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Old 7th January 2013, 02:39 PM   #111
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Yes, but phase response of LP and HP are identical. Thus sum is minimum phase, identical to LP and HP components. This is beauty of Linkwitz-Riley transform. Convolution of a Butterworth filter with itself, cascading stages, same thing.
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Old 7th January 2013, 02:44 PM   #112
jcx is online now jcx  United States
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LR4 has 360 degrees phase rotation (right axis, green dotted line)

normalized plot - fxo = 159 mHz (1 rad/s)

the green sum frequency response amplitude is flat at 1.0 - under the cursor dotted line in the 1st plot

Tg=Group delay (yellow, left axis) is in seconds for this low freq - would be x10 ms for 160 Hz XO frequency

the 1/6 Hz square wave .tran green sum shows lots of phase error

red LP is nearly a sine in the .tran plot - but with basically inverted polarity
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File Type: png lr4_tran.PNG (40.9 KB, 203 views)
File Type: png lr4_ac.PNG (49.7 KB, 200 views)
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Last edited by jcx; 7th January 2013 at 03:07 PM.
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Old 7th January 2013, 02:55 PM   #113
jmbee is offline jmbee  France
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Quote:
Originally Posted by Barleywater View Post
Yes, but phase response of LP and HP are identical.
Imo, they just seem to be, but are not : 360 between lp and hp is a reality
witch appears in transcient response of the sum. It's a bit like, for the sum, 360 had been lost.

crd
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Old 7th January 2013, 02:57 PM   #114
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Quote:
Originally Posted by jcx View Post
LR4 has 360 degrees phase rotation (right axis, green)

normalized plot - fxo = 159 mHz (1 rad/s)

the green sum frequency response amplitude is flat at 1.0 - under the cursor dotted line in the 1st plot

Tg=Group delay (yellow, left axis) is in seconds for this low freq - would be x10 ms for 160 Hz XO frequency

the 1/6 Hz square wave .tran green sum shows lots of phase error

red LP is a sine - but with basically inverted polarity
......and this is why I swear by 1st order filters.
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Old 7th January 2013, 03:03 PM   #115
jcx is online now jcx  United States
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the probelm with 1st order is that the amplitude of motion for the tweeter never goes down from the XO - only the from the tweeter's own electroacoustic/mechanical mass-spring HP

so you get more motor/spider/amplitude distortions from the driver below the XO freq, can cause higher IMD, Doppler in the passband

and you need lots of driver response overlap so the tweeter driver's HP doesn't cause a audible dip, or LF driver cone breakup resonances don't give bumps above the XO freq

Last edited by jcx; 7th January 2013 at 03:33 PM.
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Old 7th January 2013, 06:33 PM   #116
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This thread has covered a lot of ground and I can't remember all of it so if I missed something, (likely) please forgive me. I'm not a strong math guy but here goes:

Group Delay or Envelope Delay seems to be a simple concept and at once something that I haven't really been able to clearly wrap my head around. The simple part, when what goes in comes out spread over time, that is group or envelope delay as compared to if it all came out at once but late, that is latency. Latency is functionally the same as excess group delay as in time of flight from a driver under test to the mic. Right?

Is group delay one of those math functions that breaks down when approaching infinity or zero? To me it seems like group delay goes infinite when frequency approaches zero.

There was a discussion on Pro Sound Web a while back where someone stated something to the effect that: "It seem counter intuitive that a woofer has an increasingly harder time tracking a signal at low frequencies than high, but that's the way it works." I think that's wrong, so I did some experimenting.

I set up my dual channel measurement system TEF, with a Techron 7570 DC coupled 2kW power supply driving a new JBL 2242 in free air with a mic on TEF Channel One in very close proximity to the dust cap and my laser position sensor on TEF Channel Two right next to the mic "lookiing" at the dust cap. I also connected my four channel Tektronic scope to the output of the amp, the mic, and the laser for visual tracking as well. I can set cursers on the scope and get real time and or degrees between channels, like the amp and laser position.

The short of what I found was the driver physcally follows the signal at low frequency and gets later as the frequency increases. I started at 0.25Hz to be sure I wasn't a cycle off. So, if the driver gets later and later as the frequency increases, why does the "measured" group delay increase as frequency decreases if it is not a math thing? And if it's just a math thing, why should I worry about it?

I took a bunch of pictures of the set up and can't find them, I can recreate it and think I should revisit this.

Any thoughts?
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Old 7th January 2013, 07:36 PM   #117
jcx is online now jcx  United States
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engineers usually try to use math to model reality

a finite time delay becomes an infinitesimal phase at infinitely low frequency - so that works out fine

in the normal operating range of dynamic loudspeakers the SPL output is proportional to cone velocity

below the mass-spring resonance a dynamic driver displacement is proportional to the coil current caused electromagnetic force pushing against the spring constant of the spider/suspension (and the enclosed air for sealed box speaker)

in the working range for audio output, above the mass-spring resonance, the mass of the cone+voice coil rolls off the amplitude, this inertia and electromechanical coupling causes the the cone velocity to become mostly proportional to AC drive voltage

Last edited by jcx; 7th January 2013 at 07:49 PM.
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Old 7th January 2013, 10:14 PM   #118
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Quote:
Originally Posted by 1audiohack View Post
This thread has covered a lot of ground ........
Any thoughts?
Sure has......

For your measurements/observations did you look at behavior before and after resonance frequency of driver system?

I do bulk of measurements with exponentially swept sine. Pairing response recording with test sweep shows a lot. In pairing you can look at zero crossings of the waveforms and get near perfect alignment as each pair of zero crossings has unique time interval. Scanning forward/backward shows crests/zero crossings shifting in frequency dependent manner.

Getting all the zero crossing to correspond over desired bandwidth is goal of phase correction. Crest amplitude correction simultaneously is also goal. Waveform fidelity.

For experimental purposes, time delay incurred for processing to get this result is not consideration.

Achieving this result allows creation of reference conditions where questions such as this thread topic may be addressed.

Quote:
Originally Posted by turbodawg View Post
......and this is why I swear by 1st order filters.
1st order filters have perfect transient response, and without time reversal are of no practical use for improving time domain issues inherent in speaker design. The only way to get perfect sum with them in crossovers is to use identical drivers. Beaming of woofers with breakup excitation in overlap region, resonance of tweeters and IMD, driver separation at usable crossover frequency.... Yes, the simple pleasures in doing nothing new and the knowledge that one is experiencing the same speaker performance of sixty years ago.
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Old 7th January 2013, 10:15 PM   #119
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Quote:
Originally Posted by 1audiohack View Post
Group Delay or Envelope Delay seems to be a simple concept and at once something that I haven't really been able to clearly wrap my head around. The simple part, when what goes in comes out spread over time, that is group or envelope delay as compared to if it all came out at once but late, that is latency. Latency is functionally the same as excess group delay as in time of flight from a driver under test to the mic. Right?
Just think of group delay as a way to describe the relative delay between different frequencies (the curve of the graph) and latency as a constant offset (like a DC bias on the graph) that introduces a minimum delay upon which that curve rests.

In most applications the overall latency doesn't really matter (we don't care if the sound from our speakers arrives 1ms later if they're 1 foot further away, when there is nothing else to compare them to) so software that measures group delay provides a way to subtract out this latency - in ARTA the settings is "delay for phase estimation", which changes the slope of the raw phase response and thus moves the group delay line up and down a constant offset. (Since group delay is the derivative of phase)
Quote:
I set up my dual channel measurement system TEF, with a Techron 7570 DC coupled 2kW power supply driving a new JBL 2242 in free air with a mic on TEF Channel One in very close proximity to the dust cap and my laser position sensor on TEF Channel Two right next to the mic "lookiing" at the dust cap. I also connected my four channel Tektronic scope to the output of the amp, the mic, and the laser for visual tracking as well. I can set cursers on the scope and get real time and or degrees between channels, like the amp and laser position.

The short of what I found was the driver physcally follows the signal at low frequency and gets later as the frequency increases. I started at 0.25Hz to be sure I wasn't a cycle off. So, if the driver gets later and later as the frequency increases, why does the "measured" group delay increase as frequency decreases if it is not a math thing? And if it's just a math thing, why should I worry about it?
That one's easy to explain. As you found, at very low frequencies the driver displacement moves almost in phase with the electrical input, so your question is why is the sound not in phase at this point, and where is the increasing group delay at low frequencies coming from ?

Your misunderstanding is that sound is produced by (and therefore in phase with) the displacement of the cone - it isn't. It's produced by the acceleration of the cone, so the SPL is in phase with the acceleration. Because the woofer is a harmonic oscillator the electrical input and acceleration are in phase above the mechanical resonance.

Thus a long way above the resonance input signal and SPL are in phase because input signal and acceleration are in phase. A long way below the resonance (near DC) the acceleration is 180 degrees out of phase with the input signal thus so is the SPL, and that 180 degree phase shift (for a closed box) is where your group delay comes from at low frequencies.

The harmonic oscillator formed by the woofer mass, compliance and damping mimics a 2nd order high pass filter.

There's a really good image posted by bolserst in post 114 in the following thread that shows the relationship between acceleration/velocity/displacement, and amplitude/phase for each:

Drivers behave as a mass on a spring...

Note: an earlier version of the image has a mistake in it which was corrected for post 114.
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Old 20th January 2013, 08:25 AM   #120
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Quote:
Originally Posted by Barleywater View Post
Yes, but phase response of LP and HP are identical. Thus sum is minimum phase, identical to LP and HP components. This is beauty of Linkwitz-Riley transform. Convolution of a Butterworth filter with itself, cascading stages, same thing.
Barley, I think you need to do some homework on the definition of Minimum Phase.

There are several possible definitions.

One is that the Amplitude & Phase responses are uniquely linked via various Hilbert Transforms[*]. ie for a Minimum Phase transfer function, there is only ONE Phase response which corresponds to its Amplitude response. For a flat Amplitude response, the unique phase response is 0 (or 180) phase.

All-pass networks are (by definition) non-Minimum Phase.

Bear in mind also what the term Minimum Phase implies. Alternative titles might be Minimum Group Delay, Minimum Smear or Minimum Energy Delay.

A Minimum Phase transfer function will have the least Delay, Smear of any transfer function with the same amplitude response. You can dream up your own definition of Delay, Smear etc and try various phase responses to see if you can get less or better Delay, Smear etc compared with a Minimum Phase response.

[*] Various cos there is Log amplitude, Lin amplitude, Re & Im, exponential versions ... etc.
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Group Delay is by definition -d(phase)/d(freq).

But as I said earlier (and also by Dick Heyser & Bode), it corresponds to Envelope Delay (ie appear to delay a group of frequencies) only under certain conditions.
  • when GD is constant over the frequency range of interest OR
  • when amplitude is constant over the frequency range of interest.
Where it "falls down" in Minimum Phase circuits (especially for audio) can be explained by the following.

One property (and another definition) of a Minimum Phase transfer function is that there will exist another Minimum Phase transfer function that will EQ this perfectly WITHOUT ANY RESULTANT DELAY. Both these functions are physically realisable to any degree of accuracy you wish or are prepared to pay for.

As the final EQ'd circuit has NO DELAY, it is somewhat misleading to imply the original Minimum Phase circuit has a 'delay' (though it will have a GD as defined by the above math expression) unless your matching EQ circuit has real negative delay (ie a time machine).

Having said that, the concept of GD does have use in certain Minimum Phase circuits (that fullfill either of the above requirements) but these are usually at RF.

"Is Linear Phase Worthwhile?" has examples of both and also shows how excess phase (eg an All-pass network) DOES result in true delay for audio.
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But to get back to the original post .. My own work in the early 80's shows a 1ms pulse repeated at 500 - 100Hz is audibly changed by 6 x 1st All-pass networks at 1kHz in a Double Blind bla bla Listening Test.

Other work suggests that Absolute Phase of carefully recorded Bass Drums can be reliably detected.

But today, we have the possibility of much better recordings (though unfortunately, most modern recordings are worse than 30 yrs ago )

I think there is a strong possibility that Excess Phase is detectable below 100Hz. The maximum sensitivity is only slightly above that freq.

Whether it is worth correcting is another issue but I would very much like to conduct Double Blind ABC or ABX tests on this as I did in the early 80's ... especially on music.

Last edited by kgrlee; 20th January 2013 at 08:35 AM.
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