Purifi Class D

16 hours ago, Jud said:

 

You are certainly free to disagree, but that's just mathematically incorrect. It's like disagreeing that 2+2=4, though on a more complex level.

 

What the article is talking about is not a new or unique problem, but rather an issue that's been a popular topic in digital audio circles for decades: How best to reproduce the "inharmonic"/transient portions of sounds. "Inharmonics" are somewhat misleadingly named, because they are in fact made up of harmonics, but odd order ones, often higher odd order ones.  That's just a fancy way of saying that along with whatever the fundamental frequency is, the sound includes 7x, 9x, 11x, even 13x that fundamental frequency. But these odd order harmonic frequencies themselves are each sine waves.  It's just that when they all come together and interfere with each other they don't look very sine wave-ish.  These "inharmonics" dominate percussion sounds, and form the initial attack portions of the sounds of other instruments, like the pluck of a string, the hammers hitting piano strings, consonant sounds in vocals, etc. If the inharmonics are brief enough, like a string pluck, we call them transients. But everything is built up from sine waves.

Agreed. 

But back to your social point about science getting lost in PR.  Even if we accept the article's statement that a "sufficient" number of sine waves is all that is needed, this tells us nothing about its usefulness wrt current technology.  If we had a sufficient number of monkeys with typewriters, we could recreate Shakespeare.

1 hour ago, Jud said:

Must get to the bottom of this Bielefeld business… 😉

Shortcut:

https://en.wikipedia.org/wiki/Bielefeld_conspiracy?wprov=sfla1

28 minutes ago, PeterG said:

Even if we accept the article's statement that a "sufficient" number of sine waves is all that is needed, this tells us nothing about its usefulness wrt current technology.

It’s a very interesting question, one that I’ve tried fitfully and not terribly successfully to research.

Starting with the math, if we say we can hear somewhere between 14-16kHz, the 13th harmonic winds up in the 180-210kHz region. So is 24/192 hi res automatically inadequate?

There are a few countervailing factors at work in thinking about this. One is that although you can mathematically decompose a sound to various harmonics interfering, shouldn’t it be adequate to just reproduce the sound itself, IOW, 14-16kHz at the top end? I don’t know the answer.

It seems as if it ought to be enough to reproduce the “audible range.” But: Have you ever listened to Shokz, or other headphones that work by bone conduction? I was surprised at the sound when I tried them. Bone conduction can transmit sounds ordinarily considered to be ultrasonic. See for example https://www.sciencedirect.com/science/article/abs/pii/S0378595505001838 . On the other hand, higher order harmonics are mostly at rather low amplitudes, so how much are we really missing?

Finally, there’s the question of how we perceive transients versus tones. I’ve read a couple of brief references to the fact that different areas of the brain are involved in processing transients vs. tones, but haven’t taken the time to find out as much as I’d like to know about that.

2 hours ago, Jud said:

It’s a very interesting question, one that I’ve tried fitfully and not terribly successfully to research.

 

Starting with the math, if we say we can hear somewhere between 14-16kHz, the 13th harmonic winds up in the 180-210kHz region. So is 24/192 hi res automatically inadequate?

 

There are a few countervailing factors at work in thinking about this. One is that although you can mathematically decompose a sound to various harmonics interfering, shouldn’t it be adequate to just reproduce the sound itself, IOW, 14-16kHz at the top end? I don’t know the answer.

 

It seems as if it ought to be enough to reproduce the “audible range.” But: Have you ever listened to Shokz, or other headphones that work by bone conduction? I was surprised at the sound when I tried them. Bone conduction can transmit sounds ordinarily considered to be ultrasonic. See for example https://www.sciencedirect.com/science/article/abs/pii/S0378595505001838 . On the other hand, higher order harmonics are mostly at rather low amplitudes, so how much are we really missing?

 

Finally, there’s the question of how we perceive transients versus tones. I’ve read a couple of brief references to the fact that different areas of the brain are involved in processing transients vs. tones, but haven’t taken the time to find out as much as I’d like to know about that.

I have not listened to Shokz, but this is an interesting idea.  I think one reason that some people prefer vinyl is that they are feeling certain sounds that are not on a CD and may not be audible

20 minutes ago, PeterG said:

I think one reason that some people prefer vinyl is that they are feeling certain sounds that are not on a CD and may not be audible

The RIAA curve ends at 20kHz, so except for special projects, if you’re hearing ultrasonics from an LP that’s almost certainly distortion.

On 7/15/2023 at 6:06 PM, Jud said:

If read carefully, the article doesn’t actually say Fourier analysis is insufficient

It is good to remember though that human hearing can beat Fourier time-frequency analysis though. All the information persists through the transform though, but just goes through "unnoticed".

5 hours ago, PeterG said:

 

I have not listened to Shokz, but this is an interesting idea.  I think one reason that some people prefer vinyl is that they are feeling certain sounds that are not on a CD and may not be audible

The "certain sounds" are on the CD - but the playback chain may be letting the side down ... the generic distortion of digital playback ever since it was first available for consumers has been the sense that there is a lacking of life and transient energy in what they hear; but this is an artifact of sub-par electrical performance. Get it right, and all doubts are removed - it has nothing to do with formats, and whether the right encoding is used; and everything to do with how meticulously the design and implementation of the replay chain has been thought through ...

3 hours ago, Miska said:

 

It is good to remember though that human hearing can beat Fourier time-frequency analysis though. All the information persists through the transform though, but just goes through "unnoticed".

 

Human hearing doesn’t have Fourier “conjugate variables,” which vary inversely. So for example optimizing time-based factors creates less optimization of frequency-based factors. This means there is a limit to how much both conjugate variables can be optimized at once. Human hearing beats this limit.

This is a separate issue from the proof that sounds can be analyzed as composed of constituent sines.

8 hours ago, Miska said:

It is good to remember though that human hearing can beat Fourier time-frequency analysis though. All the information persists through the transform though, but just goes through "unnoticed".

Sorry, but what you just wrote does not make sense at all. Literally. If *all* information passes through the transform, how can human hearing beat it? And isn’t it the purpose of the transform of just changing the domain of the representation of the data and not alter it? What does it “notice” this information mean in this context?

4 hours ago, Jud said:

Human hearing doesn’t have Fourier “conjugate variables,” which vary inversely. So for example optimizing time-based factors creates less optimization of frequency-based factors. This means there is a limit to how much both conjugate variables can be optimized at once. Human hearing beats this limit.

 

This is a separate issue from the proof that sounds can be analyzed as composed of constituent sines.

Also, some people seem to think that the Fourier transform is fundamental to how sound is represented. This is wrong, it is perfectly possible to have a chain from audio recording to reproduction that does not perform any FT or FFT, except for the purpose of analysing the content. There are formats based on the FFT but they are optional. And, on top of it, the lossless ones also carry the difference between the signal and the deconvoluted version; so this is not an issue anyway.

3 hours ago, mocenigo said:

Sorry, but what you just wrote does not make sense at all. Literally. If *all* information passes through the transform, how can human hearing beat it? And isn’t it the purpose of the transform of just changing the domain of the representation of the data and not alter it? What does it “notice” this information mean in this context?

Well, @Jud already answered to that. But when you increase frequency resolution by making the transform longer, you lose on the time resolution because the transform covers longer section of the time. And vice versa. Since human hearing is not based on Fourier transform, it is not limited in this way either, it can detect frequency and timing independently.

The information is there, in the data, but it gets statistically distributed such way that it doesn't appear, but gets "lost in the noise".

Just like in statistics, there is lot of information there, but whether some information appears in the statistical analysis is another matter.

3 hours ago, mocenigo said:

Also, some people seem to think that the Fourier transform is fundamental to how sound is represented. This is wrong, it is perfectly possible to have a chain from audio recording to reproduction that does not perform any FT or FFT, except for the purpose of analysing the content. There are formats based on the FFT but they are optional. And, on top of it, the lossless ones also carry the difference between the signal and the deconvoluted version; so this is not an issue anyway.

But you can add the transform to the data path and it wouldn't alter the data at all. You wouldn't be able to tell whether it is there or not.

8 hours ago, mocenigo said:

it is perfectly possible to have a chain from audio recording to reproduction that does not perform any FT or FFT, except for the purpose of analysing the content. There are formats based on the FFT but they are optional.

However, the mathematics of the digital filtering that is ubiquitous in both DACs and Class D amps is almost always Fourier-based.

This is essentially the reason for upsampling: It makes it easier to design a filter that balances the Fourier “conjugate variables” of time-based and frequency-based factors.

50 minutes ago, Jud said:

However, the mathematics of the digital filtering that is ubiquitous in both DACs and Class D amps is almost always Fourier-based.

This is essentially the reason for upsampling: It makes it easier to design a filter that balances the Fourier “conjugate variables” of time-based and frequency-based factors.

The reason for upsampling is to push images of the signal as far as possible out of the audible band, to eliminate intermodulation artifacts.

3 hours ago, mocenigo said:

The reason for upsampling is to push images of the signal as far as possible out of the audible band, to eliminate intermodulation artifacts.

 

…which allows for better filtering to be designed more easily. We’re saying the same thing.

After all, if near perfect filtering were easy to do at 44.1kHz, no designer would have to bother with upsampling.

3 hours ago, Jud said:

…which allows for better filtering to be designed more easily. We’re saying the same thing.

 

After all, if near perfect filtering were easy to do at 44.1kHz, no designer would have to bother with upsampling.

Are you talking of filtering in the analog domain?

Because if you do not, then you should be remembered that upsampling is *part* of the filtering process. Upsampling is not there to *facilitate* it.

8 hours ago, Jud said:

However, the mathematics of the digital filtering that is ubiquitous in both DACs and Class D amps is almost always Fourier-based.

It assumes that, but normally no Fourier transform is computed (I am not talking about room correction, EQ etc)

10 minutes ago, mocenigo said:

 

Are you talking of filtering in the analog domain?

Because if you do not, then you should be remembered that upsampling is *part* of the filtering process. Upsampling is not there to *facilitate* it.

Digital filtering, not the final analog reconstruction filter. (The vast majority of DAC chips use sigma-delta modulation to enable a simpler, less expensive final analog reconstruction filter.)

Saying upsampling is part of the digital filtering process or that upsampling facilitates a better digital filtering process is for me a distinction without a difference.

4 minutes ago, mocenigo said:

 

It assumes that, but normally no Fourier transform is computed (I am not talking about room correction, EQ etc)

I'm simply saying filter design is almost always based on Fourier analysis (rather than some other sort of analysis, like wavelets), and therefore is subject to the problem that time-based and frequency-based optimizations are opposed. (At a practical level, the more quickly a filter cuts to eliminate frequency-based distortion like imaging and aliasing, the more it is subject to the Gibbs effect, which creates ringing - time-based distortion.)

1 minute ago, Jud said:

Digital filtering, not the final analog reconstruction filter. (The vast majority of DAC chips use sigma-delta modulation to enable a simpler, less expensive final analog reconstruction filter.

Wow, I do not know where to start to unravel your confusion. So, digital filtering without upsampling will not remove the conversion artifacts, i.e. the images. They are a product of the conversion and they depend on the sampling rate. No processing of the signal will reduce them.  I feared you were talking of digital filters, but I hoped you would not.

The sigma-delta modulation is not to enable a "simpler, less expensive final analog reconstruction filter", it is a conversion process and in fact it requires a more significant investment analog reconstruction filter. What it does is that it makes the DAC cheaper and at the same time more precise (except the very first iterations which had problems such as potentially unbound settling times and the like).

1 minute ago, Jud said:

Saying upsampling is part of the digital filtering process or that upsampling facilitates a better digital filtering process is for me a distinction without a difference.

In fact there is a very profound difference.

2 minutes ago, mocenigo said:

Wow, I do not know where to start to unravel your confusion. So, digital filtering without upsampling will not remove the conversion artifacts, i.e. the images.

The  first CD players used "brickwall" digital filters without upsampling. It was only a little while later that they began to employ first 4x then 8x upsampling.

Just now, Jud said:

I'm simply saying filter design is almost always based on Fourier analysis (rather than some other sort of analysis, like wavelets), and therefore is subject to the problem that time-based and frequency-based optimizations are opposed. (At a practical level, the more quickly a filter cuts to eliminate frequency-based distortion like imaging and aliasing, the more it is subject to the Gibbs effect, which creates ringing - time-based distortion.)

True. But the effect of ringing is overstated, in fact it is essentially absent from "true musical signal," or inaudible, as long as the source does not clip and is properly bandwidth limited. In fact, I never heard of a single study proving it is audible if these conditions are met.