Chris A, Could you explain minimum phase analysis, please.

[WMcD]

Chris,

 

In at least on post you had mentioned something was not a minimum phase system, perhaps in room echos.

 

Could you expand on what is or is not a minimum phase system and what means to us.

 

BTW in an early publication PWK was talking about using amplitude to determine phase (hazy on this) and it might have been that a Hilbert transform did this.  Maybe only with minimum phase systems?  Very hazy.

 

Thanks,

 

WMcD

[Chris A]

12 hours ago, WMcD said:

Could you expand on what is or is not a minimum phase system and what means to us.

When talking about loudspeakers and acoustic drivers, a minimum phase system simply has minimum phase shifts relative to its measured amplitude response--you can't push phase shifts down any further if the amplitude response (SPL) is already flattened.  As an example, see the amplitude and phase plot below of a tri-amped JuBelle:

 

 

There are three traces shown.  The top trace is SPL vs. frequency (scale on the left side), the next blue trace is phase relative to the driving electrical signal (scale on the right side), and the gray trace is something called "min phase", which is calculated from the SPL amplitude trace via something called a discrete Hilbert transform.  This min phase trace highlights how much induced or "excess phase" is present--the difference between the blue phase trace and the gray min phase trace.  For this case, I've done a lot of work to flatten the JuBelle amplitude response using a DSP crossover (Dx38), but there still exists significant amount of "excess phase", which is not desirable from a hi-fi perspective.  (More on this to come.)

 

In a true minimum phase system, when I correct the amplitude vs. frequency (using the PEQ filters in a DSP, upstream equalization, or even EQ using a passive balancing network/crossover), the phase also will be corrected at the same time: they're locked together.  If you look at the gray min phase trace and the phase trace in blue, you'll see that there is something else adding phase shifts.  There are at least two sources of these added phase shifts: the crossover filters themselves and nearby acoustic reflections in the room (which I've worked to minimize using close miking and time gating of the measurement).  The majority of excess phase that you see above comes from the DSP crossover filters.  In this case, they are 24 dB/octave Linkwitz-Riley filters on the tweeter, midrange, and woofer at two crossover frequencies: 560 Hz and 8 kHz. In general, the higher the order of the crossover filters used, the more excess phase will be present.

 

So the question arises: why does phase matter?  When looking at steady state response of loudspeakers playing unchanging tones, the ear basically can't hear those phase shifts.  When playing impulsive music, the story changes.  Below you will see a spectrogram plot of the above JuBelle:

 

 

Ideally this impulse response should be vertical on this plot, instead of the phase growth starting below 1-2 kHz that you see here.  This type of phase growth becomes audible at some point, and is particularly noticeable during music impulses...dynamics...that horn-loaded loudspeakers are noted for.  From personal experience, when the phase response is corrected to look more vertical in the spectrogram plot, the loudspeaker sounds better when playing good recordings. 

 

More discussion to come...

 

Chris

[Chris A]

Now the question might arise..."what are non-minimum phase systems?".  In general, anything that cannot be equalized to correct the amplitude response is non-minimum phase.  Room reflections in home-sized rooms are one example.  Room reflections overlaid on loudspeaker direct arrival energy--these are also called non-minimum phase, or perhaps a "mixed phase" system.  There are more technical definitions for both minimum phase and non-minimum phase systems but they all make use of a slew of other concepts--both physical and mathematical--that are far beyond this intuitive discussion.

 

Okay, so how about electrical and electronic/digital crossover and equalization filters?  These are non-minimum phase.  When you put these filters into a circuit that crosses the drivers in a loudspeaker, they produce a non-minimum or mixed phase system.  In particular, all-pass filters that change only the phase of an incoming electrical signal are non-minimum phase.  All-pass filters can be used to compensate for the excess phase seen in loudspeakers, but in general, they simply add excess phase.  The same thing is true for crossover filters--which is usually the source of problems that we are trying to address with loudspeakers. 

 

There is an often-heard comment on audiophile forums that first order filters sound the best when used as crossover filters in a loudspeaker.  The issue, of course, is that first order filters only attenuate the output of the individual drivers at 6 dB/octave--which is too shallow a crossover slope.  But why do these type of filters "sound better".  It's probably because they introduce no excess phase shifts.  If you had acoustic drivers (and time/physical alignment) that had lots of overlapping frequency response with their crossing drivers, then you'd probably see more use of passive first order filters. 

 

 

As it is, there are trade-offs that are made because of real-world constraints on drivers/horns, time alignments, and other phase issues between drivers versus frequency.  So some people go for the minimum interference band widths between crossing drivers (steep slope crossovers), and live with the more extreme phase shifts.  Others use more moderate crossover filters, and live with errors from both excess phase and width of the frequency interference bands.  And still others (what are usually termed "mossback audiophiles") go hard over to using only first order filters.  Pick your poison. 

 

In my case, I've learned that there are ways to correct for excess phase due to crossover filters.  One way is to use something called "finite impulse response" (FIR) filters.  These are implemented in DSP crossovers having lots of computational horsepower.  The downside is cost of the DSP crossover hardware (usually about 2X higher) and added time delays of the crossovers--which usually need to be synchronized with video output in home theater systems.  Anything below 500 Hz in these type of crossovers usually introduces prohibitive amounts of time delays, and require lots more computing horsepower and internal RAM.  So in today's hardware, FIR filters are usually constrained to use above 500 Hz.  But these filters can be used to achieve what is called "linear phase systems"--loudspeakers having no measurable phase shifts.  Great...but generally not economically feasible as yet, especially for fully horn-loaded loudspeakers.

 

 

Another approach is using combinations of low-pass and high-pass filters of differing designs (such as the Harsch configuration) to minimize excess phase growth. 

 

Another way is to use all-pass filters to correct for the excess phase of the IIR filters in DSP crossovers...and also analog filters--like passive crossovers.  These are my preferred approaches.

 

 

More to come...

 

Chris

[Chris A]

So the question might arise: "why are room (and internal loudspeaker) reflections non-minimum phase?".  This is pretty simple.  If you apply the rule that "minimum phase systems must be able to correct both phase and amplitude when EQ is applied", then you'll see why room reflections don't obey that rule.  Whatever you put into the room in terms of input acoustic energy...is reflected and comes back to the measurement microphone, and thereby cancels the direct arrivals coming from the loudspeaker.  So that test fails. 

 

 

How about all-pass filters?  They shift only the phase of the incoming signal, so EQ cannot "correct" for their phase shifts.  It may be said that crossover filters are minimum phase of and by themselves, but when used as crossover filters in a loudspeaker, they only increase excess phase, even if the loudspeaker output is EQed flat. 

 

 

Several people have asked me why I recommend not taking in-room measurements at the listening position.  You may now have a clue to what I'm going to say: you cannot correct for the room reflections using EQ (or anything other than absorption and diffusion at the room reflection frequencies).  If you take your "room correction" measurements at the listening position, you've already thrown away the opportunity to separate minimum phase direct arrival energy from non-minimum phase reflections--except at very low frequencies (usually less than 1/2 wavelength distance from the loudspeakers/subwoofers).  My advice: stop taking your measurements at the listening position--except for frequencies below ~50 Hz.  Take your measurements at one metre in front of the loudspeakers--each one, one at a time, with plenty of absorption material on the floor from the loudspeaker to the microphone position.  There it is...

 

 

As far as the subject of audibility of phase shifts in loudspeakers, this has been a contentious subject in the past--before linear phase loudspeakers were really possible.  Now there are ways to do achieve linear phase loudspeakers (at some price), but note that you're still listening in a non-minimum phase room.  So go find yourself some absorption panels (a lot of them...) in order to hear the difference between linear phase and non-minimum phase loudspeakers.

 

 

More to come...

 

Chris

[Chris A]

17 hours ago, WMcD said:

BTW in an early publication PWK was talking about using amplitude to determine phase (hazy on this) and it might have been that a Hilbert transform did this.  Maybe only with minimum phase systems?  Very hazy.

 

Perhaps I've touched on this subject enough for your curiosity, perhaps not...  If you wish to know more, all you have to do is ask, Gil...I don't want to go past the "TMI" limit...

 

 

I've got a lot more insights on the concept of minimum phase in sound reproduction, but one in particular stands out: the EQ that mastering engineers put into our precious hi-fi recordings, as if "that's okay".  It isn't.  Recordings are "minimum phase systems".  Fortunately, if the mastering engineer used IIR filters to EQ the stereo downmixes, then we can reverse the effects--perfectly, if we know what the original spectrograms of the downmixed stereo tracks looked like.  Also fortunately, I've discovered that there is a way to do this using the "1/f" (-5.5 dB/octave or -16 dB/decade) approach as a target for your demastering cumulative spectra for each music track, along with careful auditioning of the results. 

 

Why demaster, and what does demastering do?  Well, that's a subject of great interest, since we now know that we can undo the lion's share of what the mastering guy did to our music.

 

 

More to come...

 

Chris

[Khornukopia]

2 hours ago, Chris A said:

Several people have asked me why I recommend not taking in-room measurements at the listening position.  You may now have a clue to what I'm going to say: you cannot correct for the room reflections using EQ (or anything other than absorption and diffusion at the room reflection frequencies).  If you take your "room correction" measurements at the listening position, you've already thrown away the opportunity to separate minimum phase direct arrival energy from non-minimum phase reflections--except at very low frequencies (usually less than 1/2 wavelength distance from the loudspeakers/subwoofers).  My advice: stop taking your measurements at the listening position--except for frequencies below ~50 Hz.  Take your measurements at one metre in front of the loudspeakers--each one, one at a time.  There it is...

You are talking about measurements in the process of adjusting and optimizing one individual speaker using REW, correct? Measurement instructions for Audyssey, MCACC, YPAO, etc. suggest the first measurement be taken at the main listening position and the following measurements in the listening area.

[Chris A]

I have a real problem with Audyssey...as you probably know already.  The whole concept rests on assumptions which for me aren't valid (and there any many assumptions that are not stated anywhere that I've read, but that I've run into using their firmware).  I believe the concept to be fundamentally flawed--except for perhaps the lowest frequencies below 50 Hz.  I'm not alone...Floyd Toole also has problems with "room correction software" in his latest 3rd Edition book.

[Khornukopia]

The auto-EQ systems are probably designed more for simple, average home theater set-ups. It seems to work good on several systems I have listened to. 

 

So, back to minimum phase, is there an off the shelf Klipsch model that is an example of a minimum phase speaker?

[Chris A]

14 minutes ago, Khornukopia said:

So, back to minimum phase, is there an off the shelf Klipsch model that is an example of a minimum phase speaker?

 

Not that I'm aware of.  There are some examples on the diyAudio forum, but all of them are DIY using DSP correction. 

 

One company that produces them using all passive components is out of business, i.e., Dunlavy.  Dunlavy himself was a very interesting guy--like he invented log-periodic antennas in the 1950s among other things.  RIP Mr. Dunlavy.  I learned some interesting things from the brief comments that were made in that Stereophile article on him.

 

I'm working on a DIY multiple entry horn that would be much closer to a linear phase system than anything that I've owned.

 

Chris

[Chris A]

One of the comments that I recently read again (and it finally sank in) in the Danley Synergy patent--US8284976--is that the passive crossovers use non-integer order filters, use crossover point filter overlaps (which I independently found myself is necessary), and have non-constant slope filters (which Roy instituted on the original Jubilee Dx38 crossover settings). 

 

 

Chris

[Deang]

I have a really bad headache!

[JohnA]

Well, dang Dean!  Put down the bourbon!!!   BBWwwaaaaHaaHaaa! 

 

 

[Chris A]

So we've covered:

1. minimum phase for loudspeakers and crossover filters,
2. all-pass filters,
3. examples of non-minimum phase systems such as room acoustics,
4. excess phase and using the Hilbert transform to calculate excess phase,
5. FIR filters to create linear phase systems (i.e., flat phase response and amplitude response)
6. engineering definition of minimum phase using complex math (like handling real and reactive components in crossover filter design)
7. examples of minimum phase and linear phase loudspeakers, and
8. touched on recordings as minimum phase systems. 

While it seems that all of these topics are not really related, it turns out that the concept of phase and minimum phase binds all of them together for the subject of hi-fi sound reproduction. 

 

The last topic of music recordings and minimum phase is a topic of great in interest in my experience, especially if we can largely correct the equalization used to regain not only overall balance of the instrumentation and voices, but also clarity--which is lost the instant that the mastering person applies any amount of stereo EQ to the tracks.  Here is a presentation describing why this is so for concert halls and lecture halls (nominally considered non-minimum phase systems), but the same effect is also directly applicable to the minimum phase systems of music and other sound recordings. 

 

It seems odd to me that the music business would so strongly defend the practice of applying equalization across the final stereo tracks (after the mixdown process), but there seems to be little that the industry does that inspires trust and confidence by hi-fi enthusiasts, especially since the beginning of the severe loudness war music practices in 1991.

 

Chris

[Edgar]

22 hours ago, Chris A said:

Another approach is using combinations of low-pass and high-pass filters of differing designs (such as the Harsch configuration) to minimize excess phase growth. 

 

 

I've never heard of the Harsch configuration before, but I presented a simpler and better-performing solution at AES in 1999: http://www.aes.org/e-lib/browse.cfm?elib=8170. I can provide copies to anyone interested.

[Chris A]

Could you look over the things that I said above and flag anything that's not correct?  I'm particularly talking about the topic of minimum phase and crossover-type filters, but anything here is fair game.   I really don't profess to be an expert in this domain, so I have little skin in the game.  Gil directed the questions at me and I tried to answer them at a level that conversant readership might follow.  It's a subject of some interest in my view.

 

Chris

[Chris A]

I'd like a copy of your presentation, BTW...  I'll send a PM.

 

Chris

[Chief bonehead]

5 hours ago, Chris A said:

The last topic of music recordings and minimum phase is a topic of great in interest in my experience, especially if we can largely correct the equalization used to regain not only overall balance of the instrumentation and voices, but also clarity--which is lost the instant that the mastering person applies any amount of stereo EQ to the tracks.  Here is a presentation describing why this is so for concert halls and lecture halls (nominally considered non-minimum phase systems), but the same effect is also directly applicable to the minimum phase systems of music and other sound recordings. 

 

It seems odd to me that the music business would so strongly defend the practice of applying equalization across the final stereo tracks (after the mixdown process), but there seems to be little that the industry does that inspires trust and confidence by hi-fi enthusiasts, especially since the beginning of the severe loudness war music practices in 1991.

 

Chris

not all recording engineers and recordings are created equal.  i have been on both sides of the fence.  as a musician, there is always a "sound" that a musician is looking for.  on the other side of the board there always has to be some sort of eqing and compression that is benficial to overcoming things like mics, placements, etc.  where i agree with you is the over use of eq and especially compression on the recording and mastering process.  to me that just takes the life out of the music that is being attempted to be capture.  

 

these types of common place techniques can be attributed to some bad practice.  as you mention, loudness wars is the main culprit.  bad recording techniques, bad equipment choices. and my favorite, playback speakers.  i tend to get annoyed when people say, "what speakers should i get?  well it depends on the kind of music you listen to."  not realizing that what they are compensating for is the recording.  

 

any way, sorry to take this off topic.  as far as phase and all that jazz, i tend to look at it, as i do almost everything in my work, from an acoustic perspective.  i dont get into the weeds unless it messes up what i want to achieve something acoustic.  then i get the weedeater out and try to understand what is the problem i am trying to overcome.  if it turns out that other parameters, such as minimal phase looking good is a result of that, then its ok by me.  as long as it produces acoustic fruit...that is tasty of course....  

[Chris A]

One thing that I've noticed from my conversations with the "mastering guys" online is that what they consider "appropriate" is probably 3x to 10x greater into EQ and limiting (on a dB scale) than what I consider appropriate, with the guys doing most of the popular music (pop, rock, etc.) the most intrusive.  I think that taste in music is sometimes all in the mouth with some of those doing the taste tasting (i.e., music producers).  For example, see http://mixbus.harrisonconsoles.com/forum/thread-5426.html.

 

Merry Christmas, Roy!

 

Chris

[Travis In Austin]

1 hour ago, Chief bonehead said:

then i get the weedeater out and try to understand what is the problem i am trying to overcome.  if it turns out that other parameters, such as minimal phase looking good is a result of that, then its ok by me.  as long as it produces acoustic fruit...that is tasty of course....  

What kind of weed eater do you use?

[Edgar]

5 hours ago, Chris A said:

Could you look over the things that I said above and flag anything that's not correct?  I'm particularly talking about the topic of minimum phase and crossover-type filters, but anything here is fair game.  

 

It's all good.

 

I could add a little formality to the description by saying that not only do minimum phase systems have all of their zeroes in the left half-plane (or inside the unit circle if digital), but the magnitude and phase of a minimum phase system are related by a natural logarithm and Hilbert Transform. But that doesn't add anything intuitive.

 

One very important fact about minimum phase that should be intuitive is that minimum phase systems concentrate the majority of the energy at the beginning of their impulse response. In other words, when hit with a transient, the majority of their response to the transient comes during and immediately after that transient -- the response does not build up slowly to a peak and then slowly die out.

 

Oh, and despite the claims about the wonderful attributes of linear-phase filters that you see in the literature, they are decidedly not minimum-phase. In fact, their transient response does exactly what we do not  want -- they build slowly to a peak (often called "pre-ring"), and then slowly die out. So while linear phase filters definitely have their place in the world, they are not the best choice in all cases.

 

Edited December 22, 2017 by Edgar
Added natural logarithm.