No, phase does not "result" from magnitude and impulse. Magnitude and phase are both frequency-domain characteristics, whereas impulse is a time-domain characteristic.werewolf, a question if i may....
I get that perfect magnitude response = perfect impulse.
Doesn't that also equate to perfect phase response?
Isn't the full relationship of identities that of:
perfect magnitude = perfect impulse = perfect phase?
I mean we are talking infinities, ...line length, dynamic range, perfect reflectors, etc...
It just seems intuitive to me under those conditions that phase would have to be 0 degrees dead flat too ....
If not so, please shed some light , thanks!
Stepping away from the infinite....into real world line lengths..
I feel certain you've seen this stuff, but in case fellow DIYers haven't, the technology in line array rigs like
Martin's MLA YouTube,
or EAW's Anya YouTube
is simply fascinating....to me at least
Oh, I still have a pair of CLS...AcoustatX too...I agree with your assessment,
even if I've converted over to HiFi PA !
In order for a system to have a "perfect" impulse response, the system would need to have BOTH perfectly flat magnitude, AND perfectly linear phase in the frequency domain ... over ALL frequencies ... then, a "perfect" impulse response would be the result, in the time domain.
But remember ... if there's a high-pass filter at, say 10Hz, ANYWHERE in your signal processing chain ... you will no longer have a "perfect" impulse response. OR, if there's a low-pass filter at, say 40kHz, ANYWHERE in your signal processing chain ... you will no longer have a "perfect" impulse response. OR, if there's an all-pass filter at, say 2kHz, ANYWHERE in your signal processing chain (from a crossover filter, for example) ... you will no longer have a "perfect" impulse response. And yet, your ear won't detect the presence of ANY of these ...
Hi werewolf, thanks.
I wasn't trying to say phase 'results' from magnitude...not sure where that inference came from......
I use dual FFT quite a bit and am pretty comfortable with freq domain vs. time domain. I know phase is determined in the freq domain, but I tend to see it as "time expressed vs freq"....maybe I shouldn't
I think your second paragraph confirms what I was trying to say and believe to be true....if any one of impulse, magnitude, or phase is perfect....all have to be perfect. Again, talking perfect..with infinities
Any yep, I get the effects of HP and LP filters. I think that implies we even have to look at a freq past nyquist to establish where phase = 0, when considering relative phase across our limited audio bandwidth, ....?
The frequency domain has 2 components: magnitude, and phase. BOTH of these components are required, to draw a Fourier-equivalence to the time domain. Earlier you wrote that "perfect magnitude = perfect impulse". That is NOT true. BOTH magnitude AND phase must be known, to draw the time-domain "picture".Hi werewolf, thanks.
I wasn't trying to say phase 'results' from magnitude...not sure where that inference came from......
I use dual FFT quite a bit and am pretty comfortable with freq domain vs. time domain. I know phase is determined in the freq domain, but I tend to see it as "time expressed vs freq"....maybe I shouldn't
I think your second paragraph confirms what I was trying to say and believe to be true....if any one of impulse, magnitude, or phase is perfect....all have to be perfect. Again, talking perfect..with infinities
Any yep, I get the effects of HP and LP filters. I think that implies we even have to look at a freq past nyquist to establish where phase = 0, when considering relative phase across our limited audio bandwidth, ....?
It IS true that, if i showed you a perfect impulse in the time domain, you would THEN be able to tell me that the mag is flat and phase is linear in the frequency domain ... but it's best to keep the domains separate, and draw Fourier-equivalence between them ONLY when the entire picture is known (in either domain).
Along those same lines ... if I showed you a magnitude-only plot (frequency domain), and asked you to tell me the impulse response (time domain), you would NOT be able to do it. Not without SOME information that would allow you to ALSO know the phase in the frequency domain (for example, the phrase "minimum phase" may suffice!).
Finally, i don't understand your last question ...
The frequency domain has 2 components: magnitude, and phase. BOTH of these components are required, to draw a Fourier-equivalence to the time domain. Earlier you wrote that "perfect magnitude = perfect impulse". That is NOT true. BOTH magnitude AND phase must be known, to draw the time-domain "picture".
It IS true that, if i showed you a perfect impulse in the time domain, you would THEN be able to tell me that the mag is flat and phase is linear in the frequency domain ... but it's best to keep the domains separate, and draw Fourier-equivalence between them ONLY when the entire picture is known (in either domain).
Along those same lines ... if I showed you a magnitude-only plot (frequency domain), and asked you to tell me the impulse response (time domain), you would NOT be able to do it. Not without SOME information that would allow you to ALSO know the phase in the frequency domain (for example, the phrase "minimum phase" may suffice!).
Finally, i don't understand your last question ...
Thanks again for bearing with me
Ok, may I ask in another way...is it possible to have a perfect magnitude response (DC to light) that doesn't also have linear phase?
My previous last question was about where to establish phase = 0 for determining relative phase through the audio frequency spectrum. I've been taught to use the nyquist frequency for that phase = 0 reference point. But your post about highpass and lowpass filters made me realize that nyquist's mere existence means a low pass is in effect, and phase has already been effected at nyquist. So that we have to look above nyquist where phase is unaffected to find true linear phase where phase =0. Sorry for adding any confusion...this thought/idea probably isn't worth any follow up....
YES. Absolutely. So-called "all-pass" filters have PERFECTLY FLAT magnitude response, but non-linear phase ... they do NOT have "pretty" impulse responses.Thanks again for bearing with me
Ok, may I ask in another way...is it possible to have a perfect magnitude response (DC to light) that doesn't also have linear phase?
And there's several variations of all-pass filters, depending on all-pass "order", and frequency. In the frequency plane, they are characterized by pole locations just about anywhere you want in the left-half plane, and "mirror image" zero locations in the right-half plane (meaning, they are NOT 'minimum phase' filters). Further, we run into them ALL THE TIME in our world of audio ... case-in-point: the combined response of many of our favorite crossover filters in loudspeakers form "all-pass" responses
In audio? Almost NEVER.
By FAR, the ear is MOST sensitive to magnitude response from ~20Hz to ~20kHz. Phase response is a very, VERY distant 2nd-place ... which means that "impulse response" is also a very, VERY distant 2nd-place (since both mag and phase 'conspire' to reveal the time-domain picture).
Here's what that means, in practice: if someone were to show me a time-domain impulse response, and ask me how that system "sounds" ... the VERY FIRST thing i would do, is take the Fourier Transform and examine the MAGNITUDE response, from ~20Hz to ~20kHz. I'd spend a couple hours looking at that, then i'd spend a minute or two looking at the phase response over that same bandwidth. I'd spend no time ... none ... looking at the frequency content, mag or phase, past 20kHz.
(Yes, i know ... MASSIVE ultra-sonic content beyond 20kHz can cause intermodulation distortion in downstream components, behaving nonlinearly, which may give rise to audible components in the 20kHz bandwidth. But for now, i'm still referring to linear systems)
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Lol.....does death even exist?
Ok, I totally agree and get "it's better to say this : flat magnitude + linear phase = perfect impulse" ....it's a guaranteed true statement...
My "flat magnitude = perfect impulse = linear phase" is an intuitive attempt at going one level deeper in understanding all this...and I realize I may well be dead wrong here...
But even in theory, is their an example of how something could produce flat magnitude, perfectly flat magnitude unbounded by frequency ends, that wouldn't also be linear phase...
How can they not go together, they seem to be necessary conditions for each other to exist......I guess I'm just missing something simple...
Sorry if I'm hyping on theoretical extremes...but that's kind what this thread has been about it seems...
YES. Absolutely. So-called "all-pass" filters have PERFECTLY FLAT magnitude response, but non-linear phase ... they do NOT have "pretty" impulse responses.
And there's several variations of all-pass filters, depending on all-pass "order", and frequency. In the frequency plane, they are characterized by pole locations just about anywhere you want in the left-half plane, and "mirror image" zero locations in the right-half plane (meaning, they are NOT 'minimum phase' filters). Further, we run into them ALL THE TIME in our world of audio ... case-in-point: the combined response of many of our favorite crossover filters in loudspeakers form "all-pass" responses
Yes, thank you...i use all-pass all the time...sorry I didn't see this without all the ado
As i think Earl already said, the REAL problem is that too many people want black or white absolutes ... and such things are rarely, if ever, found in worthwhile endeavors.
Does phase matter? YES or NO !!! The answer is: NO, and YES.
I can construct an all-pass filter, of order 100, that will have absolutely, perfectly FLAT magnitude response. But the phase will be SO HORRENDOUSLY BAD, there will CERTAINLY be audible consequences (like, treble delayed a few seconds past the midrange) ... easily recognized, even in a mono system, played-back through a single full-range driver.
But ... but ... how can that be, if phase "doesn't matter" ???
Maybe, we have to allow for a slightly more complex answer sometimes, rather than simply "yes" or "no" ...
LOLPhase shift is all about degrees after all
The real point is this : the ear is much, MUCH more sensitive to deviations-from-flat IN MAGNITUDE, than deviations-from-linear IN PHASE.
Still beating that dead horse ...
Let's say I show you two (2) time-domain impulse responses :
1. The impulse response of a first-order, LOW-pass filter ... with single pole (-3dB) corresponding to 4kHz.
2. The impulse response of a first-order, ALL-pass filter ... with pole/zero pair corresponding to 1kHz ... followed by a first-order low-pass at 40kHz.
The first thing you may notice, is that the impulse response "tail" for #1 is SHORTER. It doesn't look like an impulse, mind you, but it "arguably" looks more like an impulse than #2, because of that shorter tail.
Which one sounds better? Which one has higher "fidelity"?
If your answer is : "i can't really be sure, until i take a Fourier Transform, and examine the magnitude response component over 20kHz" ... then we have a winner
(THIS is a really good post, i think ... in my humble opinion )
Let's say I show you two (2) time-domain impulse responses :
1. The impulse response of a first-order, LOW-pass filter ... with single pole (-3dB) corresponding to 4kHz.
2. The impulse response of a first-order, ALL-pass filter ... with pole/zero pair corresponding to 1kHz ... followed by a first-order low-pass at 40kHz.
The first thing you may notice, is that the impulse response "tail" for #1 is SHORTER. It doesn't look like an impulse, mind you, but it "arguably" looks more like an impulse than #2, because of that shorter tail.
Which one sounds better? Which one has higher "fidelity"?
If your answer is : "i can't really be sure, until i take a Fourier Transform, and examine the magnitude response component over 20kHz" ... then we have a winner
(THIS is a really good post, i think ... in my humble opinion
)
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I would say this: Once one has a very smooth, near flat, magnitude response, then phase linearity can be a factor. But if the magnitude is not smooth then the phase response won't matter. What people do is make their system have linear phase, which invariably makes the magnitude flat, and it sounds better. But they attribute much of this to the phase response, when it may well not be much of a factor.
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