- Minimum phase (in context of loudspeakers and rooms) - this is the only version of the measurement which is correctible by inversion, which corrects both magnitude and phase at the same time. Loudspeakers are generally considered min phase systems, although there may be regions within a loudspeaker which are non-min phase.
Actually, a linear, non-minimum phase system CAN be corrected with LONG filters and a lot of work, but the correction is never perfect. It can, however, be very, very CLOSE to perfect.
A pure delay system (i.e. linear phase) has no phase issues to be corrected.
- Minimum phase (in context of DSP) - this is the minimum amount of delay encountered by a signal when it passes through a filter.
No, it means that all poles and zeros of any filters involved are inside the unit circle. (or in the case of zeros, on it, but that is a singular system that is beyond this discussion presently)
- Linear phase (in context of DSP) - every frequency encounters the same delay when passing through a filter. Suppose this is 1ms (1/1000s). This is 10 full sine waves for a 10kHz signal, 1 sine wave for a 1kHz signal, and 1/10 of a sine wave for a 100Hz signal - i.e. there is frequency dependent phase rotation.
Linear phase means phase = 2* pi * f * t in terms of radians, hz, and time in seconds. So there is lots of phase shift, but the phase shift is a STRAIGHT LINE corresponding to the equation just referenced.
- Excess phase (in context of loudspeakers and rooms) - non-minimum phase behaviour introduced by the room, e.g. furnishings, room shape, boundaries, etc. The measured phase as captured by the microphone contains the loudspeaker's min phase response + excess phase. The EP is normally removed and discarded, as it can not be corrected (strictly speaking, not true - it can be partially corrected).
Excesss phase? You mean "non-minimum phase" really. No, the non-minimum phase part of a signal is not removed before calculating frequency response adjustment, it can't be, it's part of the problem. Even if you can't correct the phase (and you actually can with long FIR filters, to any tolerance required, and work) you DO want to correct the magnitude response that is created by it.
- Mixed phase (in context of DSP) - a DSP product that contains both IIR and FIR filters, i.e. both lin phase and min phase filters.
No, this is misuse. Any impulse response can be divided into its minimum phase, delay, and non-minimum phase parts. IIR filters have minimum phase poles, by definition, they can have non-minimum phase zeros if they want to. FIR filters can be literally anything you want, anything at all, that's within the filter length limits. MOST "FIR" filters are actually constant-delay filters, but sometimes that's actually not the right way. Remember a constant delay filter is ONLY zeros, and contains an exact duplication of every zero inside side the unit circle with a zero at 1/MP_zero. Yes. That's why it's constant delay, exactly (removing any zeros on the unit circle from this discussion, although obviously not from the filter!) mirrored in inside/outside pairs (quads usually, since most are complex roots). There's a discussion on this somewhere on this board, I recall, because I wrote the thing.
It shows exact magnitude responses from 3 different filters, minimum, pure delay, and some other choice (in mixed phase FIR filters, you have 3 choices for every set of zeros corresponding to one system root, both inside, one each, and both outside. This is independent for EVERY set, so if you have a filter with 50 quads of roots, you have 3^50th possible impulse responses with exactly the same magnitude response.
- Mixed phase (in context of rooms) - another term for measured phase, i.e. loudspeaker's minimum phase response + excess phase.
Ok, modulo the "excess phase" thing. When you separate something into minimum phase (including zeros on the unit circle in minimum for practicality), the remaining roots are actually MAXIMUM PHASE. Yes, you can factor a filter into 3 parts convolved together, the minimum phase, delay, and maximum phase parts. That's a better way to put it, I think.
As alluded to earlier, there is also absolute phase and relative phase. Absolute phase = where phase integrity is maintained between left and right. For e.g. if you flip the polarity of both speakers, you won't hear it. Relative phase = where the phase of left and right is misaligned, for e.g. if you flip the polarity of one speaker you will definitely hear it. Sound seems to be coming from inside your head. If you do a sweep of both speakers playing together, you will see comb filtering. Having said that, phase and polarity are not the same thing, but this post is getting too long already.
So it's clear, we are talking mostly about INTRA-PHASE (single channel phase response) here. Yes, that's audible. Sometimes. Often it's not. "It depends" and the only way to know for sure is to actually examine its effect on the human cochlear analysis. Yeah, I didn't say simple.
It took me months to understand all this confusing terminology. It is misleading to say that all phase rotations are inaudible. You have to refer to exactly what type you are talking about.
Boy, howdy you can say that again, with feeling.
