Bill, I am surprised by this response. The area under the curve, the integral, the average, its all the same thing.
what I meant to point out was that you can't look at a finite resolution picture of an impulse response and know whether it is zero-average. The average is over long (effectively infinite) times. The ir graph shows only relativly coarse amplitude over a limited time.
This only true for a high pass system. Step response is the integral of the impulse response. If the system is HP it can not support a DC signal and therefore the step will decay to zero as T>> infinity. Thus the integral of the impulse must go to zero as T >> infinity. However, for an LP system, which can support DC, the step response will asymptote to a finite value as T >> infinity. Thus the integral of the impulse must be finite.
The average of the impulse is the integral of [h(t) dt] from t=0 to te divided by the integral of [dt] over the same limits which is always a finite number divided by te, which is zero in the limit of te >> infinity.
This relates back to what I said about the negative swing of the Summa impulse in an earlier post. As the low frequency cut off of a system approaches lower and lower frequency, the negative spike in the impulse becomes smaller and smaller because more and more low frequency content is present in the impulse. As the cut off a LP system approaches DC the impulse response approaches u(t), the unit impulse, which has no undershoot at all.
Thus, when you see a large negative spike in an impulse of a speaker with low bass cut off it is an indication that the crossover is not mimimum phase and what you are seeing is the negative spike due to the HP section of the crossover. Example below for 1k Hz X-O:
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If the crossover is "transient perfect" (TP) so the system is minimum phase the woofer and tweeter impulses will sum to a perfect impulse (in the absence of high and low frequency system cut offs). Example below for 1k Hz TP X-O :
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Earl, integral and average are not the same thing, as noted above.
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The average is the normalized integral so they are proportional and both must go to zero. John, I know the math.
As to the Summa impulse I suspect that the fact that the HP of the woofer is critically damped is why the negative peak is very close to the positive one. There is no ringing in the tail from the HP on the woofer so the average must go to zero very quickly as there is nothing else to bring the average down. In the Abbey the negative peak is not as great and the tail is longer because the Q of the HP is greater.
As to the Summa impulse I suspect that the fact that the HP of the woofer is critically damped is why the negative peak is very close to the positive one. There is no ringing in the tail from the HP on the woofer so the average must go to zero very quickly as there is nothing else to bring the average down. In the Abbey the negative peak is not as great and the tail is longer because the Q of the HP is greater.
My point was to place Bill's comment and the general comment in the proper context in that it applies only to systems with high pass response. In general, the integral of a function with limits of t=0 to infinity does not have to go to zero for the average to be zero. The integral must simply be finite.
I always feel the need to have the proper context because we are not the only people reading the thread. Others might not get it.
But going back the original discussion of determining MP behavior from the impulse, which of these two impulses, if either are, of a minimum phase system? Both decay monotonically to zero, but have an integral and average of zero.
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Or which of these?
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John at no point was I talking "in general". I made the context very clear. I was talking about "acoustic transducers" which are guaranteed to be HP and to have a finite impulse response. So your "in general" comment is kind of inapplicable.
I don't know which are minimum phase, since as I said, I was guessing and I don't think it very important. What I think is important are multipath signals where energy packets appears later in time than the main impulse. These are necessarily non-minimum phase and observable in the impulse response. That there are impulses that are non-minimum phase but not multipath (monotonic decreasing IR) was not really my point or my interest.
I have mentioned to you many times that the whole concept of MP is not one that I was ever taught in Acoustics. It is a EE concept that has its uses in circuits, but its use in Acoustics seems to me to be kind of limited. Group delay is what an acoustician would probably use. The relationship between group delay, excess group delay and MP is not really very clear to me if there is one.
I don't know which are minimum phase, since as I said, I was guessing and I don't think it very important. What I think is important are multipath signals where energy packets appears later in time than the main impulse. These are necessarily non-minimum phase and observable in the impulse response. That there are impulses that are non-minimum phase but not multipath (monotonic decreasing IR) was not really my point or my interest.
I have mentioned to you many times that the whole concept of MP is not one that I was ever taught in Acoustics. It is a EE concept that has its uses in circuits, but its use in Acoustics seems to me to be kind of limited. Group delay is what an acoustician would probably use. The relationship between group delay, excess group delay and MP is not really very clear to me if there is one.
Wow, this impulse response quiz hasn't extended the notion of Clarity as Darkness one bit. I believe it was introduced to discuss possibilities of linear temporal distortions as source for loss of clarity, and loss of perception that notes and sounds from virtual sources rise from acoustically dark background. All sounds rising up nearly simultaneously from small region of space are interpreted as impulsive in start. Perceptual mechanism integrates all these sounds occurring in first few milliseconds into signature of sound. Reflections of this impulsive sound up to about 50 milliseconds mostly contribute to sense of loudness, and secondarily may modify perception of signature timbre, and provide a perception of spatial setting of the sound.
Speakers, and listening environments can, and often do have very large amounts of linear distortion both in frequency domain and in time domain, yet maintain characteristics of clarity and darkness.
Many speakers at low to moderate levels of playback have excellent clarity and spatial performance characteristics. Many single driver full range speakers do this. As speaker bandwidth becomes utilized by combination of volume and frequency content demands, speaker is heard to strain. Well before demands on speaker lead to descriptors of "blown out", "grossly distorted", or "unlistenable", loss of clarity and loss of darkness occur. The exact same drive signal applied to more capable speaker returns descriptors including good clarity and sense of darkness.
Virtually all these symptoms are producible with known, highly audible forms of nonlinear distortion. For example: When high amplitude, low frequency, low drive current frequencies produced at speakers high impedance peak are combined with higher frequency, high current frequencies of low impedance range of speaker, audible intermodulation distortion occurs.
Knowledge of this allows mitigation of symptoms by design choices of drivers, baffle systems/waveguides, crossover points, and crossover slopes.
Speakers, and listening environments can, and often do have very large amounts of linear distortion both in frequency domain and in time domain, yet maintain characteristics of clarity and darkness.
Many speakers at low to moderate levels of playback have excellent clarity and spatial performance characteristics. Many single driver full range speakers do this. As speaker bandwidth becomes utilized by combination of volume and frequency content demands, speaker is heard to strain. Well before demands on speaker lead to descriptors of "blown out", "grossly distorted", or "unlistenable", loss of clarity and loss of darkness occur. The exact same drive signal applied to more capable speaker returns descriptors including good clarity and sense of darkness.
Virtually all these symptoms are producible with known, highly audible forms of nonlinear distortion. For example: When high amplitude, low frequency, low drive current frequencies produced at speakers high impedance peak are combined with higher frequency, high current frequencies of low impedance range of speaker, audible intermodulation distortion occurs.
Knowledge of this allows mitigation of symptoms by design choices of drivers, baffle systems/waveguides, crossover points, and crossover slopes.
Yes it has. Read on...
Your expectation on clarity is "very low" when you consider fullrange drivers. Read on...
I have mentioned that the driver (cone and motor) is the most critical thing to determine clarity and darkness. Impulse response does also but not as critical. You can appreciate the effect of impulse response, slew rate (square wave response) and waterfall (that goes to zero volt within 2ms) on clarity only for complex passage, such as an orchestra at real life spl.
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