Which conventional subwoofers commit this negative overshoot blunder, on all bass transients? They all do. The only conventional woofer or subwoofer which could elude this blunder would be a system whose bass rolloff is very shallow, at 6 dB per octave or less. But there are no such systems among conventional woofers or subwoofers. Dipole woofers have a small part of their spectral range which does roll off at merely 6 dB per octave, so for this narrow spectral region they can have somewhat better bass transient response, with at least no negative overshoot for a little while (temporally). But even they, for every bass transient, commit the blunder of negative overshoot later in time, when, at a lower bass frequency than the dipole rolloff corner, their actual driver encounters its own free field resonance, and then begins rolling off below that resonance frequency at a steeper 12 dB per octave slope, which engenders the negative overshoot blunder. All conventional woofers and subwoofers in infinite baffle enclosures commit this negative overshoot blunder, since they all have rolloff slopes of 12 dB per octave. And all woofers and subwoofers in vented bass enclosures also commit this negative overshoot blunder, generally to an even worse degree, since they have even steeper rolloff slopes, of 24 dB per octave or higher.
       This blunder of negative overshoot in the time domain performance can also be correlated with performance errors as viewed in the frequency domain. In this case it is the phase frequency response (rather than the amplitude frequency response) that primarily shows the error. All conventional subwoofers have large reactance, and a low frequency resonance, within their spectral range, and this large reactance causes severe phase errors, near and below the resonance frequency, as noted above. When these phase errors exceed 90 degrees, the actual performance of the conventional subwoofer, as seen and actually heard in the time domain, goes negative and starts sucking air in instead of staying positive and continuing to push air out, for what should still be the positive portion of the output, since the input step signal is still fully positive (note that this is not a sine wave input signal, which does go negative after a while, so the subwoofer has no excuse at all for going negative). As the phase error continues to get larger, toward 180 degrees, the conventional subwoofer's actual output, as seen and actually heard in the time domain, goes farther and farther negative, sucking in air even more strongly, and thereby effectively canceling out even further (so far as the ear/brain's integrating ability is concerned) the previous positive push of air.

E.3.c.v. Irony of Misguided Design Goals in Conventional Subwoofers

       There's a bitter irony here, involving misguided design goals of many engineers, perhaps driven by their marketing departments. Conventional subwoofer drivers are put into sealed enclosures in order to extend their flat amplitude frequency response down to lower frequencies. They thereby look better at passing the test of reproducing steady tones like test sine waves (so their amplitude frequency response looks better, more extended, on paper). And they thereby also get better at playing steady bass tones, like organ notes, with full flat response down to lower bass frequencies. Furthermore, the sealed enclosures of conventional subwoofers are often opened with a vent (or port, or passive radiator), in order to extend their flat amplitude frequency response to yet lower frequencies, so they look even better on paper and are even better at playing steady bass tones like organ notes. But these various enclosures, which make the amplitude frequency response look better for steady tones, also thereby make the phase frequency response errors worse. The reactive components of the steeper rolloff slope below resonance, and of the sharper corner at resonance, as seen in the amplitude frequency response curve, make the phase frequency response errors worse.
       And here's the kicker. These worsened phase response errors also make the time domain response worse, specifically making the blunder of negative overshoot larger in magnitude and larger in area and longer lasting in time. This makes the subwoofer negatively suck in more air, thereby canceling more of the positive push bass energy it just generated. In short, it worsens the time domain response of the subwoofer. And remember, the time domain response shows the actual performance of the subwoofer as it happens in real time, which is also the way that your ear/brain hears it, in real time. Thus, the very same measures that are popularly (indeed almost universally) employed to make the conventional subwoofer look better on paper, in its amplitude response bass extension for steady tones (test sine waves or organ notes), ironically make the subwoofer's actual performance in the time domain worse.
       This irony is especially relevant to all bass transients. The sonic quality of all bass transients is intimately dependent on the quality of a subwoofer's time domain response. We've just seen above that the sonic quality of bass transients degrades when conventional subwoofers decline too soon in their bass transient response, their time domain response to a step test signal input, with the bass sonic quality becoming wimpy by losing massive impact and weight. And we've also just seen that the sonic quality of bass transients degrades when conventional subwoofers go negative, and start negatively sucking in air when they should still be positively pushing out air, making the bass quality of bass transients puffy and hollow instead of solid.
       Now, the vast majority of bass you get from all recordings consists of bass transients, not steady bass tones. Virtually all musical notes, and virtually all film sound effects, are changing over time, so they are transients, which have a start, a peak, and then soon an end (if they didn't, they would be playing unchanged for a long time). So virtually all sounds have a bass transient component (we'll discuss this further below). In contrast, very few bass events are steady tones (such as sustained notes from an organ, or background atmospheric film sound effects). In everything your hear, bass transients outnumber steady bass tones over 1000:1. So it's bitterly ironic that, with conventional subwoofers, the very design measures, employed to improve bass extension for the 1 steady bass tone, actually make bass performance worse for the 1000 bass transients, with a wimpy loss of bass impact and weight, and a loss of solidity as the bass sonic quality becomes puffy and hollow, and compression of system dynamics, with sonic confusion and even order distortion.

E.3.d. Conventional Subwoofer Region 3, Ringing

       We've just looked at two regions of the time domain response where conventional subwoofers have major failings, the first being a too quick decline of positive pushing bass energy, and the second being a negative sucking region that works to effectively cancel some of the already-too-little positive bass energy just previously pushed out. There's also a third region of the time domain response, where most conventional subwoofers also commit major blunders. And this third region also has dire, adverse sonic consequences.
       At some point in the time domain response, a conventional subwoofer's negative overshoot is finished, and its response goes back up toward the zero axis (representing zero output signal level). What does the conventional subwoofer do now?
       A few conventional subwoofer systems, those in sealed enclosures with a low Q (critically damped or better) alignment design, approach the zero axis from below, and then do not rise again above the zero axis. These few conventional subwoofer systems still commit the blunders in the first two regions of their time domain response as discussed above, so they still suffer the degradations of bass sonic quality discussed above, but at least they do not commit further errors in this third region of time domain response, and so they do not also suffer the further degradations of bass sonic quality to now be discussed. But the vast majority of subwoofers with sealed enclosures try for maximally flat, maximally extended amplitude response, which means a sharper corner in their amplitude frequency response near resonance, which means a higher Q, which means that they do also misbehave in this third region of time domain response, going back above the zero axis after their negative overshoot period is finished.
       Then, all conventional subwoofers with vented enclosures commit blunders in this third region. And some vented bass designs are worse than others. Generally speaking, those vented bass alignment designs that strive to extend their flat amplitude frequency response the farthest, to the lowest bass frequency, commit the worst blunders in their actual time domain behavior, especially in this third region, and therefore sound the worst on all bass transients.
       This again correlates with the phase errors of these various conventional subwoofers, as seen in their phase frequency response. These maximally extended vented bass designs have the steepest rolloff slopes, and that portends the worst phase errors, reaching the highest amount of phase rotation. With a step test input signal, the starting point in the time domain is the full level of the step (and an ideal subwoofer would simply stay at that full level). Thus, when a conventional subwoofer's phase error reaches 90  degrees, it will have prematurely finished its first positive excursion, and will be back down at the zero signal axis, about to go negative for phase errors above 90 degrees. Then, when a conventional subwoofer's phase error reaches 270 degrees, it will have finished its unwarranted negative excursion, and once again be back up at the zero axis. Since the phase error of all vented subwoofers (and most sealed box subwoofers) exceeds 270 degrees, their time domain response behavior will not stop at the zero axis after their negative overshoot, but instead will once again go positive, above the zero axis. And, if a vented subwoofer's phase error exceeds 550 degrees (thanks to its steep rolloff slope and sharp, high Q corner), then it will again go negative, later in its actual time behavior, as you will actually hear it, and as we can see in its time domain response to the standard step test signal.
       When a conventional subwoofer goes back up across the zero axis in its time domain behavior, after it has completed its negative overshoot, this becomes known as ringing. This appellation makes good sense. This conventional subwoofer has completed in effect one full cycle, first a complete positive excursion and then a complete negative excursion (like two half cycles). If the conventional subwoofer continues to output energy after it has in effect completed one full cycle, then it is ringing, i.e. continuing to cycle even after one cycle has been completed.
       Remember that the standard step test input signal has only one single voltage transition, and then stays fixed at a constant voltage level. So all this back and forth cycling, this ringing, seen in the output of a conventional subwoofer, in response to this simple single voltage transition as the input signal, is totally unwarranted, and represents totally spurious garbage output by the conventional subwoofer.

E.3.e. Further Sonic Problems from Conventional Subwoofer Ringing

       Many further sonic problems are caused by this ringing, spurious garbage output, emitted by conventional subwoofers.

E.3.e.i. Lingering Overhang from Conventional Subwoofers

       First, there is a lingering overhang, making bass transients sound slow, heavy, and soggy, with poor definition. The conventional subwoofer's spurious ringing has an approximate periodicity, and the human ear/brain, with its time windowing analysis capability, interprets this ongoing periodic ringing as though it were a separate bass tone, lingering after the original attack of the bass transient. Remember that the input signal consists here of just one single transition, which obviously does not linger in time, so there should not be any lingering AC signal at all by the subwoofer. And note that the conventional subwoofer's spurious ringing would likewise continue after every bass transient attack, just as it continues after this single signal transition by or step test signal.
       The sonic artificiality of this lingering, heavy bass overhang is especially noticeable to humans, hence especially obnoxious, because its cycling periodicity occurs over a moderately long time span that is typically beyond the Haas window of 10 to 15 milliseconds. When two sounds occur together, or separately but within the Haas time window, the brain tends to fuse them together so they coalesce into one perceived sound. But, if the second sound occurs after the first by a time period longer than the 10 to 15 millisecond Haas time window, then the brain hears them each as a distinct sound. Thus, with this lingering tail of spurious cycling, by conventional subwoofers, taking place and lasting beyond the 10 to 15 millisecond Haas time window, the brain hears the lingering overhang as a distinct sound, and thereby pays more attention to it, and of course recognizes it as a totally foreign sound.
       Incidentally, when audiophiles and designers speak of a woofer sounding fast or slow, they are actually addressing not the woofer's attack risetime, but rather this phenomenon of its lingering overhang, hence its slow decay. Woofer systems with a heavier, longer lasting decay (often due to this spurious ringing) sound heavier and slower, whereas woofer systems that decay faster and do not have a prolonged spurious ringing sound faster.
       There's a technical irony here. A conventional subwoofer's perceived slowness, its lingering overhang and ringing on the decay side of transients, is caused not by its inability to reach high enough in frequency extension (i.e. to be fast enough), as one might suppose, but rather is actually caused by its inability to go low enough in frequency extension, such that it converts incoming energy below its bass cutoff frequency into its own AC overshoot and ringing pattern, which temporally lingers with an overhang. If this conventional subwoofer could somehow magically extend far lower in frequency response, as low as the incoming signal's spectral content, then it could accurately obey and track this input signal, and would accurately reproduce the input signal's decay, and would not generate its own spurious, lingering AC ringing (slow-sounding overhang), and thus would sound faster. Of course, such a magical subwoofer does now exist, the TRW.

E.3.e.ii. System Transparency Loss from Conventional Subwoofers

       The second sonic problem is that this prolonged spurious AC ringing is an AC signal that competes with and thereby obscures new, succeeding program information that comes along, at all frequencies. Thus, a conventional subwoofer with this lingering overhang makes your system less transparent.
       Simply put, the loud sound from the conventional subwoofer's periodic ringing blocks and obscures the more delicate, subtle sounds that your main loudspeakers are putting out, which prevents you from hearing those subtle sounds, and which thereby degrades the perceived transparency of your system as a whole.
       And this obscuration continues for a long time, so long as the conventional subwoofer keeps ringing in its misbehaving response to the original earlier bass transient. Indeed, if there is a repeating bass transient rhythm or ostinato, the misbehaving conventional subwoofer might well be ringing virtually all the time, so the rest of the sound might be partially obscured virtually all the time.

E.3.e.iii. One-Note Boom from Conventional Subwoofers

       The third sonic problem is that the ear/brain hears the cycling periodicity of the conventional subwoofer's ringing, and reasonably interprets this cycling periodicity as an ongoing, lingering bass tone or note, at a frequency corresponding to the cycling periodicity. Thus, the ear/brain hears the conventional subwoofer's ongoing ringing as a one-note boom. The periodicity of this cycling misbehavior is dictated by the physical parameters of the conventional subwoofer, such as its various reactances, phase errors, etc. So the periodicity of this cycling ringing always stays the same, for every bass transient, even though the sound of distinct bass transients might itself be different and changing.
       For example, as a plucked jazz bass viol goes up and down the musical scale, the pitch of its transient bass notes keeps changing. But the perceived pitch of the conventional subwoofer's ringing hangover, as repeatedly triggered by these different bass transients, stays the same, because the periodicity pattern of its misbehaving ringing, dictated by the subwoofer's own physical parameters, stays the same. Hence, this conventional subwoofer will continue to strongly play the same bass note with its booming, ringing, lingering overhang, in the immediate shadow of each pluck of the jazz bass viol goes up and down the musical scale to differing bass notes. The one-note boom from the conventional subwoofer obscures the varying bass notes actually being input to the subwoofer from the plucked bass viol.
       Incidentally, because this strong one-note boom is always at the same frequency, it sounds just as if the loudspeaker has a sharp peak in its amplitude frequency response at this frequency, with extra energy at this frequency, plus the prolonged ringing that is the natural consequence of a sharp peak in amplitude frequency response. But in fact there is no peak at all in the amplitude frequency response at this frequency. The very real sonic problem, the one-note boom, that is so awfully audible, is totally hidden and undiscoverable from the amplitude frequency response. But it is very clearly revealed in the time domain response. This is yet another example where the time domain response, which shows the actual concrete behavior of the loudspeaker in real time, is more important, and more relevant to how the loudspeaker actually sounds in real time, than the amplitude frequency response, which shows only an abstract conceptual summary, and a summary at that of only one aspect of the loudspeaker's frequency domain capabilities (it ignores the phase frequency response error aspect).

E.3.e.iv. FM Distortion of Full Spectrum by Conventional Subwoofers

       An interesting fourth sonic problem is that the AC signal, represented by the spurious ringing of

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