Linear Phase EQ---your thoughts and preferences

[Frippertronix]

The issue with FFT-based EQ is the latency. You cannot have zero-latency effects with signal FFT-based algorithm, which might be annoying for real time processing.

Of course, there is a price to pay for everything. Latency is no issue if your host supports PDC and you don't play live.

Paul

Yes, seems like linear phase is "plugged" as a mixdown/mastering tool for the most part anyway.

[robenestobenz]

Christian is saying transients blur with linear phase, bluecat is saying that linear phase avoids phase problems with transients.

Are these differing opinions, or does each EQ method have a possibly negative implication for transients?

[Christian Budde]

Christian is saying transients blur with linear phase, bluecat is saying that linear phase avoids phase problems with transients.

Are these differing opinions, or does each EQ method have a possibly negative implication for transients?

Here's some ASCII Art, what's happening to an impulse:

Code: Select all

Original Impulse (or call it transient):
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-+------------->

Minimum Phase (something like this):
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-++-+-+-++--++->


Linear Phase (something like this):
      |
      |  
  | | | | | 
-++-+-+-+-++--->

As you can see clearly in Figure 1 ('Original Impulse') all frequencies are concentrated in one pulse. The have exactly the SAME PHASE and the SAME AMPLITUDE (theorem of dirac). This equals to a white spectrum.

If you now like to boost/cut/filter frequencies within this spectrum the historical (analogue) approach was to delay some frequencies (in other word change the phase) and add it to the original. This way some frequencies got boosted while maybe others got cut. The real, analog world oblige time. Thus the filter has to be causal. This means the filter can not look into the future and that's what is shown in Figure 2 ('Minimum Phase')

This may sound strange at the moment, but if we have a look at the newer digital filter and if we additional allow to introduce latency, a non-causal filter is possible. If you like you can call it look-ahead-filter [(TM) by me now ]
Figure 3 illustrates that: a) there is latency introduced b) and some peaks happen BEFORE the actually impulse happens.

Isn't there something similar in the real world?
Yes, there is: Let's consider a simple, but ideal cable, to make it easy let's consider a fibre cable. A transfer of data (e.g. binary) will be delayed because of the limited speed of light. So we have latency. In some cases the group speed isn't equal to the phase speed [fill in some physics here] and this makes it also possible that there may be some spikes before the main impulse.

Ok, but now back to the digital domain. With the introduction of cheap storage elements, it was easy to implement look ahead filters or let's call them linear phase filters. I've already introduced them in figure 3. With these filters the phase information is still the same as within the original signal. No frequency is delayed in contrast to the minimum phase realisation.

But now let's have a look again at the transient (or in this case the original impulse). The relative phase relation of both realisations is the same, but one of these has pre-echo (linear phase), while the other hase a longer post echo.

For the ear it is most important, that the transients are absolutly in phase. This is the case for both realisations!! Other phase information can hardly be detected by the ear.

to be continued...

[snooky]

the future rules!

[robenestobenz]

Thanks for the explanation, Christian.

[IIRs]

Are these differing opinions, or does each EQ method have a possibly negative implication for transients?

Each EQ method has a possibly negative implication.

The phase changes determine the EQ's character, so they are a vital part of the sound of a good analogue EQ, but often also blamed for the "un-musicality" of some digital designs.

Linear phase avoids these issues, but introduces "pre-ringing" ie: a small amount of echo before the transient happens. (afaik phase linearity is acheived by processing the signal twice, once forward and once backward, so the phase changes are equal and opposite and cancel out. This accounts for the inherent delay.. something like that anyway )

<edit> too slow!!

[Frippertronix]

Yes, thanks to Christian and IIR's, this helps!

Dave

[Blue Cat Audio]

Christian is saying transients blur with linear phase, bluecat is saying that linear phase avoids phase problems with transients.

They may blur as Christian said, but I was comparing linear EQ to analog-style IIR filter which completely change the phases of your signal, which may be more noticeable on transients.

BTW you never hear the pre-ringing of the linear phase filter as long as the filter length is small enough.

[Christian Budde]

Christian is saying transients blur with linear phase, bluecat is saying that linear phase avoids phase problems with transients.

BTW you never hear the pre-ringing of the linear phase filter as long as the filter length is small enough.

You're right. It is masked by the higher level of the pulse.
Overall, hearing tests within our institute has showed us, that the last elements in the electro-acoustical chains (loudspeaker, room) usually introduce so much phase distortion (non-linear phase), that it is hardly possible to recognise differences between linear and minimum phase. Only with headphones and clinical signals (square, saw), a difference could be heared.
(german document, chapter 5: Dissertation Swen Müller)
Especially for live events a linear-phase filter can hardly be used because of its latency.

Just some other thoughts,

Christian

[bmanic]

I might suffer from a severe case of "once you hear it, you always hear it" syndrome or simply prefere the sound of non-linear phase EQs but I've only found one linear phase EQ that doesn't fcuk up a well recorded drumkit or snappy/punchy drum beat when used in a mastering situation (or EQing a drumbus). That EQ is the Algorithmix PEQ Orange. Even the Weiss EQ1 mk2 in linear phase mode caused some weird mashing of the hiphop beats I ran trough it whereas in normal mode it sounded much better. Could be that linear phase is at it's best when EQing classical music or accoustic music with few transient heavy instruments or smeared transients because of distant miking or something (like harmonica, classical guitar, opera singing, full scale orchestra).

Probably I'm just allergic to the old implementations of linear phase EQs and should take another look at the more recent releases.

Cheers!
bManic

[Blue Cat Audio]

Especially for live events a linear-phase filter can hardly be used because of its latency.

It depends on the implementation: for example that's not the case with Blue Cat's liny EQ: it is a no-latency linear phase eq which is suitable for live events as well.

[JonnySun 2.0]

@ christian budde: What do you think about the algorithmix-Eqs?

[Christian Budde]

It depends on the implementation: for example that's not the case with Blue Cat's liny EQ: it is a no-latency linear phase eq which is suitable for live events as well.

Sorry, but that's wrong. In fact there IS a latency of at least 1 sample and 127 samples if you do not count pre-ringing! I wouldn't compensate this, that's right, but there definatly IS latency.
On the other hand, it is damn OK for live issues. It's about 3ms @44100 which equals to the way sound needs to travel 1 meter.
It also has got other issues. Testing the demo, it shows, that it attenuate the signal by -3.3dB and boosting +40dB only results in a boost of 34.7dB that is 38dB in total and not 40dB. It's even more worse tith the cut. Cuting a single band to -40dB it delivers a real attenuation of -15dB. It also introduces high frequency ripple in the range >10kHz of about 1dB.
Boost/cut of more than 1 band delivers true +-40dB.

To summarize it, i bet you are using some kind of Parks/McClellan algorithm, don't you?

@ christian budde: What do you think about the algorithmix-Eqs?

I have tested them 2 weeks ago. I was a little bit disappointed of the results. The CPU usage was kind of high. Although it does what it should there are several ways to make a more clever implementation on a PC.
It should bring the Weiss EQ1 to the PC. So - I guess - they try to reimplement it. As far as I know the EQ1 is based on Sharc-DSPs. On these it is easy to implement IIR filters and more tricky to do FIR's with it's more tricky coefficient calculation and rendering (usually FFT based). To reach the linear phase they first implement minimum-phase IIR filter and then compensate the phase with a set of allpass filters. This is known in the literature as truncated IIRs (TIIR, only to mention one name amongs others).
It introduces heavy errors after some seconds of processing, so there must be more then one set and interpolation between them must take place (with additional resets of the state variables)... [more technoblabla here]
On the PC it is more easy to implement FIR filters with its more tricky computation of the filters (DSPs do not have sin, cos, tan, ln... these must be emulated)
Although the algorithmix EQs do what they should (linear phase parametric filters) i think there is a much better way to do it (currently about to implement it in 'Electri-Q').
One other thing was ridicular: Red EQ seems to be only the oversampled equivalent to the yellow EQ, which has typical deformations of the bell curve near the nyquist frequency (samplerate/2).

Just some thoughts...

[TomBlock]

Christian,

you took the words right out of my mouth ...

BlueCat:

There is latency - and you should report it to the host so it can be properly compensated.

Greetz,

Tom

[Blue Cat Audio]

There is latency

How did you exactly compute the latency? The effect itself does add any artificial latency since it does not use any FFT of buffering of any kind. The actual "latency" you may experience is due to the filter itself, the same way you get such "latency" with any digital filter which has a higher order than 2.

-3.3dB and boosting +40dB only results in a boost of 34.7dB that is 38dB in total and not 40dB. It's even more worse tith the cut. Cuting a single band to -40dB it delivers a real attenuation of -15dB. It also introduces high frequency ripple in the range >10kHz of about 1dB.
Boost/cut of more than 1 band delivers true +-40dB.

-3db attenuation is due to the log function approximation to increase computation speed, and as you say, you get true +-40dB with more than one band. Having more precision would cost too much in CPU, and we had to find a good compromise. You don't get real time for free!

high frequency ripple

like most linear phase filters

Parks/McClellan

An "home made" kind of, yes.