Zero Delay Feedback Filter (How to test if your synth has a )- Xils-Lab White Paper -

[Ingonator]

In my own tests i did not really get that "self-oscillation" thing like described in the video.
In my test either the Resonance stayed constant (like e.g. Xils synth, Diva, Saurus with 12dB LPF) or the Resonance "peak" disappeared.

UPDATE:
Looks like i get that self-oscillation from the video when using Waldorf Largo. As the standard 24dB LP filter in Largo is not modelled on an analog filter this is not really surprising. The filter in PPg Wave 3.V behaves differently as it should be modeled on the SSM filter.


Ingo

[Ingonator]

Anyway i agree to others that only the fact of having a 0df filter design does not make a filter good or bad. The filter in Largo does not seem to be 0df but it seems to sound unique and good IMO.


Ingo

[xavier]

That's all cool.

Hi Urs,

Just saying that many analogue filters have a capacitor or even a shelving filter in the resonance path. In those cases the resonance typically vanishes in the bass and/or the upper end. Sallen-Key filters for instance usually have feedback going into the "backdoor" of the integrator, hence can't have constant Q no matter what.

That's right and other posts pointed this. But this doesn't explain raising or vanishing resonance of some digital filters which are bring by the digital delay(s) which are not taken into account in a way or in an other.

BTW : I think that most of the old electronics designers worked hard to find analogue filters with independent Q/F, and that this was part of the marketing bla-bla of these times because such a filter are musically better.

A question though: The first test is done with noise input and without self oscillation. Does anything speak against the self oscillation case? With non-0df I've often seen the amplitude rise in upper frequencies in ladder/svf configurations whereas 0df keeps it constant - if no further capacitors are modelled.

This test is an example. To be sure a filter manages the digital delay(s) correctly, various values of the Q (including self-oscillating) must be used.
I thought that things were less obvious when the filter self-oscillates as the level can't go above the internal non-linearities. On the contrary, a mid-Q can show more. But of course this depends on the filter to test.

Also, I'm a bit weary about spectrometers. The graph usually combines various bins in the higher frequencies, so that the actual peak of a single sine seems to get lost. Wouldn't a simple peak meter do a better job?

Agree with that. I thought that the spectrometers were easier for videos, but depending on the analyse windows, the FT size, things must be done carefully with them (especially for measuring less than a few dB, but when a filter doesn't manage the delay(s), then the resonance varies more than a few dB ).

Best regards
Xavier

[Urs]

I thought that things were less obvious when the filter self-oscillates as the level can't go above the internal non-linearities. On the contrary, a mid-Q can show more. But of course this depends on the filter to test.

That's certainly true for topologies where non-linear elements such as tanh-saturators are squeezed somewhere into the signal path. But that's not necessarily the case.

If you look closely at Antti's transistor ladder model, depite 9 tanh shapers the output is not clamped within a range. In fact it's hard to believe that it doesn't explode.

The great thing about a 0df version of Antti's filter is that one indeed gets a pretty stable q, whereas anything z-1 (or z-0.5 as Antti proposes) simple goes out of whack. Choice of integrators is vital though.

Nevertheless, if you start modeling DC-offsets and DC-blockers within the filter, you're lucky to get a decent range of constant q even with 0df.

[mystran]

The great thing about a 0df version of Antti's filter is that one indeed gets a pretty stable q, whereas anything z-1 (or z-0.5 as Antti proposes) simple goes out of whack. Choice of integrators is vital though.

It's not totally independent (q vs tuning) even with as 0df version; it's reasonably close, but the thing starts going flat as you increase resonance past self-oscillation. I'd call that "expected behavior" though.

[Urs]

The great thing about a 0df version of Antti's filter is that one indeed gets a pretty stable q, whereas anything z-1 (or z-0.5 as Antti proposes) simple goes out of whack. Choice of integrators is vital though.

It's not totally independent (q vs tuning) even with as 0df version; it's reasonably close, but the thing starts going flat as you increase resonance past self-oscillation. I'd call that "expected behavior" though.

Possibly. We've only ever measured with an ordinary spectrometer, nothing fancy.

But of course as soon as you have non-linearities, the signal/level modulates the cutoff frequency. Which is probably why excessive resonance lowers the cutoff in most cases, raises it in some.

[Lotuzia]

Anyway i agree to others that only the fact of having a 0df filter design does not make a filter good or bad. The filter in Largo does not seem to be 0df but it seems to sound unique and good IMO.


Ingo

Exactly. Sounding unique is probably what people expect from different instruments ( providing that unique is good, as exceptional unique badness will probably not profit to musicians )

[Lotuzia]

That's all cool.

.......

Also, I'm a bit weary about spectrometers. The graph usually combines various bins in the higher frequencies, so that the actual peak of a single sine seems to get lost. Wouldn't a simple peak meter do a better job?

Yes, visualisation and analysis methods can be discussed, but imo the test is first and merely an audio test, so for example in the first video, ears are enough by far to hear, while not seeing, the difference. Close your eyes and just listen to the first video and it becomes very obvious.

Adding visualisation is cool for a video, and analysis tools will allow you to precisely view that for example for a synth I tested with the second sweep test : resonnance is almost disapearing at 2k to reach -20db at 10khz. But thats it, like I said ears totally perceive the differences, even when some instruments tend to behave in a comparative way if you just look at the analysis tools. Our ears are much more accurate than we think, even if for most people, correlate what they hear to audio strict values is not easy.

Then some people prefer to see a precise equalizer representation when equing tracks, than just turn the controls. So well you can have both and imho its ok like this.

[hakey]

imo the test is first and merely an audio test

As some non-0df filters will 'pass' your test (whilst some real analogue filters will fail), it's first and foremost a complete waste of time, imo.

[hakey]

Out of interest, is there a 'simple' test that will objectively and accurately determine whether a filter in a given plugin is 0-df or non-0df?

[AdmiralQuality]

Wow, how did I miss THIS?

Just about everything you write here Lotuzia is wrong or at the very least, confused...

Zero Delay Feedback Filters A very simple test

The delay feedback problem in synthesis software emulation was first pointed out and named by Vadim Zavalishin, of Native Instruments back in 2008, but it was also mentioned some years before, under different names in several other papers.

It's a well known issue with the unit delay introduced by digital filters. It's not a new discovery by any means. And I was well aware of it myself when I was designing and testing the filter that became Poly-Ana's back in October 2005.

What really matters is the effect on the sound. This is most apparent in how it alters the relationship between the filter frequency and the filter resonance (or emphasis)

If that's what really matters, then you should at least be able to describe the effect on the sound. Which you get wrong below...

In hardware analog synthesizers, the filter frequency and its resonance are almost independent. When one of them is being modified the other remains almost the same.

Untrue. Adjusting resonance amount usually affected the cutoff frequency on most classic analogs I've used. Where you would experience this most prominently is when tuning the filter's self oscillation to match an oscillator. Then you'd turn down the resonance to a less extreme level and suddenly find the filter had drifted out of tune, even though the cutoff is right where you left it when you callibrated it against the oscillator. Characteristics of the signal (or lack of) going into the filter often had a detectable effect as well.

And classic analog synths CERTAINLY had varying amplitude of the resonant peak across the cutoff range of the filter. In fact the behaviors of different products were all over the place, with no one "correct" one. In particular, some filters, particularly Moog's if I recall correctly, boosted the filter output levels when cutoff was low. This was to perceptually match the volume across the cutoff range, so bright sounds wouldn't sound louder than filtered. That's just one example of a technique that throws your suggestion out the window.

Adding a delay in digital filter means computing the output of the filter with an input and the previous output creates a link between the cutoff frequency and the emphasis so modifying the frequency also modifies the emphasis.

Here is a simple test that you can make to figure out if you favorite soft synthesizer has a zero-delay-feedback filter. Apply a Mid Emphasis to the filter and sweep the filter through the full range.

With a 0df, the emphasis will keep almost the same value. In a filter design that does not manage the digital delay, the emphasis will increase as well as the frequency increases.

I just tested Poly-Ana and the resonant peak decreases in amplitude as the cutoff increases. I guess not only does Poly-Ana sport 0 delay filters, but I did such a good job it must actually search into the future to determine its feedback signal! (I'm going to take on guessing lottery numbers next! )

(Alright, actually it's because there IS a curve INTENTIONALLY tying the feedback amount to the cutoff frequency, causing it to behave exactly the way I wanted it to. This also prevents the filter from "blowing up" at high cutoff frequencies + high resonance setting. Poly-Ana's oversampling also plays a big role here, at the highest setting (16X) the resonant peak's amplitude varies the least. That's because most of the curve that's fudging the feedback amount has been pushed up into inaudible frequencies. And while 16X oversampling may seem like a lot, it's still competitive with the prediction techniques used to create "0 delay" feedback. (And also has a whole bunch of other benefits. And not just for the filters!)

A commonly held belief is that non-0df filters are unable to produce sounds with rapid onset transients, like percussion because of the delay introduced. This is incorrect, the 1 delay lag is not perceived by the ear. The 0df filter problem affects sounds at more or less mid resonance settings, when the filter frequency is varying (when is generally the case).

On that we agree.

For those who want to go find out more, and really get your geek on go here for a more scientific description of the 0df filter case.

The Test: You'll need a synthesizer (software of hardware) with a self-oscillating filter and a noise generator.

1. Open the noise generator level and mute the oscillators.

2. Set the filter frequency to a very noticeable value (500 Hz for instance)

3. Set the emphasis to a mid value (not to high, but enough to be noticeable)

4. Sweep the filter frequency toward the highest value.

In Zero Delay Feedback filters, the emphasis will remain the same, but in filters that do not manage this delay, the emphasis will grow until the filter self-oscillates.

Here you can see this test:



Yes, It's "that" simple !

Final Note: Synths that are not equipped with 0df filters are definitely NOT "bad" synths. They have their own character, filters, etc, and in a lot of situations, you wont be able to tell the difference.

You don't seem to have a technique by which you CAN determine the difference.

The same applies to synths equipped with 0df filters: They COULD sound bad, as this is only ONE aspect of all the overall character of a synth.

At Xils-Lab we're always trying to better our algorithms, and the 0df part is no exception. There are several possibilities and approaches to achieve 0df filters in the digital world, and we hope that our own way to do things will continue to evolve and will allow us to keep on offering beautiful musical instruments in the future.

We hope that this test will be useful and fun for you.

LtZ

The actual difference is VERY subtle. It has to do with the width of the resonant peak (which you can really only appreciate when filtering a noise source as regular waveforms have discreet, widely spaced harmonics and resonance below self-oscillation can only emphasize frequencies that are there at the input). The 1 sample feedback delay also affects the position (in frequency) of that resonant peak relative to the cutoff frequency. The delay causes the resonant peak to be slightly lower in frequency than the cutoff frequency, where on a real analog filter they're at the same frequency. It's hard enough to see this on a spectrum analyzer (just a slightly wrong shape at the cutoff). You'd need to have quite the ears and really know what you're listening for to be able to tell just by listening. (I believe I can, but I wouldn't be surprised if a blind A-B test proved me wrong.)

It also affects filter tuning/tracking, but this is another thing we compensate for in various ways to achieve the behavior we want. Frankly the suggestion that everyone else's filters are broken is a bit insulting. There are more than one way to address these issues, and you seem to have a rather tenuous grasp of them yourself.

I don't want to start a fight, or trash anyone's products. I just wanted to point out that many products contain exactly the filter behavior the developer(s) wanted them to. EVEN those that don't "roll dice" repeatedly trying to predict what the zero delay feedback signal would be. (Which introduces a whole bunch of its own problems and potential audible artifacts.) We own and test against real analogs too, and most of us know better than to make a glaring departure from real analog behavior like having resonance go wildly loud at the high end of the cutoff. Measuring that, or the absence of that, signifies NOTHING.

[hakey]

Just about everything you write here Lotuzia is wrong or at the very least, confused.

Yep, not just in this thread...

[AdmiralQuality]

Just about everything you write here Lotuzia is wrong or at the very least, confused.

Yep, not just in this thread...

Well, I don't know about that. But I do know what kind of response I'd get if I started a thread like this in Instruments, explaining in myth-form why most other products are substandard to the ones I (coincidentally) advertise in my signature.

[hakey]

A commonly held belief is that non-0df filters are unable to produce sounds with rapid onset transients, like percussion because of the delay introduced. This is incorrect, the 1 delay lag is not perceived by the ear. The 0df filter problem affects sounds at more or less mid resonance settings, when the filter frequency is varying (when is generally the case).

On that we agree.

Hmm - that's a strawman, imo.

No one says that non-0df filters can't produce rapid transients. What is claimed is that the difference between non-0df and 0df filters is noticeable when producing rapid transients.

[AdmiralQuality]

A commonly held belief is that non-0df filters are unable to produce sounds with rapid onset transients, like percussion because of the delay introduced. This is incorrect, the 1 delay lag is not perceived by the ear. The 0df filter problem affects sounds at more or less mid resonance settings, when the filter frequency is varying (when is generally the case).

On that we agree.

Hmm - that's a strawman, imo.

No one says that non-0df filters can't produce rapid transients. What is claimed is that the difference between non-0df and 0df filters is noticeable when producing rapid transients.

What about vs. oversampled non-0df filters? (You see my point, there's more than one way to skin a cat.)

I'd say audio-rate modulation is the torture test here. But as Urs and others have pointed out, there's a lot more going on in Diva's filters than just the 0df technique. So how do we know what we're really testing?

If you think you can come up with a methodology to determine whether a filter is "0df", please share. Do any of the synths that offer it have a switch to turn it off that doesn't affect any other part of the filter algorithm? That would be a lot more meaningful than comparing disparate products.

Personally, as it seems to take as much CPU as massive oversampling, and there are so many other benefits from oversampling, my "solution" is to just go with oversampling and let the user adjust it to taste. Really, in any sound where filter resonance is at zero, either method is overkill.