[sdiy] group delay (of filters) and listening

[Magnus Danielson]

From: "Czech Martin" <Martin.Czech at Micronas.com>
Subject: [sdiy] group delay (of filters) and listening
Date: Tue, 5 Oct 2004 11:56:59 +0200
Message-ID: <D9D56E8FA1A73542BE9A5EC7E35D37FFF39140 at EXCHANGE2.Micronas.com>

Martin,

It seems that I can trust you with bringing interesting topics to the table...

> Some (audiophile) publications make a big fuss about group delay distortions.

Finally!

Un-even group delay has long been under my suspicion. My experience is that the
more un-even the group delay is, the muddier sound, the less clarity in the
sound. The smoother and leaner transient, the better. High-Q systems have
ringing effects and gross group-delay variations around the peak.

> For us it could be different to investigate differences of filters due to this property.
> 
> I have done some experiments on this.
> 
> Test signal were:
> 
> -solo drumset
> -sine bursts
> -narrow clicks
> 
> All signals are only a few seconds long.
> 
> They where fed through a digital allpass filter. The lower frequencies
> had a larger group delay then the higher frequencies.
> The output was listened via headphones, direct A B comparison of processed
> and original data.
> 
> The experiments are not finished. Different allpass frequencies have to be tried,
> also lagging and leading high and low frequencies.
> 
> But it seems that small group delays of up to 1ms are absolutely NOT
> audible. E.g. a single real pole 1st order allpass signal can
> not be distinguished from the original.
> A 3ms difference tended to change the timbre allready.
> This is quite contrary to the waveform, which will alter with much smaller
> group delays.

It's not the delay itself but the distorsion that a certain form of delay
results in. If you toss more poles and zeros onto a certain delay problem you
can equalize the group delay to become much much less. Butterworth has the
maximum flatness in amplitude responce where as Bessel/Thompson has maximum
flatness in group-delay.

Groupdelay is the derivate of the phase responce if anybody cares about
details, so it's about "linear phase". The digital FIR filters are interesting
in that you can create filters that is linear phase thought a chockingly simple
theorem and resulting consequence is actually a great improvement in
calculation speed as well. Sometimes will the methods work for you and not
against you!

Anyway, the phase-wiggle around a resonance will become a group delay bump
(the group delay is higher at the resonance) where as the phase-wiggle at a
notch (double zeros instead of double poles in action) will cause a group-delay
valey (same thing different sign) around the notch.

When you do all-pass you avoid having the amplitude responce confuse the issues
for you, but the group-delay shift is twice than that of their normal variants.

So, we want to keep the dispersion (derivate of group delay, second derivate of
phase) well maintained and low. How low and for which frequency I can't say,
but it seems like low dispersions helps to get a clearer sound. Actually, this
is also how fiber optic people resons about their signals, not to say the
problem is equalent, but as such it is not unique.

> This is a bit surprising for me.
> This would mean that group delay is not an audible property for most
> digital or analog filter designs and applications, except in extreme cases (ringing).
> 
> Any comments?

I would rather conjecture that it's the gross variation in group delay you
should be looking for. For instance, create a 2-pole all-pass filter and set
the poles in different Q-values (and since it is an allpass filter the zeros
move along to create the allpass). Also vary the frequency around the vocal
frequency range. Now that would be much more interesting and much more related
to what is happening out there in the real world.

Now, if I am right, the higher Q value (and thus higher local group delay
distorsion) should have a higher and higher audiatorial impact. These filters
will impact on the impulse responce in more drastic way than low-Q all-pass
and it's the audiatorial sensation of an impulse which is what we "hear".
Change the impulse and the audiatorial sensation differes.
Recall that the impulses will create different gestures in the basilar
membrane. We are good at following gestures you know.

Cheers,
Magnus