Here is a bit about minimum phase in the context of applying EQ.
But audio is just as often not steady state...
This can be applied to time-varying signals (like audio -- it is the system response that is time-invariant)
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.
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.
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.
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.There are multiple outputs (port and woofer) that each have their own phase.
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.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.
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.
A pure time delay is linear phase, not maximum.Maximum-phase filters are also useful; the usual example is an all-pass filter, i.e. a filter that delays all frequencies equally (a pure time delay).
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.
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.1/2 the sample rate
Linear phase filters always have a symmetric impulse response, and conversely.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.
Given a linear phase filter, a minimum phase one with the same magnitude response has twice as much post-ringing.But for me the post-impulse decay can be equally annoying; it is often larger and longer,
A pure time delay is linear phase, not maximum.
In the face of the unbridgeable gap between frequency domain 'steady state' and the concept of the time domain transient, I give up!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.
Right, is 22kHz or more then something we need to worry about?
You've removed all the high frequencies, so the total energy has to be less. This translates to a lower peak amplitude.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.
I have been struggling to understand Minimum Phase so I did a search on google, and this old thread on ASR popped up. I have read John Mulcahy's article (also linked above), the Wikipedia article, and watched some videos on Youtube. The problem with most resources on explaining Minimum Phase is that it is impenetrable to the layman - as @mansr says, it is half an engineering degree. I would appreciate it if ASR members can check if I have understood it correctly and let me know if I am wrong. Yes, ASR is full of pedants and I am asking for some full on pedantry here
"A minimum phase system is where the phase response can be calculated directly from the frequency response using a mathematical function known as the Fourier transform. It has two important properties - it can be inverted (and thereby cancel the original signal perfectly), and it has minimum delay. Anything that increases the delay, for example room reflections, baffle diffraction, group delay from crossovers, etc. will render the system non minimum phase."
"Loudspeakers are minimum phase devices, however they are rendered non minimum phase as soon as drivers are placed in a cabinet (because of internal reflections in the cabinet), have a crossover (because the crossover changes the phase response, the only exception being a digital FIR filter), and in a room (because reflections from the room render the system non-minimum phase by introducing delayed signals which may be at lower or higher amplitude to the main signal). Regions of non-minimum phase behaviour increase as wavelength gets shorter, i.e. above the Schroder frequency where the room stops behaving in a modal fashion. Bass dips are usually regions of non-minimum phase behaviour (which is why we recommend not to fill nulls by boosting the volume), however bass peaks are usually minimum phase, which is why they can be corrected".
"Excess phase is the difference between minimum phase which is calculated from the frequency response, and the measured phase. The calculation can be windowed to take into account how many cycles are permitted when making the calculation." <-- In Acourate there is an option to calculate excess phase by inputting the number of cycles. Should I think of it as the phase equivalent of a Frequency Dependent Window (FDW)?
I do not have a complete understanding of "linear phase" - the definition is simple enough, which is that all the samples are shifted by the same amount of time over a given frequency band. However, I do not understand how this is different to group delay. Aren't they the same thing?
"A minimum phase system is where the phase response can be calculated directly from the frequency response using a mathematical function known as the Fourier transform. It has two important properties - it can be inverted (and thereby cancel the original signal perfectly), and it has minimum delay. Anything that increases the delay, for example room reflections, baffle diffraction, group delay from crossovers, etc. will render the system non minimum phase."
"Loudspeakers are minimum phase devices, however they are rendered non minimum phase as soon as drivers are placed in a cabinet (because of internal reflections in the cabinet), have a crossover (because the crossover changes the phase response, the only exception being a digital FIR filter), and in a room (because reflections from the room render the system non-minimum phase by introducing delayed signals which may be at lower or higher amplitude to the main signal). Regions of non-minimum phase behaviour increase as wavelength gets shorter, i.e. above the Schroder frequency where the room stops behaving in a modal fashion. Bass dips are usually regions of non-minimum phase behaviour (which is why we recommend not to fill nulls by boosting the volume), however bass peaks are usually minimum phase, which is why they can be corrected".
"Excess phase is the difference between minimum phase which is calculated from the frequency response, and the measured phase. The calculation can be windowed to take into account how many cycles are permitted when making the calculation." <-- In Acourate there is an option to calculate excess phase by inputting the number of cycles. Should I think of it as the phase equivalent of a Frequency Dependent Window (FDW)?
I do not have a complete understanding of "linear phase" - the definition is simple enough, which is that all the samples are shifted by the same amount of time over a given frequency band. However, I do not understand how this is different to group delay. Aren't they the same thing?
I would not think of excess phase as you suggest. I don't see the equivalence at all.
Or, are you referring to the possible equivalence with the Acourate option?
Causality has to do with the output coming after the input, which is true for any physical system. Stability has to do with the output being unbounded (going berserk) for a bounded input. Invertibility has to do with undoing what a previous system did, getting back to the response of a wire. So you generally have two situations where you cannot find a system that inverts a previous system, and those (previous systems) are both non-minimum phase. One is a time delay, because to invert it, you would need a negative time delay, such that you output a signal before you have an input, to output the proper output at time zero even though the previous system has not yet woken up. So your inverse system would not be causal, and so not physical. The other situation is that your original system has so-called zeros in the right-hand plane, which may not make sense if you haven't had much signal processing, but the issue here is that to undo/invert such an NMP system, you will need to cancel those zeros with so-called poles, and if poles reside in the right-hand plane, your inverting system will not be stable."In control theory and signal processing, a linear, time-invariant system is said to be minimum-phase if the system and its inverse are causal and stable."
Could someone who understands the above (and whatever practical problems it leads to) give a practical explanation to someone who knows squat (yes, that's me!) about control theory and signal processing?
Should read 'Hilbert transform', not 'Fourier transform'.I have been struggling to understand Minimum Phase so I did a search on google, and this old thread on ASR popped up. I have read John Mulcahy's article (also linked above), the Wikipedia article, and watched some videos on Youtube. The problem with most resources on explaining Minimum Phase is that it is impenetrable to the layman - as @mansr says, it is half an engineering degree. I would appreciate it if ASR members can check if I have understood it correctly and let me know if I am wrong. Yes, ASR is full of pedants and I am asking for some full on pedantry here
"A minimum phase system is where the phase response can be calculated directly from the frequency response using a mathematical function known as the Fourier transform. It has two important properties - it can be inverted (and thereby cancel the original signal perfectly), and it has minimum delay. Anything that increases the delay, for example room reflections, baffle diffraction, group delay from crossovers, etc. will render the system non minimum phase."
"Loudspeakers are minimum phase devices, however they are rendered non minimum phase as soon as drivers are placed in a cabinet (because of internal reflections in the cabinet), have a crossover (because the crossover changes the phase response, the only exception being a digital FIR filter), and in a room (because reflections from the room render the system non-minimum phase by introducing delayed signals which may be at lower or higher amplitude to the main signal). Regions of non-minimum phase behaviour increase as wavelength gets shorter, i.e. above the Schroder frequency where the room stops behaving in a modal fashion. Bass dips are usually regions of non-minimum phase behaviour (which is why we recommend not to fill nulls by boosting the volume), however bass peaks are usually minimum phase, which is why they can be corrected".
"Excess phase is the difference between minimum phase which is calculated from the frequency response, and the measured phase. The calculation can be windowed to take into account how many cycles are permitted when making the calculation." <-- In Acourate there is an option to calculate excess phase by inputting the number of cycles. Should I think of it as the phase equivalent of a Frequency Dependent Window (FDW)?
I do not have a complete understanding of "linear phase" - the definition is simple enough, which is that all the samples are shifted by the same amount of time over a given frequency band. However, I do not understand how this is different to group delay. Aren't they the same thing?