It seems that the idea to record, store and process audio at very high sample-rates has become fashionable. More precisely, sample-rates far beyond those suggested by the Kotelnikov/Nyquist/Shannon theorem. Over the last weeks, I ran into several debates and disputes related to the matter and thought it would be wise to highlight several of my concerns toward this trend in proper, unconvoluted form. With this in mind, let's restrict the discussion to a pure processing context.

This both includes high rate formats such as 192kHz PCM and "DXD" (i.e. 384kHz PCM) having the aim to preserve the original recording, as well the concept of manual, "DIY" resampling for processing purposes.

The central question here is:
Is it really beneficial to process at higher rates, and if yes, how much higher? ..and when does it stop?


Some better known facts:

• It is no secret that the concept of oversampling can prevent or at least reduce the amount of aliasing generated by nonlinear-processes.
• Similar to the above, it is a fact that most AD/DA converters tend to sound better at higher rates, mainly because higher rates allow them to use less aggressive filtering.

These two arguments are perfectly reasonable. With this in mind, the most intuitive reaction is a generalization close to "The more, the better". The experiment I am about to describe can be seen as a counter-weight to these points. Here's the idea, let's imagine two guys recording the following analogue signal:



It consists of two sine waves, one at 10kHz, the other at 24kHz. So far so good, high sample-rate AD's can handle the task. The "high-end" guy captures a truly high fidelity replicate of the original.

Alternatively, a "lofi" guy refuses to use any rate higher than 44.1kHz and records this:



As we can easily see, the samplerate of 44.1kHz fails at capturing the 24kHz sine wave. However, the overwhelming majority of tests and papers being published on the subject clearly show that the human hearing system is not able to detect a 24kHz sine wave (in a linear environment. More about this below). As such, it is safe to expect that the difference between both is inaudible.

Ok, both guys now decide to "master" their great recordings with a limiter at the end of the chain. This limiter is a relatively aggressive nonlinear device, so it will potentially introduce both harmonic distortion, and it's vicious brother, inter-modulation-distortion.

The "lofi" guy does just this, and ends up with the following:



Fine, we see some odd ordered harmonics appearing in the signal.

The high end guy giggles and fires up his high rate processing-chain and ends up with this:



Not good. We see odd ordered harmonics, but also a disturbing amount of so called inter-modulation-distortion (IMD: Intermodulation - Wikipedia, the free encyclopedia).

Again, in both cases, sources sounded exactly the same. But the results differ badly. See the new peak at 4kHz? It will land in its own critical band (no masking) and become annoyingly audible.

Now, here's my question, who ends up with the most fidel representation of the original?

A higher bandwidth doesn't equal "better". In fact, when it comes to nonlinear processing, it's better to use the narrowest tolerable input bandwidth (given properly anti-aliased processors).


This is a simplified experiment expecting the plugin to control all thing related to aliasing internally. My point here is the relation between processing bandwidth and IMD. The experiments clearly demonstrates the practical limits of high-rate processing (i.e. "more is not better"). In particular for chains of processors running at a very high rate.


Additionally, let me highlight another point. Many plugins use internal resampling, which in turn seriously hits the CPU performance. The idea to increase the sample rate before processing nonlinear stuff and reduce it afterwards (while saving a lot of CPU power) is tempting.

However, there is a problem. As we've seen above, it is very important to restrict the bandwidth before any form nonlinear-processing. This asks for some form of bandwidth limitation, typically right above the audible range. This leads to several contradictions:

1. What's the point of using super high rates (and bandwidths) if every nonlinear processor has to restrict the bandwidth anyway?
2. The user needs expert knowledge to properly do this filtering at the right places.
3. Linear processes such as EQing, delay, reverb and similar do not extend the bandwidth and thus, don't suffer from aliasing effects. In cases of feedback based algos, higher-rates even directly result in a lower precision. Running these at high rates is clearly not beneficial (given a high quality processor).
4. Non-technical users typically have no idea which processes really benefit from a higher rate.

This brings me to the conclusion that it is more reasonable to use standard rates and let the plugin/developer hold his promises, clean up his own mess afterwards, and gives his best to do it in the most efficient manner. More reasonable than DIY oversampling.




Experiment setup: I used a saturator to simulate the effect of a "limiter". I tried to use a popular limiter, but it turned out to create so much IMD on its own that I preferred using a more "visually appealing" type of nonlinearity (in this case a rather simple saturator). Here's the test setup:



And here's the Reaper project file (beware, it's set to a samplerate of 384kHz. In doubt, use Reaper's "Dummy audio" driver)
http://www.tokyodawn.net/labs/public/testsetup.RPP

So let's work at 192 kHz but insert "brickwall" low-pass for 24 kHz between each plugin?

yes, or, let the plugins decide. Performance won't be much better in the former case, but the complexity (and potential for misuse) will be much higher.

This filtering is more or less equivalent to plugins resampling on their own, but with the difference that they know exactly what and where it is needed.

nice read

one question if i understand correctly...

Internal oversampling in linear process (eq) is good
Internal oversampling in non linear process (com and limitars) not so good...

Very interesting post fabien

Quick question: assuming a given ADDA performs at 44.1 as good as it does
at higher sample rates, if we record the same track
at 44.1 and let's say 96,
would the audio material within the common
bandwidth (common to both sample rates) is/would be audibly different?

(Btw, slickeq is awesome!)

Informative post.

Here is a great test anyone can do at the click of a button to show the potentially harmful effects of intermodulation when working with or listening to higher sample rate audio containing (relatively strong signal) content above nyquist. I posted this before in a thread about the article that the test is linked in asking others to post their results, the thread went on for about 5 more pages after my post (I was not the OP) and to my disappointment not a single person responded with the results they got. Perhaps here people will actually take the 10 seconds to listen and post their results.

Here is the link:

24/192 Music Downloads are Very Silly Indeed

Scroll down just a hair to the test file labeled "30kHz tone + 33kHz tone (24 bit / 96kHz) [5 second WAV] [30 second FLAC]" and take a listen.

NOTE: Be sure to set your systems sample rate to 96khz before taking the test or the test is useless

So the idea is pretty simple. Nobody (unless you are like 75% dolphin) can hear a 30khz or 33khz sine wave. Actually go ahead and pull up a tone generating plugin and play a 30khz sine wave with your system set to 96khz or higher, you're not going to hear anything. However on many playback systems (mine included) when these two high frequency sine waves are played in unison (modulating) they cause audible intermodulation well into the spectrum of human hearing. I have to crank my monitors quite a bit to hear it but nevertheless it's there. Not good. So in theory higher sample rates above 44.1khz or 48khz can actually sound worse, at least as a final listening medium.

I guess I better stop composing minimalist electronic sine wave music for dolphins in-the-box at 192K and crushing the snot out of it with a clipper.

Indeed, but to be fair (towards high end ppl), most playback chains are effectively band-pass filters, which in turn tends to reduce the problem. Also, most AD and DAs do not really offer flat bandwidth for higher sample-rates, instead, they just use less steep filtering, typically starting right above the audible bandwidth.

That why I restricted the post to processing, not playback.

Thanks for the link however! Great stuff!

I tested:

- A Benchmark DAC1 feeding Hypex UcD400HG with HxR monoblock amps into Tyler Acoustic Decade D1 speakers

- A Benchmark DAC1 direct into Sennheiser HD-650 headphones

- A Mytek Stereo96 DAC direct into Sennheiser HD-650 headphones

- A Mytek Stereo96 DAC into a Sontec MEP-250EX EQ into a FCS P3S ME compressor (both engaged) back into a Mytek Stereo96 ADC into my DAW

- A Macbook laptop, both built-in speakers and with headphones using the CPU's 1/8" jack

All produced audible intermodulation with the 30khz+33khz test file I linked. So, I'd say the issue is pretty common and not just related to consumer level or none high end equipment.

Interesting.

So you're saying that the higher sample-rate creates space for more harmonic distortion, which in turn increase the possibilities of IMD?

Yes, the topic was 'inspired' by another thread about DXD.

Thanks Fabien very much, very interesting read!

Also Benchmark has something to say - John Siau: Benchmark Audio Guru | Real HD-Audio

Yes, and all HF stuff that has already been recorded.


Note that IMD increases (spreads) substantially with the initial bandwidth, and amount and strength of nonlinear blocks in the chain (i.e. in series).

It also gives an idea about why simple, monophonic instruments tend to tolerate much higher amounts of distortion than full stereo mixes.

btw, here's a very interesting observation about IMD (which finally turns out to be more of an illusion, but a very entertaining one, for nerds at least ):
http://sound.westhost.com/articles/intermodulation.htm

Thanks, just want to make sure I understand the cause of the IMD.

fabien please read my question about oversampling.. thanks!

Good and interesting stuff - thanks Fabien.

It reminds me this White Papers from Lavry :

http://www.lavryengineering.com/pdfs...lity_audio.pdf

interesting.
I downloaded your setup and halved the sinewave frequencies to 5kHz and 12kHz (a real world scenario has more energy in that area).
Now I notice that the problem of IMD caused by the saturation plugin stays, even if you change the samplerate from 384kHz to 48kHz.

So what is your advice? Should we refrain from using multiple sinewaves below nyquist or stay away from non-linear processing because it might produce coloration (i.e. artifacts)?

addition:
In your project the IMD also stays when switching from 384kHz to 44.1kHz with the sines at 10kHz and 24kHz. It seems the 24kHs gets aliased to 20kHz when the sampling rate is 44.1kHz.
I've tried adding a JS/lowpass at 20kHz before the saturator that emulates it better while keeping the samplerate high. (note: it seems sharp and dull parameters work in reverse)

Edit: I don't think this is what's happening.

what about analog, where there is infinite bandwidth ?
what happens if you process/record those two sine waves in an all analog chain in the same abusive manner ?

Analogue systems cannot have infinite BW -- infinitely fast oscillation is a nonsensical concept

IMD does occur with non-linear analogue processing.

Not necessarily good, but not potentially suboptimal in the specific way that Fabien is discussing.

The effect that oversampling a filter corrects for can be corrected for in other ways (at least, mostly - arguably well enough, and the trade-offs are arguably better perceptually and from a practical POV vs oversampling).

No, it don't ensue from Fabien's post. He is addressing fact, that when you process signal with wider bandwidth than audible band (with actual signal content outside of it) through non-linear processor, it will lead to rise of IMD at audible band. Normal (without any saturation modelling) EQ isn't non-linear processor, so it doesn't introduce any IMD.

Oversampled signal (with filters in interpolator) doesn't contain frequencies which aren't present in source, so it doesn't really apply there. (example.. when you use oversampling to create 352.8k signal from 44.1k source, there isn't any frequency content above roughly 22k.. exact number depends on the filter).

Michal

ok, bad phrase to use, but i always see it being thrown around here and i was dying to use it myself...
anyway, my point is that if you did this same processing in the analog world you would still have the IMD and it would be recorded and we would say it sounds the balls because we love analog...

IMD generally occurs at any non-linear system, were one part of source signal spectrum modulates others.. It isn't restricted to digital processing, so lets say any diode, amplifier, transformer or audio transducer is subject of IMD when passing complex signal.

Michal

Perhaps. Or we might say 'that analogue processor sounds bad'; designers typically try to reduce IMD as much as possible. Bandwidth restriction could be used to reduce IMD in an analogue system in a similar way as it does in Fabien's example.

Besides, it's not actually necessary to think about signal processing with the preconception that results achievable in the analogue domain are the holy grail But that's off topic!

Anyway, it is interesting topic. But with regard to original thread about 8fs capable FXs, I think, biggest practical difference with amount of IMD due to frequency content outside of audible range will be between 1fs (44,1 and 48k) and 2fs, mainly because of natural distribution of frequencies at sources (typical source frequency spectrum gradually decays and somewhere between 25-30k disappear in noise floor) which is also augmented by frequency response of most microphones.
Another thing is also type of work for typical hi-res music productions (like complete in DXD), which is classical, acoustic music, jazz or let's say restoration of old analog master tapes where usage of clippers, saturators or brickwall limiters are not common. From what I could see, engineers there are mostly using ITB effects as surgical EQ's to complement their analog outboard, restoration and stereo manipulation tools or "non-obvious" digital compressors for gentle manipulation with density of recording. I'm not trying to tell, IMD can't apply there, but its real impact will be probably very different, than for situation, when someone will be using projects in 384k to produce lets say EDM with tons of saturators and aggressive processors.
For final consideration of all pros/cons of particular technical process in production, that context is IMO very important.

Michal

Yes, this will happen, but it really isn't meant to be part of this experiment. I used this high rate for the whole experiment to make sure that aliasing doesn't become part of the equation. Aliasing complicates the discussion and tends to "overlay" the effect of IMD (in the bla bla sense ). The experiment expects the processor to handle aliasing on his own.

As mentioned in the original post, considerations about aliasing and AD/DA conversion performance are good reasons for using rates offering bandwidths wider than the audible band. There is no question about that.

It naturally pushes ppl to conclude that "higher rate are generally better, you can't have enough" or for the analogue engineer: "You can't have enough bandwidth".

However, The IMD experiment above illustrates a realistic and verifiable situation where this is not the case. It must be seen as a counter-weight to both arguments above. A good balance must be found and the engineer must be aware of these effects. btw, it is true for all domains (digital and analogue).

Absolutely. I am not expecting a black & white answer. Every engineer will probably find his own ideal balance and workflows (for example, keep hands off aggressive nonlinearites, or filter the "out of audible band" signals right before applying nonlinearities, or simply stay at 44.1, or whatever...).

@ -tc- : Thanks for the clarifications!