Redbook 44.1 kHz standard: theoretically sufficient timbral resolution?

Al M. · Aug 25, 2015

Orb said:
Al,
please note the context and also requirements for relaxed anti-alias filtering; which comes back quite a bit to what we are talking about - just look to what Yuri recently said.

Yes, but relaxed anti-alias filtering is an issue of practical technical implementation, not of theoretical limits.

That is the constant confusion in these discussions, practical technical implementation vs. theoretical limits. As I noted in a previous post, I do not deny that hi-res may sound better in practice, but this is a different issue than considerations of theoretical limits to resolution. The technical limits of the CD sampling rate are right on the theoretical edge of what should still allow for transparency to the signal, and in hindsight should not have been, whereas hi-res has a lot of room top spare so that its practical implementation is easier (also with regard to dynamic range). Yet it is audiophile consensus that on top-level playback equipment CD still sounds better than hi-res on second-tier equipment, which in turn performs less well on CD than it does on hi-res. It's all about the quality of implementation.

Yet the debate here is not about the practical implementation of the CD format, and the considerable difficulties that this brings with it, but about its theoretical limits of resolution, especially when it comes to sampling rate (see thread title).

Yuri Korzunov · Aug 25, 2015

Al,

Practically design of 44 and 48 kHz digital filters is most hard. Worse only develop for 22 kHz sample rate. There no reserve, like 20...22/20...24 kHz

Design 48 kHz significantly simpler 44 kHz. Due 2 times less steepness.

However, for analog filters of DAC (these filters should be anyway) better more high sample rates for providing proper suppression.

Best regards,
Yuri

Groucho · Aug 25, 2015

Yuri Korzunov said:
"Sophisticated" is:
- more length (more steep, less oscillations in passband, more supress in stop band, ...), and/or
- complex inside ("know how" certain realization of filter for faster work or decreasing of ringing, as example), and
- using double precision (64-bit floating point), especially for big number of calculations: minimizing quantization errors, avoiding of overload.

Using personal computer's (Win and Mac here) CPU power and huge memory (comparing FPGA and microcontrollers), parallel processing give wide possibilities for algorithm realization.

Also "sophisticated" algorithms can be faster and easier debugged under PC. I.e. more often improved.

What I said earlier: it doesn't matter if it is "difficult", as long as it can be burned into a chip for $0.50 - and even if we want to take the mathematical precision to 512 bits and the stop band to -300 dB or whatever (but why?), it's just a question of scaling up the silicon - it isn't truly difficult at all, it just needs a bigger or denser chip. The reason for doing this would simply be because we can, and I predict that listening tests would be 'inconclusive', but I would have no objection to doing it per se because it would be an unequivocal improvement. The danger with audiophilia, however, is that by doing it, it makes it look as though it was necessary to do it. Audiophiles are left believing that their previous 64 bit/-200 dB sound is inferior and, frankly, scuzzy; they can never enjoy listening to it again. And so the merry-go-round continues. Wouldn't it be nice, occasionally, to simply draw a line and say "We're finished. We can literally buy a transparent source for $0.50 and need worry no further. And in a shiny box with deluxe phono sockets it costs $200."

Al M. · Aug 25, 2015

Yuri Korzunov said:
Al,

Practically design of 44 and 48 kHz digital filters is most hard. Worse only develop for 22 kHz sample rate. There no reserve, like 20...22/20...24 kHz

Design 48 kHz significantly simpler 44 kHz. Due 2 times less steepness.

However, for analog filters of DAC (these filters should be anyway) better more high sample rates for providing proper suppression.

Best regards,
Yuri

Yes, but didn't we establish that many DACs don't use a steep filter these days even for CD because of upsampling and filtering from there with a gentle slope?

And again, this is practical implementation, not theoretical limits, Nyquist or otherwise. And while 48 kHz may be easier to filter, it still uses Nyquist.

Orb · Aug 25, 2015

Groucho said:
What I said earlier: it doesn't matter if it is "difficult", as long as it can be burned into a chip for $0.50 - and even if we want to take the mathematical precision to 512 bits and the stop band to -300 dB or whatever (but why?), it's just a question of scaling up the silicon - it isn't truly difficult at all, it just needs a bigger or denser chip. The reason for doing this would simply be because we can, and I predict that listening tests would be 'inconclusive', but I would have no objection to doing it per se because it would be an unequivocal improvement. The danger with audiophilia, however, is that by doing it, it makes it look as though it was necessary to do it. Audiophiles are left believing that their previous 64 bit/-200 dB sound is inferior and, frankly, scuzzy; they can never enjoy listening to it again. And so the merry-go-round continues. Wouldn't it be nice, occasionally, to simply draw a line and say "We're finished. We can literally buy a transparent source for $0.50 and need worry no further. And in a shiny box with deluxe phono sockets it costs $200."

It cannot, in the past one of the big DAC manufacturers did a paper presenting the issues with limited resources from both a hardware and algorithm perspective, but some on various forums just dismissed this saying "it is marketing... it is a manufacturer pushing their own agenda...etc", but we are talking about a chipset manufacturer that provides DACs for much more than just hifi audio.
Why do you think there is a push for more powerful chipsets these days for designs that either integrate the functionality onto a single chip or split the functions between several?

The merry go round is that some keep providing extra information that then gets ignored and we are back to square one....every month, every week, every day it seems

And btw, how many chips do you think an audio manufacturer must buy; we are talking a serious amount in terms of volume,cash, and logistics (shipment-storage-manufacturing process/line-etc), with good designs implementing multiple DAC chips in a dual or quad channel/array - but this digresses from the OP.
The best engineering designs utilise multiple individual internal hardware components such as a DSP/FPGA, with dual/quad DAC array, with I/V stage - this is ignoring due to being outside discussion scope aspects such as dual crystal clocks for 44.1 and 48 (includes multiples of those).
For "perfect" digital that is not relying upon a PC derived technical solution such as Yuri offers (so all functionality is within the audio component) is more than $200, look at the price of the Audiolab M-DAC and that was done with cutting corners that they openly admit to for cost constraints; John Westlake has mentioned so himself.
He is a pretty respected engineer (identified a bug within the ESS Sabre DAC chip while developing the M-DAC - openly discussed it on another forum) with the filters co-designed with a design partner who is a mathematician, and this product is not perfect.
BTW I am not saying audio DACs must be over $10k to achieve exceptional results and sound, in fact prices have been reducing with some stunning engineered products around the $2k-$3k mark.
Cheers
Orb

Yuri Korzunov · Aug 25, 2015

Al M. said:
Yes, but didn't we establish that many DACs don't use a steep filter these days even for CD because of upsampling and filtering from there with a gentle slope?

And again, this is practical implementation, not theoretical limits, Nyquist or otherwise. And while 48 kHz may be easier to filter, it still uses Nyquist.

Al,

What inside any third party DAC (FPGA firmware, program for microcontroller and what settings of DAC-chip) I don't know. It is "black box" for me and you.

But I know what is digital filters and price of achievement of parameters. I measures or read results, achieved by algorithms of my colleagues (other conversion and player software).

Sometimes appear stuff disclosed some details of realization of hardware. Or results its measurements.

Hardware applications have same (to software) principles of processing algorithms. There are no magic.

Other hand, impossibly deny probability of existing hardware with parameters no worse of software realization.

At last we can builtin some power PC to DAC.

But why?

In my opinion, simpler way is non-oversampling DAC or DAC with non-oversampling mode. All price invest to analog filter.

For DAC that can't pass by builtin oversampling, computer software can only filter ultrasound, that some help avoid extra sound energy, that lead to distortions in audible range (ultrasound shifting).

We can't violate Nyquist due need eliminate mirror of frequency range [0 ... sample rate/2].

Otherwise, we risk get shifted [sample rate/2 ... sample rate] to [0 ... sample rate/2] range due non-linear distortions.

Less slope (comparing digital) analog filter no good work upper [sample rate/2].

More sample rate - more analog filter suppression under [sample rate/2] due suppression growth with frequency.

I.e. digital filter must maximally clean spectrum from 20 kHz to [sample rate/2]. And [sample rate/2] must be most far as possibly from 20 kHz.

Best regards,
Yuri

Al M. · Aug 26, 2015

Al M. said:
Yes, but didn't we establish that many DACs don't use a steep filter these days even for CD because of upsampling and filtering from there with a gentle slope?

Yuri Korzunov said:
Al,

What inside any third party DAC (FPGA firmware, program for microcontroller and what settings of DAC-chip) I don't know. It is "black box" for me and you.

Yuri,

my comment was based on our previous exchange:

Al M. said:
If that's the only problem, it's easy. Upsample the CD signal to high-res sample rates and use the same shallow filter from there as for hi-res. That's what my Berkeley DAC does, upsampling the CD signal to 4 x 44.1 kHz = 176.4 kHz and filtering from there with a gentle slope.

Yuri Korzunov said:
Almost all DAC do oversampling and digital filtering before feeding of analog filter.

I may have misunderstood you here. In any case, I know at least that upsampling and filtering from there is what the Berkeley DAC does, because Berkeley Audio states as such.

Yuri Korzunov · Aug 26, 2015

Al,

May be lost of translation. English is not my native language

Upsampling algoritms is equal for most used: multiply frequency / filter / divide frequency.

Multiply and divide same for all.

Difference in filter stage.

Groucho · Aug 26, 2015

Orb said:
It cannot, in the past one of the big DAC manufacturers did a paper presenting the issues with limited resources from both a hardware and algorithm perspective, but some on various forums just dismissed this saying "it is marketing... it is a manufacturer pushing their own agenda...etc", but we are talking about a chipset manufacturer that provides DACs for much more than just hifi audio.
Why do you think there is a push for more powerful chipsets these days for designs that either integrate the functionality onto a single chip or split the functions between several?

The merry go round is that some keep providing extra information that then gets ignored and we are back to square one....every month, every week, every day it seems
And btw, how many chips do you think an audio manufacturer must buy; we are talking a serious amount in terms of volume,cash, and logistics (shipment-storage-manufacturing process/line-etc), with good designs implementing multiple DAC chips in a dual or quad channel/array - but this digresses from the OP.
The best engineering designs utilise multiple individual internal hardware components such as a DSP/FPGA, with dual/quad DAC array, with I/V stage - this is ignoring due to being outside discussion scope aspects such as dual crystal clocks for 44.1 and 48 (includes multiples of those).
For "perfect" digital that is not relying upon a PC derived technical solution such as Yuri offers (so all functionality is within the audio component) is more than $200, look at the price of the Audiolab M-DAC and that was done with cutting corners that they openly admit to for cost constraints; John Westlake has mentioned so himself.
He is a pretty respected engineer (identified a bug within the ESS Sabre DAC chip while developing the M-DAC - openly discussed it on another forum) with the filters co-designed with a design partner who is a mathematician, and this product is not perfect.
BTW I am not saying audio DACs must be over $10k to achieve exceptional results and sound, in fact prices have been reducing with some stunning engineered products around the $2k-$3k mark.
Cheers
Orb

My own active crossover DSP software is based on very large FIR filters and uses a small proportion of the capabilities of an old Intel CPU. It uses 32 bit floating point arithmetic in a terribly inefficient way (I am now tempted to change it to 64 bit to see how much CPU it takes!). Thirty years ago it would have taken quite a few PCs running in parallel to run it in real time. It could now run quite easily on a phone or tablet PC. Optimised and 'burned' as a chip it would be a trivial, low power IC. If I wanted to use 128 bit floating point it would simply be a case of scaling it up - it would be easy to parallelise the problem. (Not saying it wouldn't be a terrific amount of work, but the solution would be 'obvious' if onerous). Worst case, I might have to put several phones in a box!

The filtering in a DAC may, or may not, be more complex, and require higher sample rates and so on, but it isn't rocket science - as the saying goes. It is merely the implementation of basic mathematics to an arbitrary precision and is very amenable to parallelisation. The real rocket science was the creation of the mathematics that underpins sampled digital audio in the first place (or used to...). Sure, a single chip solution would be nicest of all, but if we are prepared to spend literally tens of thousands of dollars on a DAC, then who cares if an interim solution to the uber-DAC involves a few FPGAs or even a few circuit boards?

But why would we want to build such a beast? It is all based on the never-ending scales of precision that are possible in the purely abstract world of numbers. The physical world limits the precision of the converter itself to 22 bits or whatever, but in the mathematical world there are no limits, and once 32 bits of mathematical precision is a done deal, our imaginations run riot imagining the sonic delights that await if we could just get to 64 bits. Or if our windowed FIR filter could only be extended from 2048 to 4096 taps. And so on.

Yuri Korzunov · Aug 26, 2015

Groucho said:
The filtering in a DAC may, or may not, be more complex, and require higher sample rates and so on, but it isn't rocket science - as the saying goes.

Groucho,

FIR anywhere FIR

In each application need use available possibilities either for improving quality or speed or other without significant losses.

Al M. · Aug 27, 2015

Yuri Korzunov said:
For DAC that can't pass by builtin oversampling, computer software can only filter ultrasound, that some help avoid extra sound energy, that lead to distortions in audible range (ultrasound shifting).

Yuri,

Yes, this is interesting. On your website,

http://samplerateconverter.com

you explain (also with nice figures) under the heading "What is optimization audio?" that, with a non-optimized audio file, part of the ultrasound is shifted to the audible range due to non-linear distortions of the analog part of the playback apparatus:

While no proof what we listen upper 17 ... 20 kHz. I.e. we don't listen ultrasound.

In ideal case analog part of apparatus (DAC, amplifier) have no non-linear distortions. And music and ultrasound pass to ears as into played back audio file.

For real apparatus we have non-zero non-linear distortions. It lead to infiltration/shifting ultrasound content to audible frequency range.

It made ultrasound audible but distorted. This phenomenon called intermodulation distortions.

Of course, audible signal distorted too.

In optimized mode AuI ConverteR 48x44 remove inaudible (ultrasound) content.

It fix audibility of distorted ultrasound.

Necessity of Optimized mode applying depend on used software, hardware and audio file content.

***

This is also what Chris Montgomery appears to say, that ultrasonic content is actually harmful because with a lot of audio equipment it leads to intermodulation distortion products in the audio band (see my opening post on this thread and the link to his article there). Yet Amir posted a rebuttal in post #11. What would be your response to that?

Yuri Korzunov · Aug 27, 2015

It is not new minds. At old my site version I reffered to one article (can't fast find link now) that described ultrasound trouble.

Also there was placed links to ultrasound files for testing the apparatus.

These files contains simultaneous 30 and 33 kHz sines. It's intermodulation give 3 kHz (=33-30) product, that can be listened.

Sometimes need increase volume for listening of intermodulation products.

Also sometime need run sweep sine 0 ... ultrasound. As example, sample rate 96 kHz, sweep 0 ... 48 kHz.

Trouble also appear due no proper filtration of aliases during playback (reason can be from player software to DAC).

It simply checked via sweep sine.

We can listen: Tone increased > silence (sometimes) > tone decreased > increased > decreased > ....

If apparatus work properly tone increased only and sound finally disappear after 16...20 kHz.

Volume of intermodulations can be different for different systems: from listened clearly to very-very quiet, or inaudible for any volume.

Here system: audio file - audio player software - driver operation system - DAC - amplifier - speakers.

In audio file we can cut all over 20 kHz.

Audio player, driver, DAC can give non-proper resampling that come to audible range.

From audio player to speakers can appear non-linear distortions that come to audible range.

Now I write article that have detailed description of optimization audio. There will many figures, that, I hope, add more clarity than description in words

Some time ago I added non-optimized mode of resampling. It is traditional mode like rest resamplers.

Personally, I consider optimized mode as more "right".

WARNING: Need be careful with listening of ultrasound. We can't listen it, but ultrasound can damage our ears.

amirm · Aug 27, 2015

Yuri Korzunov said:
These files contains simultaneous 30 and 33 kHz sines. It's intermodulation give 3 kHz (=33-30) product, that can be listened.

As you know, there is no piece of music that all it has are ultrasonics at those frequencies.

Sometimes need increase volume for listening of intermodulation products.

No doubt if you make the ultrasonics those high tones, and then turn up the volume, at some point you will hear the modulation. The issue I raised in my post is that this is not a realistic test case. Ultrasound content in real music is at far, far lower volume than the music. This means the intermodulation will be lower volume yet.

That said, what you are doing with giving an option to remove ultrasonics is just right and the point I made. Which is, I like to get the high resolution master. Should I by chance have these issues, I can remove the ultrasonics at my choosing, rather than having that signal processing done by someone else.

Yuri Korzunov · Aug 27, 2015

High-res records have musical stuff, as example, 22 and 24 kHz, or 21.9 and 22.6 kHz.

Here need consider difference between frequencies and its multiply values.

I.e. we have intermodulation products:

1. 2 kHz = 24-22

2. 4 kHz =24*2-22*2=48-44

3. 6 kHz =24*3-22*3=72-66

...

Or DXD contains DSD's "legacy" noise. For non-DXD-optimized software/apparatus can appear troubles.

Removing ultrasound should be made properly:

- minimal harm to audible range (flat passband, linear phase or minimal distorted phase [for minimal phase filter])

- deep (pro level about -170 ... -200 dB) supression of ultrasound and resampling aliases in stop band (simultaneously with ringing and filter length minimization),

- minimal transient band (simultaneously with ringing and filter length minimization).

Better choise is IIR filter for these purpoces.

However for music production need realtime and low latency (delay for processing).

It provide IIR filters with more phase and frequency (into passband) distortion than can provide to IIR.

Here need separate goals of:

1. Filtration (for remove harmful ultrasound)

2. High sample rates (for better aliases suppression with analog filter, that should be anyway for restoring analog from digital signal).

Digital pre-filtration can some reduce aliases energy too.

Orb · Aug 27, 2015

Groucho said:
My own active crossover DSP software is based on very large FIR filters and uses a small proportion of the capabilities of an old Intel CPU......

And how does that old intel CPU compare to what you said

Groucho said:
What I said earlier: it doesn't matter if it is "difficult", as long as it can be burned into a chip for $0.50

Even the very top current DAC chips from say ESSTech, AKM,etc still have constraints in terms of tap lengths, oversampling,algorithms implemented,etc.
This is why many separate the functions from those DAC chips, with an additional benefit improving on generic filters co-efficients/tap lengths.

Remember a CPU has a pretty solid processing/low level cache capability even for an older one, especially compared to DAC chips used for audio.
Cheers
Orb

Ron Resnick · Jul 29, 2023

amirm said:
What happens in a digital system at 44.1 Khz is that any harmonics greater than 22.05 Khz get chopped off completely. . . . The next harmonic is well above 22 KHz. In an analog system, there is more gradual roll off so the treatment is different. The latter may recreate more than a pure sinewave. But you ear chops off those extra harmonics just the same. So their preservation didn't do one any good since the ear is band limited.

But this completely neglects phase information above the range of human hearing. Air motion tweeters and super-tweeters that go up to 40kHz and higher are not there only to reproduce the harmonics of audio frequency information.

analogsa · Jul 30, 2023

Ron Resnick said:
tweeters and super-tweeters that go up to 40kHz and higher are not there only to reproduce the harmonics of audio frequency information.

There are no harmonics of recorded audio above 22.05kHz in redbook, just noise. Not sure if passing it through the amplification chain is a great idea, let alone torturing the tweeters.

audiopro92 · Dec 14, 2023

https://www.sciencedirect.com/science/article/abs/pii/S0378595505001838

Not our ears, bone conduction.
Spatial cues in music (live recordings in a large hall or outside at a concert) can best be listened to and enjoyed with high frquency range or hi-res amplifiers and source material. The "air" and sense of separation between instruments and even fine details in midrange frequencies can be rendered by extending the levels of 16 KHz to 18 KHz; and ultrasonics can also play a role in sonic presentation.

Al M. · Dec 14, 2023

audiopro92 said:
https://www.sciencedirect.com/science/article/abs/pii/S0378595505001838

Not our ears, bone conduction.
Spatial cues in music (live recordings in a large hall or outside at a concert) can best be listened to and enjoyed with high frquency range or hi-res amplifiers and source material. The "air" and sense of separation between instruments and even fine details in midrange frequencies can be rendered by extending the levels of 16 KHz to 18 KHz; and ultrasonics can also play a role in sonic presentation.

Unfortunately, the no-cost accessible text in the linked paper gives no technical details. Yet from others studies that I have read, bone conduction requires energization of the skull that far exceeds normal stimuli, including music through air. Thus, for hearing music under normal circumstances it appears pretty much irrelevant.

And by the way, "hi-res" recording or not, most microphones hardly have any extension beyond 20 kHz. That includes those of the much lauded "golden era" of recording, where rmicrophone roll-off often was significant even below 20 kHz.

audiopro92 · Dec 16, 2023

Al M. said:
Unfortunately, the no-cost accessible text in the linked paper gives no technical details. Yet from others studies that I have read, bone conduction requires energization of the skull that far exceeds normal stimuli, including music through air. Thus, for hearing music under normal circumstances it appears pretty much irrelevant.

And by the way, "hi-res" recording or not, most microphones hardly have any extension beyond 20 kHz. That includes those of the much lauded "golden era" of recording, where rmicrophone roll-off often was significant even below 20 kHz.

hearing - Can humans perceive sounds above 20 kHz? - Biology Stack Exchange
Recording the Unheard World of Ultrasound with a Commodity Microphone Let's Record Ultrasound (ericdraken.com)

The human auditory apparatus is incredibly sensitive to changes in dynamic range. For example, in an anechoic chamber, we can hear our own blood flowing and our own heartbeat as though these sounds were being amplified in real-time!

Harmonic generation circuits in source components, quantization effects of digital filters, and the influence of the amplifier on the signal (linear response) and/or how it rolls off / where it declines on the frequency spectrum can combine together to produce varying degrees of sonic presentation; each unique to one another. Make just one change and the sound accordingly becomes different.

When listening, are we using a brick-wall filter on a DAC or CD player that cuts off at 20 KHz rather than not; or does it gradually decline (roll off)?
Under the best lab conditions, humans can hear from 12 HZ to 28 KHz. Ultrasonic frequencies - Animal echolocation; ultrasonic frequencies are all around us. With all this taken into account, listening to music with headphones or near-field listening on speakers that support high frequency bandwidth would be an ideal way to experience the benefits of high-res audio. And on that token, we know not what equipment was used to make the recordings we listen to. Above all, we should remain curious.

- DMK

Redbook 44.1 kHz standard: theoretically sufficient timbral resolution?

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