the misbehaving conventional subwoofer, creates sidebands around every musical note, every vocal sound, every sound effect - even those in the midrange and treble spectral regions. Because the subwoofer is putting out high acoustic energy, its spurious, misbehaving ringing strongly modulates the air pressure in the room that represents all the rest of the program. Moreover, this modulation is the worst kind of modulation, Doppler or FM distortion, which Klipsch has shown to be far more audibly obnoxious than other kinds of distortion (e.g. AM distortion), even in small amounts. The human ear is inherently nonlinear, so it acts as a detector or demodulator of these FM distortion sidebands. Thus, the spurious ringing, by conventional subwoofers' misbehaving response to every bass transient, actually causes distortion of all the rest of the program that is playing, making even midrange and treble information sound dirtier and more artificial, as well as more temporally smeared and hence less transparent and less fast (FM distortion temporally smears the sound by effectively jittering the signal's temporal reference).
       And yes, this distortion is clearly audible. To give you a sneak preview of some discussion below, one of the biggest and most surprising sonic benefits of the TRW subwoofer is that it makes the whole system sound cleaner and clearer and faster and more articulate, even for midrange and treble information. This proves that this FM distortion of the room air and ear, by conventional subwoofers and woofers, is clearly audible, and that the TRW offsets and effectively erases this distortion (below we'll explain how).
       It's another bitter irony that, even though an important benefit of subwoofers is the reduction of FM Doppler distortion from the woofer cone, by offloading some excursion from the woofer cone, conventional subwoofers then undo this benefit by re-introducing FM Doppler distortion in a different way, via their spurious ringing that modulates the air and your ear. And it's doubly ironic that employing vented enclosure designs for conventional subwoofers, in order to make their flat amplitude response extend lower in frequency, thereby makes this spurious ringing worse, and therefore causes worse FM distortion of the whole rest of the spectrum output by your system.

E.3.f. Erroneous System Waveform with Conventional Subwoofers

       There's a further sonic problem caused by conventional subwoofers, with their errant time domain response. For your system as a whole to accurately reproduce the input signal waveform, all loudspeaker drivers should be contributing the correct kind of signal at the correct time. The ideal subwoofer, for each bass transient that comes along, should put out a signal that acts as an energy pedestal or foundation, for algebraically adding to the signal that is simultaneously put out by all the other loudspeaker drivers in your system, and this pedestal should remain at full and constant height (for the step signal input, acting here as an indicative test probe). This pedestal from the subwoofer is very important, because there is so much energy in the bass region, so the subwoofer effectively elevates the energy put out by the other drivers to the correct height, so that the signal from your loudspeaker array as a whole achieves the correct height and the correct waveform shape for accurate replication.
       But we have seen that conventional subwoofers fail to put out the correct pedestal height, in all three regions of their misbehaving time domain response. In the first region, conventional subwoofers decline too quickly, instead of maintaining the correct signal height as a pedestal. In the second region, they actually go down to negative height, putting their supporting pedestal underground instead of high above the ground. And in the third region they oscillate spuriously between various heights above and below ground, for their supporting pedestal.
       Thus, conventional subwoofers fail miserably to perform their time domain duty of providing a full height, correct pedestal for the signal waveform put out by all your other drivers. Conventional subwoofers put out the wrong signal levels at the wrong times, so when their acoustic output is algebraically added, instant by instant, as a supporting pedestal to the acoustic output from your main loudspeakers, the summed result is a royal mess, a very inaccurate signal waveform that is presented to your ear by the system as a whole. Without the correct pedestal, the waveform put out by your system as a whole is all wrong, especially because the bass region with its high energy constitutes so much of what should be the overall signal waveform's full and accurate content. By failing to put out the right waveform energy at the right time, conventional subwoofers fail to furnish the required high energy pedestal needed for your whole system to achieve correct waveform dynamics and accuracy. And then conventional subwoofers compound their felony by their spurious behavior later in time, their negative overshoot and ringing, which adds to your system the wrong spurious garbage sounds at the wrong time.
       In short, conventional subwoofers, by providing a wildly and grossly inaccurate pedestal, doom your system to putting out a very inaccurate signal waveform. This creates many sonic degradations of your whole system's output (degradations beyond poor quality bass from the subwoofer itself), these system degradations including compromised dynamics, obscuration and distortion of the whole spectrum, and an overall system sound that simply sounds wrong and unnatural, like artificial hi-fi instead of real music, real voices, real sounds. Once you train your ear to hear this wrongness, you'll have a hard time accepting the sound of systems with conventional subwoofers ever again. Once you hear the TRW subwoofer in direct comparison, and hear how the TRW creates a correct pedestal and thereby makes the whole system sound right, you'll never want to go back to a conventional subwoofer, ever again.

E.3.g. TRW Time Domain Response

       As promised, we've discussed the many, many sonic problems that conventional subwoofers create, due to the many ways in which they make a royal mess of time domain response. Now, what about the TRW subwoofer? How does its time domain response contrast with conventional subwoofers?
       Simple. The TRW subwoofer's time domain response is essentially perfect. All those many gruesome errors in time domain response committed by conventional subwoofers: gone, since they never arise in the first place. All the many degrading sonic consequences discussed above, created by conventional subwoofers' time domain misbehaviors: gone, since they never arise in the first place. How's that for contrast?
       How can the TRW subwoofer possibly have no problems whatsoever with time domain response in the bass, when all conventional subwoofers have so many problems that are so severe? How can it be so radically different, so radically opposite in its behavior and performance?
       Simple again. The conventional subwoofer is inherently an AC device, so it gets into progressively worse trouble at very low frequencies, especially because it has high reactance at low bass frequencies. The TRW subwoofer is just the opposite. The TRW is inherently a DC device, so it is perfectly happy reaching down to ever lower bass frequencies, without limit, and without misbehaving, and the TRW does not have any reactance at very low frequencies.
       In its time domain response to our standard test signal, the step, the TRW is essentially perfect. It reproduces the step accurately, and thus reproduces all bass, both bass transients and bass steady tones, accurately. The TRW's time domain response to the step test signal is the opposite of conventional subwoofers; the TRW does not start declining and wimping out too soon, and it does not have any negative overshoot, and it does not have any ringing. Obviously, then, all the many sonic problems discussed above, which conventional subwoofers cause by their too quick decline and negative overshoot and ringing, simply don't exist for the TRW.
       The TRW simply reproduces essentially perfect quality bass. Conventional subwoofers, in complete contrast and opposition, make a royal mess of bass quality, and also even manage to mess up midrange and treble information in so doing. In contrast to conventional subwoofers, the TRW keeps pushing positive airflow and pressure, so long as the input signal instructs it to. This means that the TRW's bass quality gives you far superior impact and weight (since it does not decline too soon), and solid, tight definition (since it does not go negative), and dynamics (since it does not partially cancel its own previous output, nor the output from your main loudspeakers), and sonic waveform accuracy in itself (since it does not spuriously ring), and sonic waveform accuracy from your whole system (since its creates a correct pedestal for the waveform put out by your main loudspeakers).
       Plus, the TRW gives you overall system sound throughout the whole spectrum that is far cleaner, clearer, faster, more articulate, more natural, and more accurate (since it does not distort nor time smear, via FM distortion, the wide spectral range acoustic signal put out by your main loudspeakers (indeed, we found that the TRW even acoustically reduces the FM distortion inherent in your main loudspeaker system, as will be discussed below).

E.3.h. Time Domain Response Summary

       Audiophiles, accustomed to comparing conventional subwoofers with each other, naturally talk first and primarily about how low in bass frequency a subwoofer extends, and how loudly it can play bass. The TRW does extend far lower in frequency and play louder than all conventional subwoofers. And these are important factors, to be sure, in producing better quality bass and greater quantity of bass. But, as a wary audiophile might note, these differences are merely differences of degree, and make the TRW merely a bigger, better, badder subwoofer.
       On the other hand, the differences in time domain performance we have just discussed above, between the TRW and conventional subwoofers, are emphatically not merely differences of degree. The TRW behaves in a wholly different way in its time domain response, and thereby produces a wholly different type of bass. And remember that time domain performance is more important, and more directly indicative of what we hear, than frequency response is, since signal change happens in real time, since subwoofer driver behavior happens in real time, since subwoofer output algebraically adds with main loudspeaker output in real time, and since we hear in real time (with our brain doing temporal integration and time-slicing analysis).
       It is in the time domain performance that we can most clearly see that the TRW is a radically different type of subwoofer, which is fundamentally the opposite of conventional subwoofers, and which has strengths at low bass frequencies (indeed down to DC) where conventional subwoofers are riddled with severe weaknesses. Since it is the primary responsibility of subwoofers to capably handle exactly these same low bass frequencies, we can see that conventional subwoofers are miserable failures at their primary job, and therefore cannot even truly be called subwoofers. The TRW is the only subwoofer.

Part III: Relevance

       We've been taught all our lives that human hearing extends only down to 20 Hz, and that the deepest bass musical instruments extend only down to 20 Hz (16 Hz for the rare 32 foot organ pipe). So how and why could a subwoofer that goes any lower than 20 Hz, like the TRW, even be relevant to human hearing, or relevant to program content?

A. The True Fundamental Concept of Frequency

       The TRW is actually worth getting instead of a conventional subwoofer, just for its vast superiority in time domain response, which is so important and has so many sonic benefits, as just discussed above. But, for many audiophiles who are accustomed to thinking primarily in terms of bass frequency response and deep bass extension, there might be lingering doubts about the relevance of investing in a subwoofer like the TRW that goes below 20 Hz, and whose frequency response extends flat so far below 20 Hz, indeed down to DC. After all, we've been taught that there is no program content much below 20 Hz, and furthermore that humans can't hear below 20 Hz. So what's the point?
       Moreover, the many, technically knowledgeable engineers, who design all our equipment, are extremely well versed in the concept of frequency, since the concept of frequency, and frequency response as a design tool, is their major stock in trade. They have largely been satisfied at designing and specifying our equipment down to just 20 Hz, especially transducers such as loudspeakers, which are very difficult to design for lower bass frequencies. So shouldn't we take a clue from these professional design engineers? Don't they know what they're talking about, and designing equipment for?
       As a matter of actual fact, no. Nearly all design engineers in fact have a fundamentally erroneous view of frequency response, and don't even truly understand the basic concept of what frequency is and means. Since frequency is their key stock in trade, and frequency response is their key design tool, their erroneous understanding means that they have questionable right to even be designing our equipment in the first place.
       You see, the popular but erroneous view of the concept of frequency and frequency response, shared by most design engineers, is based on a model of sine waves, sine waves at specific single frequencies. But the true definition of a sine wave at a single frequency is a single sine wave pattern that stays absolutely the same, unchanged, for a period of time that lasts forever. In the real physical world there is no such animal. Forever is a very long time.
       Moreover, we would not want such an animal as our program material. A single sine wave that stays the same, unchanging forever, cannot contain or convey any information whatsoever. And we want our program material, be it music, voice, or film sound effects, to give us information. The only way that our program material can convey information is to keep changing, and indeed it conveys information only to the extent that it does keep changing, from one minute to the next, from one moment to the next.

B. Program Content: Change and Transients

       The very definition of music involves a series of notes or sounds that change over time, as do the definitions of vocal singing, vocal speech, and sound effects. These changes totally invalidate the sine wave model of frequency, since that model is based upon and requires a single simple sound to stay the same, unchanged, forever.
       Why? Because change logically implies that every musical note, every vocal sound, every sound effect sound, must have a temporal beginning and a temporal end (an end to make way for the next note or sound in the changing pattern, and obviously a beginning when this sound began to make the change from the previous, different sound).
       This temporal beginning and end, indeed any temporal signal change that does not regularly repeat forever (as a single simple sine wave does), brings with it a wholly different conceptual view of what frequency is. This different conceptual view shows the true, correct conceptual way to look at frequency. And it is also the view that is correctly relevant to our actual program material, because our program material is continually changing.
       Any and every sound that has a beginning and an end actually contains not a single frequency, nor even a few distinct frequencies, but rather in fact contains an infinite number of frequencies, and an infinitely dense spread of frequencies, and a spread that has a very, very wide spectral range. Any and every change in sound likewise actually contains a very wide spectral spread, of an infinite number of frequencies that are infinitely dense. And, because all our program material does convey information, all our program material in fact consists of a very wide spectral spread of frequencies, an infinite number of frequencies with infinite density along the frequency axis.
       Thus, our program material is properly modeled as a series of transients, not as a sine wave or sum of sine waves. A transient, as its very name implies, is temporally present and with us only for a temporary period of time (as opposed to a sine wave's presence forever, by definition). A transient is a transient, who temporally passes through our presence, entering and then departing, as it starts and then later stops. This fundamental transient nature, of all our program material, is what makes and allows our program material to convey information (musical, vocal, or sound effect).

C. True Frequency Content of Transients

       There is also a correct engineering way to model transients. A transient marks a change or transition in the signal. The simplest possible test signal, which can be used to model all transients with their changes or transitions, is a step test signal, which contains but one single, simple transition in the signal (an impulse is also usable, but it technically contains two transitions, up and then quickly down again, so we'll stick with the simpler step as a test signal model). So, let's now ask the key question: what is the true, actual frequency content of a step signal transition? And, of particular relevance to our subwoofer discussion here, how low in frequency does this frequency content extend?
       The answer is simple. A step signal transition contains energy at all frequencies, spectrally extending an infinite number of octaves all the way down to zero Hz (DC)(an infinite number of octaves because each octave, each halving of frequency, takes you only half of the distance remaining to zero), and all the way up to infinity (or to the high frequency limit implied by the risetime of the signal source).

(Continued on page 150)