent resolution.

 

[kwkarth]

I depends upon with whom you speak.

 

[Pio2001]

Quote:

Why exactly are you concerned about a ringing at 22,050 Hz? In my understanding it would theoretically be better to accept it, as 22 kHz are known to be inaudible. Theoretically a steep filter with massive ringing barely affects transient response at audible frequencies, in contrast to your favored smoother filter with reduced ringing which moreover may affect amplitude response.
.

To put numbers on it, filters used in DACs are very far from the regular 6 db per octave found in speakers. They don't start until 20 kHz, and reach minus infinite soon after. Compared to speaker crossovers, they can be viewed as brickwalls.
But compared to Sinc filters, they are very smooth. A Sinc filter can let everything pass unaffected until 22049 Hz, and reach minus infinite at 22050 Hz.
 
I prefer smoother filters (0 db at 21 kHz, minus infinite at 22 kHz, for example) because I had the possibility to compare them in the 12 -16 kHz range. At 13 khz, the ringing introduced by a brickwal filter was very annoying, while a filter with a transition band from 12500 to 13500 Hz produced a very good result. The treble loss was subtle, and there was no ringing at all.
 
At 22.05 kHz, it shouldn't matter. I'm just keeping the same what sounds better at 13 khz.