Digital Signal Processing - How it affects phase and time domain

The peaks of the group delay for the sum get bigger as the filter order increase when a delay is introdused
At some level that group delay variance can be heard
I don't follow that, I guess you're talking IIR.???

It doesn't matter what is the order of linear phase xovers; order doesn't change group delay because there is none.
Impulse peaks need to be time aligned.

Unlike IIR xovers that need impulse initial rises to be time aligned.

Se the group delay axis is a bit coace
They all are unless fully smoothed 😉

Here's same 1/4 WL fixed delay, same 1/24th smoothing
but blue is now Excess Group Delay...what we really want to see imo.
Note it needs the sub to complement and flatten it at low corner
1721851133493.png
 
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My experience is that a sharp linear phase system high pass can sound like a pre-echo.
Kind of like hearing a very faint drum whack before the loud real one. Could be heard both indoors and out.
Reminds me of the sound of a powerful firecracker, right before explosion, .....the sound of air sucking inward before going boom..

This was with a 72 dB/oct high-pass at around 30-31Hz. Twas all the tap count could pull, that I had available at the time.
I haven't bothered with any further linear phase system high pass work , other than trying to figure out how weave it with IIR to get the most benign phase alteration, but still safe high-pass, possible.
Just my 2c impressions 🙂
How long was your fir filter in terms of taps, or more importantly in seconds?
 
Group delay is related to phase delay. Derivative
So there clearly must be group delay

You do understand I promote linear-phase speaker tuning? Yes?
Which has flat phase and therefore no group delay?


Remember is the sum of the two signals with a time delay. Ther must be a phase difference somewhere
Hey, you directed me to whack out a correct tuning introducing an incorrect delay....
Of course it's going to adversely effect the summation !

The whole sceptisism towards steep filter comes from this thesis
http://lib.tkk.fi/Dipl/2008/urn011933.pdf#page100
Thesis schmesis !
I prefer to use my own ears and measurements!
 
Ok, the thesis includes controlled listening tests with several people so I prefer that.
On a sidenote I hear those artifacts on steep filters myself.
And your messurements show a sharp phaseshift off axis that gives a big phase delay of axis
Not my ideal design
 
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How long was your fir filter in terms of taps, or more importantly in seconds?
Great question. And agreed, it's "FIR time" that counts, not taps..

The most obvious pre-echo has been from the longest FIR time employed. Which for me has been 65k taps at 48khz. Using PC convolution.
Linearizing the sub response, the sub high pass that is, made for an obvious pre-echo.

Learned later that the pre-echo issue is the lin-phase hpf, not the number of taps.
However, the amount of FIR time and the order of a lin-phase high-pass will make pre-echo worse (if sufficient taps are available to provide low corner freq resolution.)
For me, unless I can get acoustic response flat to DC, Lol, it's IIR high pass!
 
Why is linear phase important? It is of axis so no longer linear phase even if filters are linear phase.
Remember real LR filter has constant 360 degrees phase difference
Linkwitz and Reyley discussed how it performed of axis.
 
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The most obvious pre-echo has been from the longest FIR time employed. Which for me has been 65k taps at 48khz. Using PC convolution.
Linearizing the sub response, the sub high pass that is, made for an obvious pre-echo.
longer FIR IRs have more low energy spread around the IR peak, right? Intiuitively I would have assumed that more taps, i.e. wider windowing would have less detrimental effects. Are you saying your hearing experience seems to contradict that?

EDIT: longer symmetrical, ie phase linear, FIR IRs have more energy far out of the center of the IR peak, they "die down" slower in distance from the IR peak. Thlought that would increase precision.
Learned later that the pre-echo issue is the lin-phase hpf, not the number of taps.
However, the amount of FIR time and the order of a lin-phase high-pass will make pre-echo worse (if sufficient taps are available to provide low corner freq resolution.)
For me, unless I can get acoustic response flat to DC, Lol, it's IIR high pass!
If you care please eloborate on that. Was it actually FIR "effects" that you heard or was it the IIR high pass, which does significantly shape phase in the low octaves. It must, as math dictates 🙂 Been trying to hear effects of such myself, still not convinced how to rate my hearing experiences....
 
Why is linear phase important? It is of axis so no longer linear phase even if filters are linear phase.
Remember real LR filter has constant 360 degrees phase difference
that, to me, is a very good question. Up to now I thought that if the global system's phase response is not linear, i.e. if you have a two way system with perfectly summing LR4 IIR crossover inbetween which introduces a phase shift of 360 degrees around the crossover point, the system at least does not produce anything different being ON axis or OFF axis. Is my assumption incorrect?

EDIT: for this thought experiment, let's assume a mathematical perfect system, or maybe the next closest physical analog, a coaxial speaker system.
 
Why is linear phase important? It is of axis so no longer linear phase even if filters are linear phase.
Remember real LR filter has constant 360 degrees phase difference
Linkwitz and Reyley discussed how it performed of axis.
To the extent that magnitude response doesn't vary off-axis, from on-ax....neither does phase.
So having linear phase/ no group delay with linear phase on ax, extends to off-ax too, given a good acoustic design.

Linear phase is so important once you see/hear it...... imo/ime.
Probably not due to phase audibility itself other than low frequencies, dunno ....but do know it simply provides for easy excellent tuning results.
 
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LR writes about it much better than I ever can
https://www.linkwitzlab.com/JAES/jaes_papers76.htm
me nitpicking:
  • LR is actually SL - Siegfried Linkwitz 😉
  • I tried to talk about coaxial sources, but I only mentioned this in my edit. sorry about that. SL talks about non-coincident drivers which are way more frequent in actual speaker designs. I'm just theorizing with my questions - does the phase shift introduced by IIR crossovers actually introduce (more) problems off axis in a coaxial system? my intuition is that it does not.
 
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longer FIR IRs have more low energy spread around the IR peak, right? Intiuitively I would have assumed that more taps, i.e. wider windowing would have less detrimental effects. Are you saying your hearing experience seems to contradict that?

Yes, impulse is spread out with low freq. Like shown in post #146 3-way, and #104 4-way.

My "theory" is the longer tap count provides for a longer time window too, for generating the FIR filter. When we look at non-normalized impulse peaks of drivers sections, the peaks on low freq section are miniscule compared to high. Linear Fourier math at play.
My "theory" again, is that the increased time span widow of long FIR time, let's the higher freq energy prevail earlier in time vs lower freq energy.
Again pure speculation...just trying to find a rational explanation for what i hear.
 
Of axis is of axis and introduce the same path length difference independent of design.
Path length difference is phase differense leading to group delay.
You dont care, I do

Oh man, you presume far too much...
As in "you don't care, I do"....

Sure, path length differences matter.
So, good acoustic design works to minimized path length differences.
Like trying to achieve as close as possible to 1/4 wavelength, center-to-center spacing between, drivers sections throughout xover region.
That's what I do with the acoustic design. I've built 11 generations on unity/synergy's which as far as I've seen, have the shortest path length differences of any speaker, apart from maybe full-range eletrostats.

Linear-phase xovers are icing on the cake of a good acoustic design. Period.
And ime, steeper only makes them work better.

Believe what you will with the papers you read...
And must say, pls don't ask me for any more measurements, which i sense you are using just to display/debate your preconceived notions.
 
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