Okay, so I don't understand what causes EQ's to pre and post ring. I have read that this is related to the gibbs phenomenon, but I don't really see the connection. I understand the difference between linear and minimmun phase EQ's though (at least in practice). I also understand that EQs delay the existing signal, phase distort it and then mix it back with the original, is this phase delay the cause of ringing?

Here are a few almost paradoxal thoughts on EQs I do also like to get your take on:

- Is EQ ringing a necessary part of any EQing whether done in physical world by objects like walls in or any EQ devices? I think so, but doesn't this mean that walls and different parts of instruments and such also change the phase of a signal and cause this ringing? If that's the case, wouldn't there be a way to "correctly" EQ a signal so that there is none of this ringing / phase change. But what if say a string sounds DULL, is there a way to make it sound brighter without EQing it in some way? Is the EQ ringing going to be a necessity with dull sounding oscillator, if you want to make it brighter?


- If I create two sine waves in a DAW at 200 and 800hz, I can boost the other by 4db without any phase change or ringing, thus EQing without any artifacts. If I do same thing with an EQ I get ringing and phase change. Why can't any EQ boost harmonics in similar way to what I just did in my DAW, without creating ringing or phase change? Simply by looking at what's already there and boosting it! I could layer simple in-phase sine waves on tracks to boost certain frequencies without ringing and phase shift, correct?

Thanks a lot, it's really hard to find any material on this. But maybe some of the seasoned EEs here can answer.

Big ringing bump to the nerd frequency!

No takers?

Try moving this thread over to the Geekslutz forum.
iz

That's a lot of questions to answer in one post, plus some of those concepts need a background knowledge to be understood.

Ringing means oscillation, and it happens in several situations, the Gibbs phenomenon links a certain type of ringing with the frquency response of a given system. Described in simple words the response of a very steep LPF to transitions will cause an initial overshoot plus several oscillations around the desired output for a certain settling time (the picture in the wiki page describes the phenomenon pretty well). On the other hand a LPF with a smooth transition and a gentle slope will have a longer settling time than its steep counterpart but no overshoot and/or ringing.

Another kind of ringing can be caused by feedback. In several filter topologies (both digital and analog) part of the output is fed back to the input to create the desired frequency response. Feedback can be positive or negative. Negative feedback means that the output is phase inverted before being fed back to the input and positive means nothing is done to it. It's important to know that while positive feedback can prove itself useful in certain situations it can also cause instability and self-oscillation. Just to make an example we cause positive feedback every time we place a mic in front of a speaker that's monitoring its output).
A common use for positive feedback is in shaping the knee of a low or hi pass filter. The higher the Q the more the feedback required. At some point the feedback will be too much and the filter will start to self-oscillate. A circuit near the threshold of self-oscillation will have a tremendously boosted frequency response around the cutoff frequency, which will translate in a continuous tuned ringing.

Phase response can also cause ringing. If a circuit uses negative feedback, a phase inversion due to a bad inherent phase response of the system itself might gradually turn negative into positive feedback, causing all the trouble I've just described above.

Big spikes in the frequency response cause big time ringing, a real room response has plenty of them, bad news is that you can't eliminate them, good knows is that those are also what make a real room sound real.

As for eq's, if you don't want ringing (which in this case I agree on the fact that's it not the most pleasant effect in the world) avoid sharp cuts and boosts, use wide broad boost and cuts instead.

Overshoot, ringing and settling time occur in compressors also.

Yeah indeed, that's a lot of questions and I am not afraid to do a lot of reading also to understand this. I just can't really find anything fundamental on the internet, maybe someone else knows where to look?

Let's just stick to equalizer ringing though, and not, for example feedback to not complicate things.


If I have understood correctly, the frequency response of an EQ causes this ringing, so why is it impossible to construct an EQ that simply boosts individual harmonics by generating in phase sine waves? Similar to what I did in my sine wave example. Perhaps I am understanding this incorrectly and ringing (however slight) is always there with a specific harmonic series, if some parts are louder than in a non-ringing series? In other words, do you always get ringing in harmonic series if the loudness relationship of harmonics is specific? I would say that's incorrect...

Hopefully someone can understand my question By the way, it's purely theoretical, I can't hear this ringing sound on an EQ almost ever, but still want to learn about this.

As always, thanks for contributions. And mods if you read this feel free to move the thread to the geekslutz forum, that appears to be a better place for the question indeed.

Oden, technically and Fourier-wise we are talking of lots of sine waves with different phase relationships in a complex wave form. Maybe you won't notice artifacts when EQing typical synth sounds, but for example, a busy mix, or even a distorted power guitar will indeed show the artifacts you mentioned.

Filter resonance is another example

Feedback is part of an eq implementation, and it's one of the reasons for which an eq can ring.

Those eq exist, they're called linear phase and they still can cause ringing. Phase response in this case doesn't matter, if you create a sharp transition in the frequency response, you'll get it.

I really don't understand how your example would relate to any real world case... BTW If you could filter an audio signal into a high number of narrow bands (no phase shift) and boost just one of them you'd still get ringing.

The ringing you're talking about is the time domain counterpart of sharp edges in the frequency response. There's absolutely nothing you can do to eliminate it. It's a bit like saying, this LPF makes the sound duller, but I like the sound of it, is there a way to get a LPF that sounds this good without making the sound duller ?!?

Understood, but does this all mean that a harmonic series ALWAYS will have ringing if it has frequency response of an EQed harmonic series.

Example of 4 scenarios:

#1 I have a harmonic series of 400hz(-10dbfs) and 800hz(-20dbfs), which is generated by pure sine waves with my DAW's signal generator.

#2 I have harmonic series of 400hz (-13dfs) and 800hz(-20dbfs), similarly created in my DAW. I now boost the first harmonic with a tight EQ by 3db.

#3 I again have the harmonic series of 400hz (-13dbfs) and 800hz (-20dbfs). This time I create an additional 400hz (-10dbfs) sine wave in my daw, sample align it and combine with the original signal. End result is again the same.

#4 My non-noiseshaped noise floor is at -96 Dbfs. I boost the 400hz by 86db and 800hz by 76db with an infinitely tight EQ. Again, same end result.

Now, do all these scenarios have the same amount of ringing? Is ringing really an intrinsic feature of specific harmonic series, in which case it arguably makes no sense to even say EQs ring?

Also, I really do not understand how #3 is comparable to a linear phase EQ, could you elaborate that a bit?

BumP...

Hi - I was interested in your post because I have just dealing with this issue myself. I noticed various ringing and overshoot behaviour in my eq plugins as I was doing a few experiments and wasn't very happy about it! So to get a better behaved filter I wrote a simple filter (I use Reaper which has a handy scripting language for writing effects) that behaved the same as a real world passive resistor / capacitor filter. It gives a relatively gentle 6db per octave slope, but if you want it steeper then you can simply stack a few up one after the other. Theres nothing about the digital effect or the passive RC real version that causes any ringing or overshoot at all, so its just a nice, smooth, clean filter with no added artifacts. Measures right and sounds good to me You couldn't practically achieve the really steep 'surgical' style eq curves like that, but a non ringing eq is perfectly possible.

Did you have a look at Christian Budde's Dual Linkwits Riley filter?

In any case I am interested in the reaper script, did you share on the forums?

Wow this thread is ages old, surprised to see replies here. In the case that anyone else is tackling with concept of EQ check out the DSP guide by Smith...

Anyway, non-ringing EQ is not possible using the conventional means. What you may have is a filter optimized to ring as little as possible at the cost of other things (namely frequency "resolution").

I was just about to reply and recommend his DSP guide before noticing the latest post

Hiya. Thanks I just took at look at the filter you mentioned I'll stick the Reaper script for my filter on here. This is the lowpass version for now - had to upload it as a txt file - just delete the extension to use it straight in Reaper. If you want it I'll put on the highpass in a bit...
The thing I was dealing with you can see in the attached jpg. The upper waveform is from a square wave lowpass filtered by the linkwits riley filter at around 6.5K and 24db per octave. You can see the overshoot followed by the ringing what are all added artifacts. (I'm not adverse to artifacts and various mojo, I just like to have control!) The lower trace is from my Reaper script - 4 instances in a row to add up to the same 24db per ocatve. The smooth rounding of the corners is just the same as you would get from the analogue equivalent (setting aside parasitic inductances, power supply hum etc etc lol!) No ringing or overshoot.

Its not the same technique as 'standard' DSP and doesn't have the same feedback mechanisms that cause the ring. Its just a sim of a passive analogue RC filter...

Lovely Thanks a lot! If you have time a HP would be very nice indeed!

Sometimes I get a 1.5 db increase at the cutoff when I go very extreme on the slope on low freq's with the linkwitz :D

nulls with the simple 6 db js filter...

Yeah - I've had trouble before eq'ing out deep bass and finding its left it sounding muddled and un-precise. Probably those same resonance / ringing effects messing up the time aspect - pain in the bum!

Apologies - I just realised the lowpass script I posted before gives the -3db point at a slightly lower frequency than it should! The highpass and the new attached lowpass here are properly adjusted!

P.S. Have you checked out the Variety of Sound plugins? I really like the Boot EQ and Baxter EQ. Some of that stuff is very good indeed...

Hey Oden,

here's my attempt..

ok.

Mhhh... probably not.

generally, yes. But I think we have to go back to a handful basics. The term "ringing" is easy to confuse with other things.

First of all, when engineers use the term ringing in relation to filters, they mean a visual effect appearing in the impulse response representation. More clearly, they do not mean "frequency magnitude ripples", "filter resonance" or anything related to the ringing of a bell.

Look at these two impulse response plots below. On the left, you see the frequency response alternating with the group delay response (= phase shift expressed in time). To the right, you see the according impulse response:



The first filter is of the linear phase type. In this case, the frequency vs delay plot draws a flat line. Accordingly, the impulse response is symmetrical. The impulse rings "in" and "out" after the event.

The second filter is of the minimum phase type. That is, it uses the smallest amount of delay possible to achieve its task. The task, in this case, is the low pass filter behaviour you see in the frequency magnitude plot. Note that both filters have practically the same frequency magnitude. The second filter however, distorts the original phase relationship, it clearly delays some frequencies by stronger amounts than others. Looking at its impulse response, you can see that the filter rings "in" almost instantly, and visually, only rings "out", although to a much stronger degree.

Just for reference, a pure wire's impulse response looks like an infinitely small spike. That is, it doesn't change the original impulse at all.

The stuff appearing before and after the original impulse is what we call ringing. The steeper a filter is, the stronger the impulse response ringing has to be. Note that pre and post ringing doesn't always have to look wavy (see: MA or Gaussian impulse).

Many misunderstandings arise from the fact that most music producers/musicians and even audio engineers never bother understanding mathematical definitions.

Point is, in order to understand the impulse response of a filter, it is absolutely crucial to understand what the dirac impulse represents in itself! The dirac impulse is an infinitely (or in bandlimited systems: a maximally) small spike at unity gain. This little spike contains all (representable) frequencies of the system. All possible frequencies from 0Hz to Nyquist. As such, it really is infinitely wide! The blank areas before and after the spike are essential parts of the dirac impulse. They really are "filled", but all waves stack up in such a manner that they cancel out to silence right before and after the visual spike. Imagine a single 1Hz event, it's 1 sec long, yet it's in that spike. Fascinating, eh?



With this in mind, it's much easier to understand ringing. When the filter does his work, it will trouble this perfect stack and reveal previously hidden content (either after and/or before the visual spike).

Yes, they do. Have you ever seen mechanical engineers hitting their their machines with a hammer to find cracks in the structure? That's the same principle. They send an impulse through the system and listen!

In theory, yes. Via re-synthesis and/or additive synthesis. Problem is, nobody has found a way to re-synth a sound without using conventional filter and their ringing.


Yes correct. In the real world, ringing only appears with short, wideband signal (such as drums). Keep in mind my explanation of the dirac impulse. The filter doesn't add anything, it only uncovers what's been there in the dirac impulse since the beginning.

How it rings can be a desirable audio quality as in Inductor EQ.

This isn't really related. How a filter rings purely depends his frequency and phase magnitude.

Inductors have a nonlinear behaviour which has a "sound", but still exhibit exactly the same ringing as any other filters having the same freq and phase response.

Thanks for your lengthy explanation fabien, while I found the answers long time ago, your answer is much easier read than some of the books.

The answer is that indeed, EQ adds artifacts, while circular convolution/synthesis needs not to. I remember writing a response to one of your mastering forum threads regarding very similar issue. In the end I asked if you would like to finally make a plugin that cures all of these issues IE. a straight up fourier sample editor (not based in FFT to allow sample sizes that are not power of two). Have you considered it? Still thinking such editor would be awesome development and could be vital in curing old samples of the machine gun effect. Not to mention the other tricks possible with such capability. Maybe some editor has such feature built in, but I sure haven't found it. It's a shame, really. Drawing up samples in the time domain is such a standard feature, but frequency domain is a no go...

These rules are universal and appear in all filtering approaches. FFT is used to look at data from a different perspective, sames physical effects apply.

A filter basing on frequency domain convolution (FFT>manipulate>Inv.FFT) has exactly the same effects as a filter basing on time-domain convolution (FIR or IIR).

Yes, but my approach is not based on the filtering approach at all. Rather it would be a combination of circular convolution, frequency addition and phase manipulation (none of which EQ can really do, the concept is different). With this type of editing it would be possible to create any signal possible only bounded by the limits of digital audio (just as if you were drawing a sample).

The part about the text of curing the ills of EQ were not very serious, because we are long way off from that indeed. Rather editing in the frequency domain would have many other uses, and could eliminate the artifacts on a short sample level. Indeed this approach only works on short samples or it will get out of hand. Still, a basic spectral editor would be useful for special FX design and general sample editing.