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Minimum Phase

DonH56

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#22
But audio is just as often not steady state...
Yes, had something else in mind and that was wrong. Or rather it is true but too limited. I corrected it to this:
This can be applied to time-varying signals (like audio -- it is the system response that is time-invariant)
Sorry about that, I did say to check my off-the-cuff babbling, and you did!

Thanks,
Don
 
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andreasmaaan

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#23
The quote is misleading:
The reflex, ABR. bandpass and transmission line principles certainly do extend the
frequency response of loudspeakers, or permit a reduction is size when compared to
a conventional scaled enclosure and this has led to their wide adoption. However,
concentrating on the frequency domain alone does not tell the whole story. Although
the frequency domain performance is enhanced, the time domain performance is
worsened. The LF extension is obtained only on continuous tone and not on tran-
sients.
In this respect the bandpass enclosure is the worst offender whereas the true
transmission line causes the least harm.
Yes, the time domain performance is worsened. But that is because we are now dealing with a summed response that has been high-pass filtered at 24dB/octave as opposed to 12dB/octave. Of course the transient response of a 24dB/octave filter is worse than the transient response of a 12dB/octave filter.

And I don't know much about that source, but the statement "the LF extension is obtained... not on transients" doesn't make any sense. The LF extension is there. Play a steady state signal and you have LF extension. Play a transient and you have LF extension (with double the transient smearing of a closed box system). Perhaps it's just a clumsily worded sentence.

In the sealed case, the transducer is obviously a cone attached to a coil. Energise the coil and the cone will start moving instantaneously. Reverse the current and it will start to reverse. For sure, there's a phase lag, springiness of air in the box etc. but it is easy to see that pre-processing the signal can lead to ideal behaviour because there's only one output.
Think of a multiple driver system with crossovers. Despite the fact that the output comes from multiple outputs (drivers), the summed response can be phase corrected.

The same is true of a vented system. There are multiple outputs (port and woofer) that each have their own phase. These outputs sum outside the box, and the summed response itself has a (summed) phase. This phase can be corrected.

The bass reflex box is simply not the same. The output of the port is derived from the backwave of the cone. For its output to be in phase with the front wave it has lag behind by half a cycle - it cannot be coincident with, or ahead of, the front wave even with the magic of DSP; if we advance the port output we also advance the cone output. A transient must be smeared unavoidably. Once it gets going with a repeating waveform, no problem.
It seems that you're imagining the port and the woofer as though they both output at all frequencies. But the opposite is the case. The driver is not outputting anything at the port resonance. So if DSP corrects the phase response at resonance, that does not affect the direct radiation from the driver.
 

Cosmik

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#24
There are multiple outputs (port and woofer) that each have their own phase.
They each have their own phase, but not individually controllable because the port output is derived from the cone output. If we change the phase of the cone we automatically change the phase of the port.
It seems that you're imagining the port and the woofer as though they both output at all frequencies. But the opposite is the case. The driver is not outputting anything at the port resonance. So if DSP corrects the phase response at resonance, that does not affect the direct radiation from the driver.
All steady state-centric. When the driver 'kicks off' for the first time, the port isn't yet resonating. Once it gets going, it all works perfectly - until you try to stop it.
 

andreasmaaan

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#25
They each have their own phase, but not individually controllable because the port output is derived from the cone output. If we change the phase of the cone we automatically change the phase of the port.

All steady state-centric. When the driver 'kicks off' for the first time, the port isn't yet resonating. Once it gets going, it all works perfectly - until you try to stop it.
The driver isn't "kicking off" at the port resonance. It's still, and not producing any output. At higher frequencies, where the driver is producing output, the port isn't. The whole system can be corrected.
 

mansr

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#27
What frequency is ringing anyway? Is it ultrasonic? I thought ringing isn't really a big concern with music unless it's badly mastered with clipping.
1/2 the sample rate
Not quite. The so-called ringing is at the filter cut-off frequency. For reconstruction filters, this is typically at or slightly below half the sample rate, but it doesn't have to be.
 

mansr

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#28
Linear-phase filters usually have a better-looking impulse, much cleaner with much less "ringing" around it, but it is often symmetric with a little ringing after and before the impulse.
Linear phase filters always have a symmetric impulse response, and conversely.

But for me the post-impulse decay can be equally annoying; it is often larger and longer,
Given a linear phase filter, a minimum phase one with the same magnitude response has twice as much post-ringing.
 

DonH56

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#29
A pure time delay is linear phase, not maximum.
Thank you, must have not remembered that one rightly. Long, long time since those graduate courses and I am fundamentally an analog guy. Should have pulled out O&S or one of my other references but I was tracking down a test bug and didn't take the time yesterday (Sunday, working again...)

All these corrections should serve to keep me from posting on things I am not actively using or designing, too easy for senility to creep in and cause misinformation.
 

Cosmik

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#30
Supposing I don't want 24dB/octave roll-off from my bass reflex speaker, but in fact I want 12dB/octave. Why
The driver isn't "kicking off" at the port resonance. It's still, and not producing any output. At higher frequencies, where the driver is producing output, the port isn't. The whole system can be corrected.
In the face of the unbridgeable gap between frequency domain 'steady state' and the concept of the time domain transient, I give up! :)
 

andreasmaaan

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#31
Let me try again @Cosmik, and please banish from your mind that I’m interested for present purposes in the steady state amplitude response.

At the frequency of the port resonance, the driver output is zero (or in the real world, negligible). If we correct the phase at this frequency, it is only the output from the port that we are correcting.

Do you agree thus far?
 

RayDunzl

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#32
Right, is 22kHz or more then something we need to worry about?
As for the frequency, not for me.

There may be a "spreading" of the energy. In the example, the (illegal) Impulse is full scale, but after a little manipulation to create ringing example (upsample, downsample), it is 0.444dB down at the peak.


1546884059079.png


In this contrived example, the ringing maximum level is at -25dBfs (or so).
 
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mansr

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#33
There may be a "spreading" of the energy. In the example, the (illegal) Impulse is full scale, but after a little manipulation to create ringing example (upsample, downsample), it is 0.444dB down at the peak.
You've removed all the high frequencies, so the total energy has to be less. This translates to a lower peak amplitude.
 
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