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Discussion Starter · #1 ·
Until all processing, equalization, and crossover functions are handled completely in the digital realm using digital connection between source and prepro, with 20 or so DAC's for the resultant channels, we're stuck with analog solutions.


So, if the goal was designing a phase coherent system, could this be done using a typical prepro and analog devices? Let's assume (to keep it as simple as is possible) that mid/high drivers acceptably in phase using passive XO's, and just limit the discussion to low frequency information.


Here are the issues that concern me:


(1) Speakers are at different distances from the listener. Delay can bring everything in phase, but what happens when you take low frequency information from the right surround and right front speakers (that was common information) and send that to the same subwoofer? How would you properly apply delay to keep things in phase?


(2) Different crossover points. Even if you use a phase coherent Linkwitz-Riley crossover for sub/mid separation, it is my understanding that such crossovers are only relatively phase coherent between outputs on a single channel, but that the absolute phase is dependent on crossover frequencies. So, if you set the low freq. XO point on the mains to 60Hz, and the surrounds to 80Hz (for example), then would the low frequency information not be out of phase between the two (again, considering the case of common information played through both front and rear speakers simultaneously)?


(3) Processing done on select channels. Does a Linkwitz Transform alter the phase of the signal passing through it? Parametric EQ? Even supposing equalization is done in the digital realm (BFD), would there not be a net "processing lag" applied to that information? Does that require an appropriate delay to be added to all channels that were not processed in order to maintain proper phase throughout the system?




So, starting from scratch, say you have five channels of discrete audio in analog form. Assume that the sub LFE channel has been compiled into the L/R main channels. Assume that all five channels will need sub/mid crossover at some frequency. How would you design the crossover and processing (EQ etc.) for the system? How many phase adjustments would it take, and where would they be placed? I know the result would go against the KISS theory of audio reproduction, but I'm interested in knowing, in principle, how a completely phase coherent system would be designed.
 

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Bigus,


there is no way to do this in the analog domain, because there is no pure, ideal delay circuit in the analog domain. So, you would have to do it digitally, and you could, if you had a few DSPs. But it would be a lot of programming.


Now, you could design a compromise system that would work, but it would depend heavily on the speakers, because their separate delays between drivers would probably be a big factor.


If you decide instead to apply the KISS theory, try Dunlavy speakers. They are the most time coherent out there. If you had 5 of the same Dunlavys and a sub, it would be pretty darn time-aligned.


Tim
 

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Discussion Starter · #3 ·
Out of curiosity, what kind of circuit is used in prosound gear (all analog, btw) that has a delay adjustment? Usually it is from 0 to 2ms. From your description, it must have some problems... can you explain a little more about that without writing a book on the subject?


Also... I said "delay" circuit, but can the same thing be accomplished with an adjustable phase? I know those are commonly used on subwoofer and other crossovers, and are analog. What is the difference in a "phase" and a "delay" circuit?


Maybe I was confusing things and mixing terms in the first post. I suppose there is a difference between delay and phase that I didn't really differentiate. So, "time aligned" is not really possible with analog means, but the question was really "phase coherent."


Shouldn't phase coherency be more important than time alignment in the overall scheme of things? Or... couldn't you use the pre/pro's digital delay adjustment to set a delay for each channel that gets you pretty close, and then use an analog phase adjustment after active crossovers to treat the issues I brought up in points 1 through 3 above?





Here's the deal... if I cross over the surround speakers at a different frequency from the mains, and sum all that information into a common sub, then I want that information to at the very least be in phase before being summed (for cases where sub information is shared among multiple channels in the source material). Time aligned would be nice, in phase is critical IMO.


What would it take to accomplish that?
 

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There is one big point that you are missing, and I will first write it down in a very simple logical equation. Note, this is definitely *not* a mathematically correct statement:


time = phase


The basic concept here is a "phase" delay is the exact same thing as a "time" delay. But, as frequency is the time derivative of phase, the same time delay at different frequencies corresponds to different amounts of phase. This is why a "linear phase" filter has a constant time delay. However, there is no ideal analog filter that has an "all-pass" magnitude response, while at the same time having a "linear-phase", or constant time delay, phase response. You can get close, but if the speakers are not time-coherent (or, equivalently, phase coherent), then that is not what you want anyway.


As to what analog circuits show up in pro gear to implement a phase shift, I don't know, but a lot of pro mixers perform the signal processing in the log domain.


Bottom line, what you want can *certainly* be done, but it is very complicated. You need to understand filters and you also need to know the specific requirements of your system. This would be very difficult because unless you know the transfer functions of the DSP filters that differ between front and back, you can't "invert" them.


Tim
 

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Discussion Starter · #5 ·
After some more research, I believe I understand what you are saying. Current analog phase adjustments are frequency dependant... that means the phase shift varies with frequency. Therefore, you can only set phase coherence at one frequency (typically the crossover point), but cannot maintain phase coherence throughout the frequency range.


I understand now that active crossovers (or any crossover, of any design, for that matter) act much in the same way. They phase shift the signal depending on frequency. The best you can hope to achieve is that the outputs of various passbands shift the same relative to other passbands.


Now for the tricky part... I also understand that the amount a crossover phase shifts the signal is dependant on not only the frequency, but also the crossover points. Therefore, while two channels may remain phase coherent within the channel, they may not be phase coherent between channels (if XO points are different). And the difference in phase between them will be dependant on frequency (AFAIK).


Now for the million dollar question: if the phase difference between channels with differing crossover points is dependant on the frequency of the source signal, then can a phase adjustment circuit which is also dependant on the frequency of the source signal be constructed so that the final phase between channels is coherent?
 

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The last time I worked with a pro who designed crossovers, it was 1982 and we were just starting to think about crossovers that work in the digital domain. The puzzling thing was the claim that digital crossovers could be made that would not introduce phase shift. The math seemed to indicate that there would be phase shift no matter how you accomplish the separation of frequency ranges.


Let's back up a second -- in the analog domain, there are no crossovers without phase shift. Or time delay. But what makes crossovers objectionable is not phase shift, it is crazy discontinuous loop-the-loop phase shift. Smooth, gradual phase shift seems to be a characteristic of speakers that image well, where you say "Omigod! Listen to that orchestra!" and nutty phase shift characteristic of sound that makes you say "Omigod! I hear a &*$#%& speaker!"


This search for perfect phase coherence with multiple speakers implies that one listener will sit in one spot and never move. Or that you will have a monaural system. Or headphones.
 

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Discussion Starter · #7 ·
Interesting that digital crossovers might have to introduce phase shifts as well. I had assumed that there would be a way to avoid that, but 'fo sho' I had never attempted the math to see if that was actually true or not.


If you are knowledgeable in this area, I'd be ever so greatful if you could answer a question for me, which is really at the heart of my problem:

If I use Linkwitz-Riley crossovers for each channel, but use different low/mid crossover points for some of the channels, and sum that low frequency information to a common subwoofer, will I have phase problems with source material that plays a common low frequency into multiple channels?


I understand (now) that all crossovers shift phase. I understand that L-R have a nice and gradual shifting with the same shifting done for each passband. I have a suspicion that the amount of shifting is dependant not only on input frequency but also crossover points. If so, would that not cause problems in the scenario described above?
 

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I love theoretical discussions!
Quote:
(3) Processing done on select channels. Does a Linkwitz Transform alter the phase of the signal passing through it? Parametric EQ? Even supposing equalization is done in the digital realm (BFD), would there not be a net "processing lag" applied to that information? Does that require an appropriate delay to be added to all channels that were not processed in order to maintain proper phase throughout the system?
Yes, Yes, Yes, and not not really.

Parametric EQ does add phase shift. Even digital EQ adds phase shift. Actually, digital EQ is almost always done with an IIR filter in a "bi-quad" structure (that means that there are two quadratic equations - one in the numerator, one in the denominator - in the transfer function in the Z-domain. This is being the scope of this discussion though). This type of filter models an analog filter very very well. So well, that the phase response of the digital filter is identical to that of the equivalent analog prototype. It is just more accurate, less noisy, and easier to change the parameters (ala parametric EQ) than in the analog domain.


Here is a curious thought: any irregularity in the magnitude response (what most people call the "frequency" response) of your system caused by the room (or another element) will be accompanied by a corresponding phase shift. For example, if you have a peak (resonance) in your system at say 65 Hz (say 10 dB, with a "Q" of 1.0), you will also have a phase shift at 65 Hz. Here's the kicker: that phase shift is the same as what would be introduced by simulating the same magnitude response via a parametric EQ (analog or digital IIR). It also happens to be the same, but opposite of the phase response of the opposite magnitude response (a dip of 10 dB with a "Q" of at 65 Hz). So, if you correct the room repsonse by using a parametric EQ to introduce that dip in the magnitude response, you will actually correct the phase of the sound that you hear, rather than adding a nasty phase irregularity, which is what most people would have assumed. So, EQ isn't the nasty beast that some people think. Applying it intelligently can correct not only magnitude response problems, but also phase response problems as a side effect. Unfortunately, fixing a dip in the resonse is not so easy. On paper, it works, but in reality, fixing just a 3 dB dip will require 2x the power output; fixing a 10 dB dip requires 10x the power; 20 dB requires 100x the power. Most dips need to be ironed out by smart placement of the speakers and of the listener.


[ You can 'see' the phase response problem of the room's response (that peak I was talking about) by looking at the measured impulse response of the system. A system with said peak (resonance) will have a ringy impulse response. DSP theory tells us that, on paper, impulse reponse can be found by the convolution of the phase response with an impulse. An irriegular phase response gives an irregular impulse response. So correcting a ringy response (mostly in the bass: boomy, muddy, innaccurate sounding bass) is often as easy as flattening the magnitude response, and letting those same filters fix the phase resonse simutaneously as a side effect.]
 

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Discussion Starter · #9 ·
Whoa, pretty cool. That would make me feel a lot better about using a Linkwitz transform to flatten bass response, or a parametric EQ (even digitally executed like the BFD) to do the same.


I'm still stuck on the different crossover point thing though. Really... if you could tackle that one I'd buy you a beer or something. :)


Take two channels for simplification: one channel has a three way L-R 24db/oct active crossover with XO points at 80Hz and 300Hz; the second has a three way L-R 24db/oct active crossover with XO points at 100Hz and 300Hz.


The crossovers are each phase coherent within themselves, meaning that at the XO points the high/mid and low/mid outputs are in phase. However, it is my understanding that the absolute phase is shifted depending on both input frequency and XO points. If that is true, then what happens when you play a common ~60Hz or ~80Hz tone through both channels, and then sum the low pass of each channel into a common subwoofer? Would you not have phase alignment problems between the two channels playing the same source tone?


Expanding on the question a bit, what changes when the XO points are 80/300 and 80/250 on the two channels, respectively?


And, if there really is a problem here, is there any way to correct it?
 

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Discussion Starter · #10 ·
bump in case some genius gets bored and wants to tackle that question. :)
 

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Discussion Starter · #11 ·
^^ still hoping ;) ^^
 

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I would imagine you might have cancellation problems from having more than one source playing the same tone.


If you really want to play around with phase and delays, something like the dbx Driverack 260 might be handy.


I have one which I use in an active DIY 3 way system.


It's a digital crossover and EQ unit that also allows you to adjust delays and phase for any of the drivers independently.


Cost was under $700.


As soon as I can work out how to accurately measure phase response I'll start seeing what kind of difference tweaking it does.


Steve
 

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Bruce,


I have the demo program but have been having problems getting it work with my laptop. Hopefully it will do all the things I need when I sort them out.



Steve
 

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Bigus' question is interesting. In general, sending signals through two paths, each with flat amplitude response but with complicated and non-matched phase responses and them summing them would lead to an overall system with non-flat amplitude response. However, some systems have "minimum-phase" characteristics that provide the properties described by macboy: phase is predictable from amplitude and vice versa. I think that in these systems, the phase responses through the two flat-amplitude system, though complicated, may not cause cancellations.


Not up on Linkwitz, but if these are designed to achieve minimum phase, then I think that this is the key to eliminating the cancellations.


Of course, this is all about summing the two signals coherently before the sum goes to a single speaker. The more interesting question is whether any system could remain coherent if the signals were sent to two speakers in the same room. I expect we could get some differences of opinion about that. And there is a fun question about the audibility of absolute phase we could go after...
 

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Steve,


Yea, my observation is that you need a notebook designed for multimedia capabilities i.e. a full-duplex soundcard.


My old Hitachi notebook uses Yamaha media control devices in my Control Panel, the Yamaha software supports full-duplex mode.
 

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Discussion Starter · #17 ·
lol. :) Someday I'll run across someone that really knows their Linkwitz stuff. :D


I think LR crossovers are designed to be mimimum phase, but can't seem to find a referenct to that effect when I search for it. Maybe I'm confusing that with something else I read along the way.


There are two things I am missing: I don't know how the selection of crossover points in a LR crossover affect the absolute phase (or, even the frequency dependant phase) shift, and I don't know the phase shifting characteristics of the typical phase adjustment circuit.
 

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Try the horses mouth. Siegfried Linkwitz has a website at www.linkwitzlab.com which contains a wealth of information. He also responds to most email requests.


I believe his email is [email protected]



If he can't tell you no-one can.


Steve
 

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Discussion Starter · #19 ·
doh!


You know, I've looked at that site before and I guess it never dawned on me to see if that information was there... you're right, it probably is. Thanks for dragging me outta "stupid" mode. ;)
 

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IIRC L-R 4th order xovers have a zero degree phase offset, which is actually a 360 degree phase offset, i.e. some actual time differential.
 
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