How about we talk about the room contribution to delay? Care to post your RT60 for discussion, or even an .MDAT?
Higher Q tracks input signal more closely; Here is john K's paper about it.
file:///C:/Users/DLD/Downloads/Box-Q.pdf
file:///C:/Users/DLD/Downloads/Box-Q.pdf
Look at the link i posted previously to the geocities page. It is not terribly difficult to run a signal through a system in matlab/octave, but in this case, that is exactly what was done on that page. Oh, wait, look John k just reposted in post #63
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Except that you don't have to increase the size of the box to create a Q of 0.5
But if you did increase the box size you increase LF sensitivity which might be appealing to some.
Regardless where the name comes from
"A critically damped system has a damping ratio (ζ) of 1, which prevents oscillations and allows the system to return to equilibrium in the shortest time possible without oscillating. In a critically damped system, the quality factor (Q) is defined as:
Thus, a critically damped system has a Q factor of 0.5."
The discussion of Filter Q/shape is really just a discussion about group delay and decay. At some point enough transient distortion that is perceptible, occurs, but frequency and intensity of the distortion vary based on filter place and shape.
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A box does not "need" a greater volume to provide a lower Q.
Q is adjustable using EQ
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I might be confused but it appears that none of your tests of various Q's are volume matched and thus the results are invalid.
I'm not entirely sure as to why the step response might need favoring. The only time I have ever considered a step response, even in passing, is when I've connected a 9-volt battery up to a loudspeaker to see if the woofer is still working. Sure, the step response excites the intrinsic resonance of the system, but it is an input signal that is quite unusual and is highly unlikely to occur on music program material.
That's an excellent example. Settling time seems to be around 50ms, which is very good since we have a −3dB point of 20Hz, which is quite a low frequency, so things are happening rather slowly in that vicinity.
That's another good example. Here the settling time seems to be about 120ms. This is approximately double that of the closed-box system with the same −3dB point of 20Hz.
As shown in the two time-domain response plots, it is evident that the step response of the closed-box loudspeaker is more highly damped. That is entirely known from filter design theory. But what useful information does it convey to us when it is very, very unlikely that a loudspeaker is ever going to be asked to reproduce step responses in practice?
@mark100 Can you please provide the time-domain response waveforms when the input is a 20Hz two-cycle toneburst, and maybe a 30Hz two-cycle toneburst as well? They would likely be interesting to see, and much more of a real-world musical signal than any step input.
The matching of the acoustic sound pressure levels is an important consideration. It is complicated a little if we have a test signal with fundamental at the resonance frequency Fc, which in a Q=0.7071 closed-box system is −3dB at Fc, while for a Q=0.5 closed-box system, it is −6dB. That 3dB difference will play a significant role in the psychoacoustic perception of the two sets of responses. Add in some higher frequency content, say at 1.5Fc or 2.0Fc, and a listening test is fraught with difficulty.
To try and alleviate this issue, one would need to EQ the signal at Fc by 3dB for the Q=0.50 closed-box system to make it at least somewhat psychoacoustically equivalent, otherwise one's perception will be swamped by the significantly reduced (50%) acoustic power being put forth by the Q=0.50 closed-box system, which can easily trick the listener into thinking that the bass is "tighter".
Can you please measure a short toneburst, consisting of one or two cycles of a 28Hz sinewave signal? That frequency would be close to what appears to be the −3dB point of your subwoofer.
That's a good point. Note that the superior pulse response (good choice of test signal, and better than a step) comes about largely as a result of the extension of the bass response.
I think it would be more convenient if @mark100 posted an impulse response so that you can examine the response to any arbitrary input signal you have in mind.
OTOH, as there is no reason why the real sub wouldn't follow its LTI model one could as well just filter the input signal with whatever highpass (or total system response) one likes to choose.
If it did, the listener would also hear the "click" sound due to all the high frequency content that is carried in the signal, and might regard it as "noise" of some kind. The interesting thing about using a step as a musical signal is that it would excite the low-frequency resonance in each listener's individual loudspeaker system, and so would sound different from one system to the next.
Is that really the case? After all, the music signal is continuous. The driver must continuously respond to the waveform it is being fed.
It doesn't need to have settled to a zero state in order to start responding to the next portion of the signal.
I think that the ability of a loudspeaker system to accurately reproduce the peak levels associated with the instrument is the dominant factor that's coming into play here.
In this instance, is the "overshoot" purely a product of the loudspeaker system, or is it being heard as a combination of loudspeaker interacting with the acoustics of the room (e.g., reverberation time)? Of course, that cannon signal may also cause the woofer to temporarily exceed its linear excursion capabilities.
Measuring a short toneburst/pulse (not an impulse) is likely to be an even better tool, both audibly and visually, for determining how well a loudspeaker performs in its low-frequency range.
In any case, just measuring the low-frequency response will tell us most of what we need to know, and is probably a lot easier to interpret, e.g., where is the loudspeaker's −3dB low-frequency cut-off point and what is its asymptotic roll-off rate.
Thank you for the suggestion. However, impulse responses have a somewhat low signal-to-noise ratio. I'd much prefer seeing what @mark100's system can do on a toneburst without the shortish nature of an impulse making interpretation of dynamic response more difficult due to its wide-band nature. I'd prefer a signal full of low-frequency energy to give me a nicer visual representation, which others may also like to see. I've seen low-frequency toneburst-like and pulse-like signals present in many music waveforms, so the signal that I have requested is much more relevant to an actual use case than either a step or an impulse.
Why do you think so? When the log sweep used to create is long enough (10's of seconds) and loud enough (reasonable levels like 90dBSPL) the SNR is the highest of all methods available to measure an IR.
And then use that IR in a convolution (easy to do with Adobe Audition, but Audacity also offers a convolution plugin, and of course good old SoX) with whatever test signal, like unit step, square wave, non-windowed N-cycle sine burst, real music snippet, what have you....
Is a testing technique that is not part of music invalid? I don’t think so or else we wouldn’t have any testing that explores the limits of electro mechanical performance. Don’t soldiers do calisthenics and get tested on their performance, even for promotions? Yes. Are calisthenics ever used in warfare? No. My point is, valid data can be derived from very specific testing techniques that don’t resemble the real world. Is step response the only test we should do? Oh heck no! There should be many, including the tone bursts that you seem to like. The data taken as a whole give us a better picture of loudspeaker performance.
Step response is a valid test, and
Critically damped speakers have useful applications.