Low THD saturations that sound incredibly amazing

[plusfer]

I've noticed that there are emulations of analog equipment saturations that sound really good (without reaching the clipping). When I listen to them and make comparisons with dry, I can hear a significant difference. However, when I measure them, the THD is very low, around -70 dBFS o less in some cases.

I'm not an expert, just a hobbyist, and there are many technical aspects that are beyond my expertise. I've already experimented with creating saturations using waveshapers and other techniques like bias, negative feedback, etc. I've also tried adjusting the waveshaper based on the input or output, working with transients, and so on. The issue I'm facing is that I can't achieve an obvious and pronounced sound if the THD is not high.

For instance, when I use tools like plugindoctor or VST plugin analyzer, I observe saturations like those from UAD that have very low THD content, but I can clearly hear that they add a punchy quality to the low frequencies. When I measure the harmonic content in the low frequencies, it's actually quite low. I've noticed a similar phenomenon with Nebula emulations and preamp programs, which have an almost -100 dBFS THD, but they still sound incredibly good. This has left me feeling confused and puzzled.

what might I be missing or not understanding?

[gambero]

THD is just one small part of the big picture. There are a lot of other factors that go into making a blackbox model of any piece of equipment, which are measured through different types of analysis, and they all add up into making the emulation more accurate.
There might be some behaviours of the original machine that you might not be measuring or that you're measuring partially by using certain types of analysis. For example, some nonlinear behaviours might be stateful, and it's pretty hard to measure with simple static i/o function analysis. Harmonic distortion is often frequency-dependant (which you can replicate by having preemphasis and deemphasis filters before and after the nonlinearity, for example).

[Music Engineer]

I suppose that you also ensured that the frequency response of the device is flat? Because if not, then *that* tends to be the most important sound-shaping feature, even before we talk about nonlinear distortion. Assuming that this is the case, then one additional thing is the timing, i.e. the question "when" certain frequency components occur and also (maybe even more so) the question, whether they are more smeared out over time or more temporarily localized. When you talk about "punchy quality to the low frequencies" and assuming we have a flat frequency response and low-to-unnoticable THD (i.e. no additional harmonics on the low frequencies are created), then my first guess would be that the process does something about this timing. Adding more punch to low frequencies sounds like the bass events tend to get more localized in time. I don't really know how I would go about achieving this effect in realtime - allpass filters tend to do the opposite: smear out transients. Maybe one would need some sort of "inverse allpass" - but that would be a non-causal process, so not really doable in realtime (easy in non-realtime, though). Well...I'm assuming to use IIR allpasses here, because a *true* allpass is necessarily IIR (unless it's a pure delay, if I'm not mistaken) - one might probably approximate an anticausal allpass as FIR filter in realtime. But whatever is going on, when "punch" is involved and there's no obvious frequency boost or harmonic distortion going on, I'd be on the lookout for how the transients are manipulated. They are important for "punch".

Disclaimer: Take all of this with a grain of salt. I'm speculating here a lot and I don't know much about analog emulations.

[Music Engineer]

One measurement, I could imagine, is to create a (low-frequency) sinusoid with a (Gaussian) envelope, pass it through the process and look at what happened to the envelope at the output side. Is it more smeared out in time than the input envelope or maybe more localized? Also (even before that): has it been shifted or is it still in the same position? It may also make sense to use asymmetric envelopes instead of Gaussian shaped ones - some sort of smooth attack-decay shape like this one:

https://www.desmos.com/calculator/mjmsrjcgsu

because that's more realistic. Natural acoustic events do not have Gaussian (or otherwise temporarily symmetric) envelopes - at least not the percussive types of acoustic events

[plusfer]

Yes, I mean that the frequency response is always flat, including the phase.
Also, when looking at the harmonics in different parts of the spectrum, they generally tend to be higher in the low end, but not high enough to be noticeable to the ear.
There's something about the dynamics that I can't understand or explain.

Yes, there are many things to try, but conducting a test of "dynamic performance in time" (I'm not sure if that's the correct term, but the test involves passing a sine wave with various changes in amplitude and then analyzing the transients, release, etc.), many of these emulations appear so static, they don't seem to reflect what is actually heard.

The same happens with preamplifiers, which seem to modify the signal very little if you look at the tests, but when you listen to it, there is a significant audible difference.

[Music Engineer]

Yes, I mean that the frequency response is always flat, including the phase.

Now - that is indeed somewhat mysterious. If amplitude and phase response are flat *and* there's no noticable harmonic distortion going on...what else could it be? ...hmmm... Maybe it is some sort of interaction between various frequency components that is not being measured? (again: wild speculation). One such interaction would be intermodulation - but that kind of interaction is usually always tied to harmonic distortion - in waveshapers, these two always go together - they are like two sides of the same coin. But maybe there's some more complex process going on where this is not the case.

Also, when looking at the harmonics in different parts of the spectrum, they generally tend to be higher in the low end,

That is the frequency dependency of the distortion that gambero mentioned. Before going into the nonlinear distortion unit (think: waveshaper), the lows can be boosted and then cut back again after the distortion (think of low-shelving filters with opposite (and therefore cancelling) gain settings). This has the effect of applying more distortion to low frequencies

which seem to modify the signal very little if you look at the tests, but when you listen to it, there is a significant audible difference.

Hmm...maybe you should post some of your test results...maybe plots and/or wavefiles of input and output signals to see more precisely, what you are actually measuring there.

[Synthman2000]

The THD might be low but it is affecting all of the spectrum that passes through it. Probably in differing amounts as well. You can look at the Hammerstein graph to see harmonic content vs frequency. Do not forget that not all pass through characters are flat. They often have a bump here and there or a roll off etc. Also don't entirely ignore other characters like cross talk, though the contribution is quite small usually.

And in some products where oversampling is not present or working and it is non linear it could even be aliasing.

Distortion is not always 'warmth' it can be ghastly.

[mystran]

Yes, I mean that the frequency response is always flat, including the phase.

Now - that is indeed somewhat mysterious. If amplitude and phase response are flat

This alone tells you nothing.

Let H(z) be a (strictly) minimum-phase filter, then the inverse filter 1/H(z) is also minimum-phase and H(z)/H(z) is unity by pole-zero cancellation. So you can take basically any minimum-phase EQ as pre-emphasis (as long as it's strictly minimum-phase: no zeroes on the unit circle, so no deep notches), stick it in front of your non-linearity and then use the inverse filter as post-emphasis and it'll all measure flat in amplitude and phase(!) until you start getting enough distortion that it skews the analysis by upsetting the pole-zero cancellation.

[Music Engineer]

Of course! That's why the sentence continues as:

"....*and* there's no noticable harmonic distortion going on."

with an emphasis on the "and". That second part was important. Surely, any nonlinearity in between the two cancelling filters would show up as some sort of harmonic distortion, right?

[urosh]

Yes, I mean that the frequency response is always flat, including the phase.

Can you give examples of this analog modeling plugins that have flat frequency response? I don't remember ever seeing such beast, which is to be expected because analog gear is never flat, especially "tone" equipment that is typically modeled.
When analyzing THD, have you matched level in PD to be the same as level at plugin input in DAW?

[plusfer]

Yes, I mean that the frequency response is always flat, including the phase.

Can you give examples of this analog modeling plugins that have flat frequency response? I don't remember ever seeing such beast, which is to be expected because analog gear is never flat, especially "tone" equipment that is typically modeled.
When analyzing THD, have you matched level in PD to be the same as level at plugin input in DAW?

for example, APE EQ saturation https://www.analoginthebox.com/product.php?id=2687
UAD API vision channel strip (LINE mode)

When analyzing THD, have you matched level in PD to be the same as level at plugin input in DAW?

yes

[urosh]

UAD API vision channel strip (LINE mode)

This is neither flat nor low (at higher input levels at least) distortion.

ApiMagnitude.PNG

ApiPhase.PNG

ApiDist.PNG

[plusfer]

Thanks urosh for the graph.
I can assume, without seeing the freq in the graph, that at 40 Hz the harmonics reach approximately -35 dbfs, and then throughout the spectrum at -55 dbfs.

I really can't achieve saturation with such low harmonic content that it becomes such an evident effect

[gambero]

I believe that some audio buzzwords we hear thrown around sometimes can misguide us when looking at the "science" behind it, and I think we're all succeptible to that to some amount. Maybe the punchiness you're looking for isn't coming from saturation but from some other property.