Understanding Sample Rate

[Spacehound]

20 minutes ago, The Computer Audiophile said:

Just like my wife and I were discussing over breakfast this morning :~)

There is  a nice selection of emoticons at the top. EG 

[Spacehound]

4 hours ago, mansr said:

Politicians are a subclass of criminals, right?

Most politicians are too incompetent to be criminals, even the ones in prison.  After the failure of their  Whelk stall MQA shilling would be a good match for their 'abilities'.

[firedog]

2 hours ago, Summit said:

To understand the effect of different sample rates that @beerandmusic have been asking about, it’s not enough to quote Nyquist-Shannon Sampling Theorem and think that as long as the samples are above that rate nothing else are of importance. Just try to play DSD at those sample rate and see. Its more, much more premises that comes in to play if we are looking to reproduce the sound as close as possible in SQ to the master tapes.

DSD doesn't really have much relevance to the question here. First,  whether it sounds better than PCM or not is a matter of taste and not some kind of "fact" due to its' level of resolution. Just like there are people who prefer it, there are people who don't. And a nice article can be written on why it is inferior technically to PCM.

 

But none of that matters - just listen to what you like. 

 

Second, any issue you think there is with sampling rate at PCM also applies with DSD. Both are sampling. The same ideas that push for recording PCM in 4X and 8X rates push for DSD recording in 2X, and 4X rates. I'm fine with the sound of DSD, but it has its' own issues, just like PCM has some of its own. 

 

And just as an aside, we live in a digital world - I  don't want the sound as close as possible to the sound of "master tapes" - I want the master digital file, which is what about 99% of masters are nowadays.

[crenca]

1 hour ago, mansr said:

The sampling theorem assumes infinite sample precision. With a limited number of bits, we get quantisation error which is a non-linear distortion. This happens at any sample rate and has nothing to do with aliasing. With TPDF dither, the quantisation error is (mostly) turned into white noise at a level determined by the bit depth. If the sample rate is increased, the quantisation energy is spread over a wider frequency range, thus reducing the level of dither noise at any specific frequency. Doubling the sample rate gives the same improvement as extending the sample precision by one bit. In other words, not very efficient. A high sample rate does, however, bring another benefit in that it enables the use of noise shaping. Instead of the quantisation noise being spread evenly over the full spectrum, it can be concentrated at high frequencies where there is no signal of interest. This is very useful since a high-rate flash ADC with a small number of bits, say 8 or less, is much easier to construct than a slower ADC with high precision. Low-resolution noise-shaped sampling at a high rate, 10 MHz or more, followed by a digital low-pass filter can thus be functionally equivalent to high-resolution sampling at a lower rate. In fact, it can be better since there is no need for an analogue anti-aliasing filter, and the digital filter can be designed with just about any characteristics we desire.

 

This is the most concise summary of these realities I have ever read.  Really for the first time, I now understand why delta sigma DAC's are the norm in the market right now...thanks!!

[mansr]

5 minutes ago, crenca said:

This is the most concise summary of these realities I have ever read.  Really for the first time, I now understand why delta sigma DAC's are the norm in the market right now...thanks!!

I was talking about ADCs, but the same concepts apply in reverse too.

[crenca]

1 minute ago, mansr said:

I was talking about ADCs, but the same concepts apply in reverse too.

 

Ah shucks, I thought I was on to something...I will have to re-think now

[firedog]

9 minutes ago, crenca said:

 

This is the most concise summary of these realities I have ever read.  Really for the first time, I now understand why delta sigma DAC's are the norm in the market right now...thanks!!

The key is translating the word "efficient" to it's meaning in the actual DAC: cheap. 

[crenca]

15 minutes ago, firedog said:

The key is translating the word "efficient" to it's meaning in the actual DAC: cheap. 

 

Why do you say that?  You don't mean "cheap" as in "cheapness" do you?  Most modern manufacturing and industrial design is very radically "efficent", most certainly the digital revolution to have been what it is because of this single minded approach to efficiency has brought with it the ability for everyone in the first world, and a very large percentage of those in the 2nd and even 3rd worlds to possess computing power unheard of a couple of decades ago...

[adamdea]

5 hours ago, Spacehound said:

Sandyk,

I just picked your above post at random so I could 'reply' to you. Don't read anything into it.

Thought you might find this of interest:

One of 'our' latest computers. It may look like something out of Babbage's workshop but it isn't.  It  has a very strong potential to render all other computers as obsolete as the slide rule.  And 'we'  have already increased its power tenfold since September 2017.

 

 

 

Off topic, Mr Hound, but as a matter of interest do you think there is any chance it might  undermine blockchain as well? 

[pkane2001]

10 minutes ago, adamdea said:

Off topic, Mr Hound, but as a matter of interest do you think there is any chance it might  undermine blockchain as well? 

 

All encryption-based technology that relies on the difficulty of computation can become useless should quantum computing become a reality.

[adamdea]

1 minute ago, pkane2001 said:

 

All encryption-based technology that relies on the difficulty of computation can become useless should quantum computing become a reality.

Yes. agreed.  I'm not sure whether blockchain avoids this by having a distributed register. But I'm a bit hazy

[Summit]

2 hours ago, mansr said:

The sampling theorem assumes infinite sample precision. With a limited number of bits, we get quantisation error which is a non-linear distortion. This happens at any sample rate and has nothing to do with aliasing. With TPDF dither, the quantisation error is (mostly) turned into white noise at a level determined by the bit depth. If the sample rate is increased, the quantisation energy is spread over a wider frequency range, thus reducing the level of dither noise at any specific frequency. Doubling the sample rate gives the same improvement as extending the sample precision by one bit. In other words, not very efficient. A high sample rate does, however, bring another benefit in that it enables the use of noise shaping. Instead of the quantisation noise being spread evenly over the full spectrum, it can be concentrated at high frequencies where there is no signal of interest. This is very useful since a high-rate flash ADC with a small number of bits, say 8 or less, is much easier to construct than a slower ADC with high precision. Low-resolution noise-shaped sampling at a high rate, 10 MHz or more, followed by a digital low-pass filter can thus be functionally equivalent to high-resolution sampling at a lower rate. In fact, it can be better since there is no need for an analogue anti-aliasing filter, and the digital filter can be designed with just about any characteristics we desire.

 

“The sampling theorem assumes infinite sample precision”  Yes and that’s the problem with theorem.

 

I agree on dither and noise shaping.

[Summit]

1 hour ago, firedog said:

DSD doesn't really have much relevance to the question here. First,  whether it sounds better than PCM or not is a matter of taste and not some kind of "fact" due to its' level of resolution. Just like there are people who prefer it, there are people who don't. And a nice article can be written on why it is inferior technically to PCM.

 

But none of that matters - just listen to what you like. 

 

Second, any issue you think there is with sampling rate at PCM also applies with DSD. Both are sampling. The same ideas that push for recording PCM in 4X and 8X rates push for DSD recording in 2X, and 4X rates. I'm fine with the sound of DSD, but it has its' own issues, just like PCM has some of its own. 

 

And just as an aside, we live in a digital world - I  don't want the sound as close as possible to the sound of "master tapes" - I want the master digital file, which is what about 99% of masters are nowadays.

 

DSD does have very much relevance to the question here, which is sample rate. DSD have a much higher sample rate than PCM. My point is that Nyquist-Shannon Sampling Theorem is not presenting all important factors. It’s much more premises that comes in to play if we are looking to reproduce the sound as close as possible in SQ to the master tapes. I don’t fancy DSD, but that is not the question here.

 

“The assertion made by the Nyquist-Shannon sampling theorem is simple: if you have a signal that is perfectly band limited to a bandwidth of f0 then you can collect all the information there is in that signal by sampling it at discrete times, as long as your sample rate is greater than 2f0 . As theorems go this statement is delightfully short. Unfortunately, while the theorem is simple to state it can be very misleading when one tries to apply it in practice.”

 

“It is a common misconception that the Nyquist-Shannon sampling theorem could be used to provide a simple, straight forward way to determine the correct minimum sample rate for a system. While the theorem does establish some bounds, it does not give easy answers. So before you decide the sampling rate for your system, you have to have a good understanding of the implications of the sampling, and of the information you really want to measure. The difficulty with the Nyquist-Shannon sampling theorem is that it is based on the notion that the signal to be sampled must be perfectly band limited. This property of the theorem is unfortunate because no real world signal is truly and perfectly band limited. In fact, if a signal were to be perfectly band limited—if it were to have absolutely no energy outside of some finite frequency band—then it must extend infinitely in time.”

 

“What this means is that no system that samples data from the real world can do so perfectly—unless you’re willing to wait an infinite amount of time for your results. If no system can sample data perfectly, however, why do we bother with sampled time systems? The answer, of course, is that while you can never be perfect, with a bit of work you can design sampled time systems that are good enough. Often, in fact, the advantages one gains by processing signals in sampled time far outweigh the disadvantages of sampling, making many sampled time systems superior to their continuous-time equivalents. To understand how to make a sampled time system that’s good enough we must understand what happens when a signal is sampled into the discrete-time domain, what happens when it is reconstructed in the continuous-time domain, and how these processes affect the quality of the signal.”

 

http://www.wescottdesign.com/articles/Sampling/sampling.pdf

[beerandmusic]

EXCERPT

Though you can't make a direct comparison between the resolution of DSD and PCM, various experts have tried. One estimate is that a 1-bit 2.8224MHz DSD64 SACD has similar resolution to a 20-bit 96kHz PCM. Another estimate is that a 1-bit 2.8224MHz DSD64 SACD is equal to 20-bit 141.12kHz PCM or 24-bit 117.6kHz PCM.

In other words a DSD64 SACD has higher resolution than a 16-bit 44.1kHz Red Book CD, roughly the same resolution as 24-bit 96kHz PCM recording, and not as much resolution as a 24-bit 192kHz PCM recording.

Both DSD and PCM are "quantized," meaning numeric values are set to approximate the analog signal. Both DSD and PCM have quantization errors. Both DSD and PCM have linearity errors. Both DSD and PCM have quantization noise that requires filtering. In other words, neither one is perfect.

PCM encodes the amplitude of the analog signal sampled at uniform intervals (sort of like graph paper), and each sample is quantized to the nearest value within a range of digital steps. The range of steps is based on the bit depth of the recording. A 16-bit recording has 65,536 steps, a 20-bit recording has 1,048,576 steps, and a 24-bit recording has 16,777,216 steps.

The more bits and/or the higher the sampling rate, the higher the resolution. That translates to a 20-bit 96kHz recording having roughly 33 times the resolution of a 16-bit 44.1kHz recording. No small difference.

[mansr]

28 minutes ago, Summit said:

“The sampling theorem assumes infinite sample precision”  Yes and that’s the problem with theorem.

There is no problem with the sampling theorem. Quantisation is a separate problem with its own theorems.

[mansr]

8 minutes ago, beerandmusic said:

The more bits and/or the higher the sampling rate, the higher the resolution. That translates to a 20-bit 96kHz recording having roughly 33 times the resolution of a 16-bit 44.1kHz recording. No small difference.

That's a nonsensical comparison.

[Spacehound]

59 minutes ago, adamdea said:

 keydsOff topic, Mr Hound, but as a matter of interest do you think there is any chance it might  undermine blockchain as well? 

It could make 'bitcoin'  type mining extremely quick. My blockchain knowledge is almost non existent, but we have made totally unbreakable quantum encryption key  distributors  for some years but they are not a big seller.

The  prototype computers, which hopefully will soon be expanded sufficiently to be 'all purpose',  are already more than a million times faster (as far  we can measure)  at what they are good at  than the world's biggest supercomputers but AFAIK they won't crack quantum encrypted keys - the keyholders know something has had a try.  But the boxes above only distribute keys,  they are not involved in the encryption method itself.

[Spacehound]

39 minutes ago, pkane2001 said:

 

All encryption-based technology that relies on the difficulty of computation can become useless should quantum computing become a reality.

Yes

[beerandmusic]

11 minutes ago, mansr said:

That's a nonsensical comparison.

Excerpt Cambridge Audio

 

There are some important details worth knowing when making a comparison between DSD and a FLAC file, for example. The first is that DSD is not magically better than its rivals. A ‘standard’ DSD file- often referred to as DSD64 is roughly equivalent to a sample rate of 24/88.2kHz. ‘Double DSD’ or DSD128 samples that single bit of information 5.6 million times a second to give you a signal equivalent to 24/176.2kHz. Again, this is a sample rate that can be reproduced by formats that are not DSD. Higher rates exist but they are very, very rare.

 

Against this, there are some more logical answers why many DSD recordings sound very good indeed. Studios that master music in DSD specialise in high quality recordings of extremely good musicians. Because of this, DSD material includes some sensational music and if you’re a fan of classical music in particular, you’ll find that some of the finest performances by orchestras and composers have been captured in DSD and thanks to the care and effort that went into them, they sound fantastic even before any of the benefits of the format come into play.

DSD isn’t currently a mainstream format and there’s a chance it won’t ever truly be something there’s a huge choice of music in. Despite this it does have some truly stunning recordings in exceptionally high quality and thanks to its inclusion on our network streaming products, it’s something you can enjoy as part of your wider listening.

[Summit]

13 minutes ago, mansr said:

There is no problem with the sampling theorem. Quantisation is a separate problem with its own theorems.

 

Yes it is. What’s stipulated in a theorem is not always working in real practice, because those theorem assume thing like perfectly band limited etc. If all that was needed was to follow Nyquist-Shannon sampling theorem, no filtering for example would be needed.

[Spacehound]

9 minutes ago, beerandmusic said:

Excerpt Cambridge Audio

 

There are some important details worth knowing when making a comparison between DSD and a FLAC file, for example. The first is that DSD is not magically better than its rivals. A ‘standard’ DSD file- often referred to as DSD64 is roughly equivalent to a sample rate of 24/88.2kHz. ‘Double DSD’ or DSD128 samples that single bit of information 5.6 million times a second to give you a signal equivalent to 24/176.2kHz. Again, this is a sample rate that can be reproduced by formats that are not DSD. Higher rates exist but they are very, very rare.

 

Against this, there are some more logical answers why many DSD recordings sound very good indeed. Studios that master music in DSD specialise in high quality recordings of extremely good musicians. Because of this, DSD material includes some sensational music and if you’re a fan of classical music in particular, you’ll find that some of the finest performances by orchestras and composers have been captured in DSD and thanks to the care and effort that went into them, they sound fantastic even before any of the benefits of the format come into play.

DSD isn’t currently a mainstream format and there’s a chance it won’t ever truly be something there’s a huge choice of music in. Despite this it does have some truly stunning recordings in exceptionally high quality and thanks to its inclusion on our network streaming products, it’s something you can enjoy as part of your wider listening.

What has any of that got to do with what he said?

[beerandmusic]

7 minutes ago, Summit said:

 

Yes it is. What’s stipulated in a theorem is not always working in real practice, because those theorem assume thing like perfectly band limited etc. If all that was needed was to follow Nyquist-Shannon sampling theorem, no filtering for example would be needed.

i agree, there is no problem with the theorem itself, where the problem is, is in the misappropriation of the theorem....

 

e.g. it's just semantics that mansr is challenging you on.

[beerandmusic]

13 minutes ago, Spacehound said:

What has any of that got to do with what he said?

absolutely nothing...i am just finding and posting excerpts that state why DSD can be superior to CD.

he can choose or ignore any excerpts i post....his argument isn't with me, but with the manufacturers.

 

here's another:

The sound quality difference between DSD and PCM is subtle, and primarily in the very low level information we hear as spaciousness cues.

[beerandmusic]

19 minutes ago, Spacehound said:

What has any of that got to do with what he said?

 

It also appears in wikipedia:

Because of the nature of sigma-delta converters, one cannot make a direct comparison between DSD and PCM. An approximation is possible, though, and would place DSD in some aspects comparable to a PCM format that has a bit depth of 20 bits and a sampling frequency of 96 kHz.^[25] PCM sampled at 24 bits provides a (theoretical) additional 24 dB of dynamic range.

 

So if mansr has an itssue with it, he should simply modify it in wikipedia.

 

I have done this on a few things where my edits became the accepted "wikipedia answer"....if mansr's disagrees with above statement, he should take the time to correct it, so the world isn't misinformed.

 

It's not easy to get your final input in wikipedia because you are challenging the world, not just CA. 

[pkane2001]

15 minutes ago, beerandmusic said:

I have done this on a few things where my edits became the accepted "wikipedia answer"....

 

Please tell me it wasn't the Nyquist-Shannon sampling theorem page!