Does a speaker in an anechoic chamber has minimum phase behavior?

[René - Acculution.com]

I think that this is a good reference: https://vbn.aau.dk/ws/portalfiles/portal/227876517/2007_M_ller_et_al_AES_Journal.pdf. I agree with everything, but I would take out a polarity flip as a separate fourth system, as opposed to the three they have here (MP, LP, AP). Note how they very clearly state how "Neither the phase nor the group delays should be interpreted as a delay of the signal as a whole.". This is exactly because phase delay and group delay are only apparent delays, where we have missed out on what actually happened right as we turned on the system. Was there an immediate output or not?

 

[René - Acculution.com]

One thing to provoke a little bit, and I think that I mention it in the video I made: There can be no delay in a minimum phase system. If there was, it could not be inverted, as we would need a negative time delay, looking into the future. But, there is an associated phase delay and group delay. But they are general different from the "actual delay" (transient delay, latency, transport delay, initial delay) whatever you want to call it. How phase and time relate, is one of the most misunderstood concepts in engineering.

Also, think about a first order low pass system and a first order high pass system. They have the transfer functions w0/(s+w0) and s/(s+w0). They each have their respective phase and group delay. But, add them together, and you get a 1. They sum to unity. No distortion, no delay. Where did the delay go? It was never there to begin with. There was phase, and we sometimes calculate apparent delays from phase. But usually, it is better to just stick with phase.

This actually also ties in with people saying that the sound in a bass-port is delayed half a period. They are conflating delay and phase delay. But I am working on an article on that topic.

 

[gnarly]

Thank you Rene, for continuing to stress the difference between constant delay and phase.....that in fact, phase has no real delay, only an apparent delay.
As I saw Dick Heyser say in an old SynAudCon video, the apparent delay is the only way phase can be mathematically described, but it is not real delay.

I think this is the most fundamental concept in understanding time and phase alignment.
As in "do not pass go until grasped" lol
Took me a long time to see, but wow...how much incredibly simpler time and phase get, once seen.

 

[dasdoing]

well, the phase shifted signal might start at the same time, but it's peak is delayed.
perhaps "time smaring" would better describe it?
however, I personaly don't care for the math. if an all-pass filter aplied to one side of a headphone results in a lateral shift, than for ME it proves it is an (audible) delay

 

[René - Acculution.com]

well, the phase shifted signal might start at the same time, but it's peak is delayed.
perhaps "time smaring" would better describe it?
however, I personaly don't care for the math. if an all-pass filter aplied to one side of a headphone results in a lateral shift, than for ME it proves it is an (audible) delay

Which peak?

 

[dasdoing]

Which peak?

I don't know how to answer mathematicly, but in REW it looks like this (note the filter):

a pure impulse:

phase shifted:

this is the filter

 

[René - Acculution.com]

I don't know how to answer mathematicly, but in REW it looks like this (note the filter):

a pure impulse:

View attachment 300430

phase shifted:

View attachment 300431


this is the filter

View attachment 300432

Well time smearing is probably a good word for the effect of peaks seemingly being delayed.

 

[René - Acculution.com]

An all pass filter can approximate a true delay, but would need to be of infinite order to perfectly do so. Still, within a certain frequency range it is close enough.

 

[gnarly]

Who would posit that an all-pass filter is 'not' a delay? That's easily shown with a non-audible testing scheme.

I would contend that.

Sure, an all-pass will show a relative fixed delay, one side of a xover to another, comparing both sides of it well away from xover frequency.
But what about the phase rotation around the xover freq, the entire range in between the far ends of response where group delay is assumed relatively constant ????
How helpful is that phase rotation, ever???? Unless you have a juggling act already going on, in need of more juggling? ( IMO, if that's the case, drop the damn juggling balls and start over)

So many folks make the mistake of using group delay as a substitute for a true constant delay...imso.
They are simply not substitutes. True delay is independent of frequency, and should equate to nothing beyond geometric ToFs to acoustic centers.
Phase rotations, and group delay, like in an all-pass filter, are completely frequency dependent. Nothing constant about them other than as already decribed.

 

[René - Acculution.com]

@gnarly I'm not sure what in my statement you have a contention with.
An all-pass filter does have delay (frequency-dependent) and it can easily be measured without resorting to subjective evaluation.
Nothing in my statement is incorrect. I suggest to read it again and not read between the lines.

This is a confusing topic for many audiophiles, but it seems there are some "experts" on here trying to confuse the situation further. This is a topic that's been sorted out many decades ago.

It is not about confusing anyone, it is about clearing up confusion and long-held beliefs. A rational function allpass filter is not a pure time delay, although it for sure has frequency dependent phase delay and group delay. Its phase goes asymptotically towards a finite value for high frequencies, and so it can only mimic a time delay at lower frequencies. So an impulse or any other infinite bandwidth signal will be distorted when run through it. So seemingly, it has not been sorted out, since it is still being contended here.

 

[gnarly]

hi etierevad,

i think the root of many debates about the 'delay' from all-pass, are simply about what do we mean by 'delay'.
The prime root being, do we mean a single constant, fixed time across all frequencies.......or some other form.

I've watched mathematicians, signal processing folks, audio folks......debate what delay and 'group delay mean.
Seems they each have an interpretation taught to them, that often can't converse in prime basics.

Personally, I think it's a grave injustice to conflate delay, which I take to be a constant time, with other frequency dependent translations....
But I'm a simple dude, just trying to put stuff into buckets I can understand and act on...

 

[BenB]

I have found it very informative to generate Minimum Phase filters (and other types of filters) in matlab, and then convolve those filters with an abrupt onset of a pure sinewave. We often know the frequency magnitude and phase response of a textbook filter (2nd order L-R high pass, for example) so we know in advance what the steady-state relationship between the input and output will be for a perfect tone. However, the time domain response of what happens before it settles is intriguing, and can provide good insight. The (MP) output reacts immediately, without delay, but still diverges from the phase of the input.

 

[dasdoing]

I am so afraid to say something wrong, but to my understanding one is delay meassured in time, the other meassured in fractions of the wavelength. so saying phase delay is not delay is like saying a step is not a distance because an elephant step is longer than a mouse step.

 

[dasdoing]

as to why there is output at 0 time even with a phase shift, wouldn't this be because in a minimum phase system the phase shifted signal is basicly put on top of the input signal? so there is delay, but part of the signal, the original, is not delayed. only when they overlap we get cancelation or summing and create the magnitude alteration. I could be still understanding it totaly wrong here

 

[René - Acculution.com]

I have found it very informative to generate Minimum Phase filters (and other types of filters) in matlab, and then convolve those filters with an abrupt onset of a pure sinewave. We often know the frequency magnitude and phase response of a textbook filter (2nd order L-R high pass, for example) so we know in advance what the steady-state relationship between the input and output will be for a perfect tone. However, the time domain response of what happens before it settles is intriguing, and can provide good insight. The (MP) output reacts immediately, without delay, but still diverges from the phase of the input.

Yes I did that too in my video. It is seen how the immediate output can be very close to zero, as if there is a true time delay, at the frequencies where group delay and phase delay are almost equal.

 

[René - Acculution.com]

I am so afraid to say something wrong, but to my understanding one is delay meassured in time, the other meassured in fractions of the wavelength. so saying phase delay is not delay is like saying a step is not a distance because an elephant step is longer than a mouse step.

The issue is that phase delay is defined for a sinuoidal signal that has no beginning time. To see the true transient initial delay, one needs to calculate how that system in question reacts transiently to a particular signal. So yes phase delay is a type of delay but not the only type, whereas phase is unique.

 

[René - Acculution.com]

as to why there is output at 0 time even with a phase shift, wouldn't this be because in a minimum phase system the phase shifted signal is basicly put on top of the input signal? so there is delay, but part of the signal, the original, is not delayed. only when they overlap we get cancelation or summing and create the magnitude alteration. I could be still understanding it totaly wrong here

For any system there is a transient response and a steady state one. MP and NMP can have an immediate output. But if some of NMP is coming from a true time delay then there will zero on the output for that amount of time for any input.

 

[KSTR]

The issue is that phase delay is defined for a sinusoidal signal that has no beginning time. To see the true transient initial delay, one needs to calculate how that system in question reacts transiently to a particular signal. So yes phase delay is a type of delay but not the only type, whereas phase is unique.

I've always felt phase delay is a problematic naming convention. Phase offset would be much more adequate IMHO, which is an angle and runs modulo 2pi. The apparent visual time offset between the waveform plots then runs modulo one period, and this finally can be converted to a time measure when frequency is given.

 

[René - Acculution.com]

I've always felt phase delay is a problematic naming convention. Phase offset would be much more adequate IMHO, which is an angle and runs modulo 2pi. The apparent visual time offset between the waveform plots then runs modulo one period, and this finally can be converted to a time measure when frequency is given.

Yes rarely is it needed to involve the delay when you can just state the phase and work the issue out from there. But the other way around can make for a nice example: Two drivers that are not distance aligned so there is an associated transport delay. How well can an all pass filter on the nearer driver compensate for that with a phase shift. I think I will make that.

 

[KSTR]

i think the root of many debates about the 'delay' from all-pass, are simply about what do we mean by 'delay'.
The prime root being, do we mean a single constant, fixed time across all frequencies.......or some other form.

I've watched mathematicians, signal processing folks, audio folks......debate what delay and 'group delay mean.
Seems they each have an interpretation taught to them, that often can't converse in prime basics

This!

Actually I think the basics are very simple:
- An all-pass is a filter which passes all frequencies with the same constant magnitude. Phase vs. frequency is arbitrary by definition and can be anything from flat zero to random noise.
- When observation bandwidth is limited (say, to 20kHz), an all-pass can be setup to have the same exact phase response within that bandwidth like a true time delay and thus is a time delay when viewed as a black box. This class of all-passes is commonly referred to as delay all-pass.
- Another class of all-pass are phase shifters that emulate or counteract simple phase transfer-functions. A typical example would be a phase shifter in a 2.5way active speaker for the woofer path that has the matching phase response of the band-limited "assistent" second woofer (the .5-way), for correct summing and lobing.