Originally Posted by Oden

- 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?

Originally Posted by Ciozzi

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.

Originally Posted by Oden

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.

Originally Posted by Ciozzi

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 ?!?

Originally Posted by Oden

Big ringing bump to the nerd frequency!

Originally Posted by pokey sticks

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.

Originally Posted by pokey sticks

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.

Originally Posted by Oden

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").

Originally Posted by Durk

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?

Originally Posted by pokey sticks

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...

Originally Posted by pokey sticks

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...

Originally Posted by Durk

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

Originally Posted by Oden

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.

Originally Posted by Oden

I understand the difference between linear and minimmun phase EQ's though (at least in practice).

Originally Posted by Oden

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?

Originally Posted by Oden

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?

Originally Posted by Oden

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?

Originally Posted by Oden

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?

Originally Posted by Bassmankr

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

Originally Posted by FabienTDR

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. In other words, 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.

Originally Posted by FabienTDR

These rules are universal and appear in all filtering approaches. FFT is just 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).