Hi-Rez - Another Myth Exploded!

[gregorio]

We're not talking about the waveform here.  A digital reverb does not see a waveform nor a sound.  It does not see the samples as connected in any way, shape, or form.  It applies the process to each individual sample as its own entity.  All laws related to waveform capture and reproduction aren't really applicable in digital processing.

Digital processors that aren't very, very bad like the one demonstrated above use interpolation, but it is cheap and full of aliasing.  The only reverb I have ever seen that doesn't alias without resampling is 2C-Audio's Aether.  It's clean for the whole band and has zero aliasing, but processing time can be up to two hours for a 5 minute audio file.

I'm not sure I understand your question. You say that digital reverb only sees the samples, rather than the waveforms but then you show diagrams of how the reverb would see the waveform from the samples?

I agree of course that the reverb would only see the samples, now the actual digital signal processing mathematics itself I'm afraid is beyond my knowledge. Mention Fourier or Laplace transforms and my eyes glaze over! All I can tell you is that oversampling would be useful for a few digital processing tasks where the output of the process would result in frequencies above (or near to) the Nyquist Point, but algorithmic reverb is not (to my knowledge) one of them.

G

 

[PelPix]

Let me simplify it.  I misspoke:
If you feed a digital reverb three samples, it effectively sees a triangle wave, not a sine wave.  It connects the samples with straight lines.

 

[gregorio]

Yes please.  I also have a question about conflicting notions of 'bandwidth' relating to the transmission of digital signals between devices using various standards but I fear that might be too OT.

OK, but I need to keep this simple. We have our samples with their values (stored in the bits). These samples are not a direct copy of our original waveform but a representation. If we look at this data graphically, say in a DAW or some other audio software, when we zoom in we would see a series of blocks or "stairs" which resemble a wave form. If we increase the sample rate then these stairs become a little smoother a resemble the wave-form more accurately. This visual representation is a little misleading and causes quite a few people to assume that the higher sample rate is closer to the original and therefore better. We need to look at it a little differently. That staircase is not ultimately what will be output to our speakers, it is just a representation at this point in time. This representation contains all the information of the original waveform plus some unwanted information (the stair or stepped pattern). If only there was a way to get rid of this unwanted information (the error signal), because obviously "sample data" - "error signal" = "original waveform". The great thing is, it turns out that everything in this error signal is above the Nyquist Point. In other words, all a DAC has to do is to convert the sample values into voltages, apply a filter to remove everything above the Niquist Point and we have a perfectly linear reconstruction of our original waveform.

In it's simplest form this is all a DAC does. In practice though it's a little more complicated. We've got another filter here (named appropriately the reconstruction filter) and it suffers from the exactly the same problems as the filters mentioned in the OP. So DAC manufacturers have come up with a variety of schemes to get rid of the filter artefacts, oversampling, upsampling, doing some of the filtering in the digital domain, etc, etc. There is one other potential problem which DACs have to overcome, timing errors between the samples (jitter). Jitter is quite a big subject but essentially all DACs have jitter reduction circuitry. Any decent DAC should remove any jitter and pretty much eliminate the problem.

That's all I've got time for at the moment, no doubt there will be some more questions.

G

 

[gregorio]

Let me simplify it.  I misspoke:
If you feed a digital reverb three samples, it effectively sees a triangle wave, not a sine wave.  It connects the samples with straight lines.

Why on earth would it do that? As I said, I do not know the details of how individual reverbs do their DSP, what z-transforms or Fourier maths they employ but a fundamental tenet of the Nyquist-Shannon Theorem is that it's based only on sine waves (not square, triangle or sawtooth waves). All digital audio signal processing math is therefore also based on sine waves.

G

 

[anetode]

Quote:

Let me simplify it.  I misspoke:
If you feed a digital reverb three samples, it effectively sees a triangle wave, not a sine wave.  It connects the samples with straight lines.

Depends on the implementation. Remember that the math behind nyquist shannon allows you to calculate an infinite number of dots along the curve connecting each sample if you really want to, just that they are unnecessary to store the audible waveform. I'm not sure where this obsession with straight lines is coming from.

 

[PelPix]

Quote:

Depends on the implementation. Remember that the math behind nyquist shannon allows you to calculate an infinite number of dots along the curve connecting each sample if you really want to, just that they are unnecessary to store the audible waveform. I'm not sure where this obsession with straight lines is coming from.

I'm aware, it's just that everyone's implementation is terrible.  For some reason interpolating the points between is difficult for VST plugins because they have to be real-time.  I'm not sure of the actual mechanics.
 

 

[Anaxilus]

Quote:

OK, but I need to keep this simple.

Thanks, I'm sure some readers will appreciate the quick lesson in the basics.

apply a filter to remove everything above the Niquist Point and we have a perfectly linear reconstruction of our original waveform.
 

I guess I need to look deeper in the actual theorem then.  Hopefully it's not anything much more complicated than basic calculus.  Sounds like applying approximations using a sandwich theorem but probably something else entirely.  I'll try to have a deeper look at the theorem and make some sense of it.

In practice though it's a little more complicated. We've got another filter here (named appropriately the reconstruction filter) and it suffers from the exactly the same problems as the filters mentioned in the OP. So DAC manufacturers have come up with a variety of schemes to get rid of the filter artefacts, oversampling, upsampling, doing some of the filtering in the digital domain, etc, etc.

Seems I'm most interested in the details and specifics of what's happening here.  Sounds like where all the fun is happening.

There is one other potential problem which DACs have to overcome, timing errors between the samples (jitter). Jitter is quite a big subject but essentially all DACs have jitter reduction circuitry. Any decent DAC should remove any jitter and pretty much eliminate the problem.

Isn't this one instance where interpolation comes in?  At this point you are basically recreating what you think should be there, but the actual data is simply lost never to return yes?  Does the DAC actually remove or eliminate jitter or does it compensate for it?  Two very different things it seems.  Or are we talking Extrapolation here?
 That's all I've got time for at the moment, no doubt there will be some more questions.

^  

Edit - Upon further reading it seems everything we are discussing is premised upon interpolation as the single fundamental principal.  I see.  And the wheel under the Hamster goes round and round, round and round. 

  Hmmm.....
 
 

 

[PelPix]

Now, there's something of note anyone who studies waveforms and how they're sampled needs to understand:
"A higher sampling rate does not increase resolution, it increases bandwidth."
This is a contradictory statement.  We're talking about a line that is going up and down.  The more times it goes up and down within a certain period of time, the higher the frequency.
Resolution is bandwidth!
 
 
Common sense would say that higher sampling rate waveforms are better because you get the little tiny details in the waveform.  However, waveforms as a visual representation make no sense.  Even though everything about them tells your brainn that those details are shorter and quieter, the little tiny details you're seeing aren't shorter or quieter than the big ones, they're higher in pitch.

 

[gregorio]

Now, there's something of note anyone who studies waveforms and how they're sampled needs to understand:
"A higher sampling rate does not increase resolution, it increases bandwidth."
This is a contradictory statement.  We're talking about a line that is going up and down.  The more times it goes up and down within a certain period of time, the higher the frequency.
Resolution is bandwidth!
 
 
Common sense would say that higher sampling rate waveforms are better because you get the little tiny details in the waveform.  However, waveforms as a visual representation make no sense.  Even though everything about them tells your brainn that those details are shorter and quieter, the little tiny details you're seeing aren't shorter or quieter than the big ones, they're higher in pitch.

Resolution is the accuracy with which we measure the sample points, in other words, the bit depth. I'm not really sure I understand when you say the tiny little details are higher in pitch. Providing these higher pitched details are within the spectrum of human hearing they can be perfectly reproduced with a sample rate of 44.1kS/s. We could increase the sample rate to 88.2kS/s, so we can record audio frequencies up to 44kHz but there's no real point. Either we filter these >22kHz frequencies during recording or the ear filters them on playback, either way, they're gone.

Yes, I agree with you, common sense would indicate a higher sampling rate would give more detail. Unfortunately, common sense is wrong in this instance. Some of sampling theory is counter-intuitive. Going back to my analogy of measuring and storing a circle, common sense would indicate more points is more detail (and accuracy) but more than 3 points does not give more detail or accuracy because with 3 points we already have perfect reconstruction of the circle. In audio sampling >2 sampling points per wave provides perfect accuracy, you can't get better than perfect. So the only limiting factor is that any waveform we want to digitise must be lower than half the sample frequency. With a sampling rate of 44.1kS/s we can perfectly digitise signals up to an audio frequency of 22kHz. At this point the limiting factor is the human ear.

G

 

[gregorio]

Seems I'm most interested in the details and specifics of what's happening here. Sounds like where all the fun is happening.

In a sense, yes. This is where we run into the old electronic engineering trade-off problems: Accuracy verses speed verses cost. In that post I was just trying to lay out the basic fundamentals of how digital audio works. At the end of the day, all the specific details and the various manufacturer claims, need to be put into context of the fundamentals.

Edit - Upon further reading it seems everything we are discussing is premised upon interpolation as the single fundamental principal.  I see.  And the wheel under the Hamster goes round and round, round and round. 

  Hmmm.....

Mmmm, sort of. If you are talking about quantisation errors (the inherent inaccuracy of assigning an infinite number of potential values to a finite number of digital values), this problem is elegantly solved using dither. Dither yields a perfect result plus some noise (the digital noise floor), 16bit provides a digital noise floor about 1000 times lower than the noise floor of the most dynamic recording. Have a look at my other thread here for more detail.

G

 

[gregorio]

People probably buy hi-rez not because it is simply high-resolution, but most of the time it is mastered better than their 16bit cousins.

I'm sure this is true, on occasion. I also think placebo effect maybe in operation on many occasions. The main reasons why I started this thread is to demonstrate that there is no technical reason why a 16/44 recording should be mastered to any lesser quality than a hi-rez recording. If done properly a 16/44 recording should not be distinguishable from a 24/96 and if anything should in theory be of higher quality than a 24/192 recording. So, in the case of it not being placebo effect, why is a 24/192 recording sometimes mastered better than a 16/44 one? There's only one explanation, to re-enforce the notion that hi-rez is better than CD, so they can charge more for the hi-rez version.

As a consumer, I am angered by this whole marketing strategy. There is no reason why I should not expect the highest fidelity and mastering standards to be available at 16/44.

G

 

[judmarc]

Any self respecting, well educated audio professional would not use sample rates of 176.4kS/s or higher unless forced by clients.
 
 
Ah, then apparently Keith O. Johnson of Spectral Audio and Reference Recordings, both of which are held in a fair amount of awe by their audio manufacturing and studio recording peers, respectively, is neither self respecting nor sufficiently well educated in your opinion?
 
Your opinion, and discussions about it, are interesting to the extent they are well informed, but I am seeing a fair amount of myth mixed with information here.
 
There are at least two reasons for use of higher resolutions that have academic and engineering backing.
 
- There has been academic work done indicating that when material was recorded with substantial information above audibility, listeners in blind testing preferred playback that included the ultrasonic portion over playback with the ultrasonic portion removed.  I can give you a link to the paper if you're interested.  If 20-22kHz is no longer the upper limit of interest, the other numbers, including sample rate, must be adjusted accordingly.
 
- From an engineering standpoint, higher sample rates, or upsampling, allow you to apply the necessary filtering with less chance of audible artifacts.

 

[gregorio]

Ah, then apparently Keith O. Johnson of Spectral Audio and Reference Recordings, both of which are held in a fair amount of awe by their audio manufacturing and studio recording peers, respectively, is neither self respecting nor sufficiently well educated in your opinion?

I stand by what I said. There are only disadvantages to >176.4kS/s, no advantages. If they are using these sampling rates it is either because they are ill informed or because they are "cashing in" on the hi-rez bandwagon (IE. Not self respecting).

There are at least two reasons for use of higher resolutions that have academic and engineering backing.
- There has been academic work done indicating that when material was recorded with substantial information above audibility, listeners in blind testing preferred playback that included the ultrasonic portion over playback with the ultrasonic portion removed.  I can give you a link to the paper if you're interested.  If 20-22kHz is no longer the upper limit of interest, the other numbers, including sample rate, must be adjusted accordingly.
 
- From an engineering standpoint, higher sample rates, or upsampling, allow you to apply the necessary filtering with less chance of audible artifacts.

I would be interested in that paper but please don't quote the thoroughly discredited Oohashi paper again. If you are referring to the Oohashi paper you do realise that is was written by a doctor of agriculture (who makes and sells ultrasonic products) and that it was published in a neuroscience magazine under the heading of "Advertising"? If you had read my original post you would realise that there is no instrument energy above 88.2kHz and no way with standard studio microphones to record it even if there were!

Again, if you had read the original post you would have seen where I stated that there are potential advantages with regard to filter implementation with a sample rates of 88.2kS/s and 96kS/s. However, higher than this (176.4kS/s and above) there are in fact only disadvantages, from an "engineering standpoint".

Lastly, please inform me of what myths are in the information I've posted.

G

 

[anetode]

Quote:

 
Your opinion, and discussions about it, are interesting to the extent they are well informed, but I am seeing a fair amount of myth mixed with information here.

That's rather ironic.
 
The study you mention, and I know which one because it inevitably gets brought up in these discussions, has about as many holes in it as the study that purported to link vaccines to autism. A more-or-less neutral take on it is available @ http://en.wikipedia.org/wiki/Hypersonic_effect
 
The filtering you mentioned is thoroughly discussed in the first post of this thread. It is questionable whether sampling higher than 96khz brings any benefits because of filter limitations.
 
What's worth mentioning, however, is that just because someone uses a high (192khz) or ridiculous sample rate, doesn't mean that the product can't sound good, measurably and subjectively transparent to the human ear good.
 
And then there are the lesser used techniques, like trading bit depth for sampling rate in 2.8224 Mhz DSD sampling methods. There's even a Korg with a 5.6mhz ADC for double the DSD goodness! Note that this method is also not without controversy: http://en.wikipedia.org/wiki/Direct_Stream_Digital#DSD_vs._PCM
 
I think that given time there will be breakthroughs in signal processing that will allow the designers to cheat thermal limitations and allow for much closer to flawless audio recording at up to the hearing bandwidth limits of a whale. Luckily, us humans have much more modest demands.

 

[gregorio]

And then there are the lesser used techniques, like trading bit depth for sampling rate in 2.8224 Mhz DSD sampling methods. There's even a Korg with a 5.6mhz ADC for double the DSD goodness! Note that this method is also not without controversy: http://en.wikipedia.org/wiki/Direct_Stream_Digital#DSD_vs._PCM
 
I think that given time there will be breakthroughs in signal processing that will allow the designers to cheat thermal limitations and allow for much closer to flawless audio recording at up to the hearing bandwidth limits of a whale. Luckily, us humans have much more modest demands.

In modern professional ADCs, oversampling by 256 or 512 times (11mS/s or 22mS/s approx) is virtually ubiquitous. I talked a little about it earlier in the thread (here).

From my understanding, there will not be any break throughs in signal processing when it comes to maintaining accuracy at very high sample rates. To do so would require a re-write of the laws of physics. Dan Lavry explained it very well in his white paper (linked to on the first post) and it's still just as true today as when it was written 7 years ago.

G