Time Dilation, Part 1:
Page 2
This does not mean, as is sometimes inferred, that the measurement becomes unreliable below 167Hz—the problems begin much higher in frequency than that. What it does mean is that the frequency range is divided up into slices 167Hz wide, and any features of the loudspeaker's response that occur within one slice will be agglomerated in the measurement. That's of little consequence at a frequency of, say, 10kHz. But below 1kHz, this resolution amounts to a mere six frequency slices—obviously not enough to reveal useful detail.

Figs.1–3 (originally published in the English magazine Hi-Fi News) show just how serious the ramifications are of frequency resolution of this order. To generate them, I first created a simulated impulse response, in MLSSA's native TIM file format, for a closed-box (acoustic-suspension) loudspeaker having a resonance frequency of 60Hz and a total system Q of 0.707 (ie, a maximally flat or Butterworth bass alignment). To this were added six simulated cabinet resonances, at frequencies from 145 to 691Hz, with Qs and relative levels equivalent to those identified by W.R. Stevens many years ago, in measurements of a real loudspeaker cabinet (footnote 2). Then the impulse response was analyzed with MLSSA using time windows of 6ms, 23ms, and 217ms, the last being the longest available at the selected sampling rate.

Fig.1 shows the frequency response and cumulative spectral-decay ("waterfall") plots obtained at the longest, 217ms window length. Here everything is as it ought to be. The bass response falls monotonically to be –3dBr at 60Hz, just as it should, and all six resonances are clearly resolved, both in the frequency-response and waterfall plots. This is nirvana, so hang on tight to it.

Fig.1 Results of analyzing a simulated speaker impulse response using MLSSA, here with a time window of 217ms: a) frequency response, b) cumulative spectral decay.

Fig.2 shows what happens when the time window is reduced to 23ms: in the frequency-response graph the bass rolloff is no longer quite right, and the individual resonance peaks are beginning to merge. In the waterfall, matters are even worse: only the 691Hz resonance is now clearly resolved. With the 6ms time window (fig.3), absolutely everything is obscured. The merging of the resonances makes it appear as if the speaker has a lower-midrange hump in its response, while the waterfall has become a meaningless mélange. And this, remember, is typical of results achieved by reviewers who, as I do, use their listening rooms for time-windowed speaker measurements (footnote 3).

Fig.2 Same as fig.1 but with measurement time window reduced to 23ms.

Fig.3 Same as fig.1 but with measurement time window reduced still further, to 6ms.

The tragedy of this situation is not that it prevents accurate measurement of a speaker's bass response. As we will see, that is a problem that can be overcome quite easily. What really hurts is that this time-window limitation prevents the identification of cabinet resonances in just the frequency range where they typically occur. Cabinet resonances are known to be a major factor, perhaps the major factor, in determining a loudspeaker's sound quality, yet most reviewers who have gone to the trouble and expense of arming themselves with MLSSA or one of its clones will be unable, for the reasons described, to identify them. Nor will they be able to identify resonances in the speaker stand, which may be just as significant.

Still got that chosen expletive at the ready? Insert here.

The nearfield maneuver
The standard means of circumventing this time-window restriction to obtain an accurate picture of bass performance is to perform a nearfield measurement, a technique developed more than 30 years ago by Don Keele (footnote 4) when he worked at Electro-Voice. This suppresses the room's contribution by placing the measurement microphone close up to the center of each of the speaker's bass radiators. I say radiators rather than diaphragms because, in the case of a reflex (ported) design, the port radiates sound as well as the bass driver, and both contributions have to be accounted for.

With the room's contribution suppressed by such close microphone placement, the measurement window can be opened out sufficiently to provide the frequency resolution necessary to capture an accurate bass response. This can then be stitched together with the farfield response (measured conventionally, with the microphone 1m, or whatever the chosen distance, away) to create a response trace that covers the entire audible spectrum. But there are significant limitations to this approach. First, there is some uncertainty involved in weighting the contributions when more than one bass radiator is involved. Second, nearfield measurement does not capture cabinet diffraction effects, which means it does not represent the true farfield output at higher frequencies—something that can cause errors when combining the near- and farfield responses. Third, and most important in the current context, nearfield measurement tells you nothing useful about radiation from the cabinet walls, so it does nothing to solve the problem of quantifying cabinet (or stand) resonances.

To achieve that, there is no alternative but to improve the frequency resolution of the conventional farfield measurement process. And that, as already described, entails widening the measurement time window. But how can this be achieved without a tall pole or anechoic chamber?

The first step, naturally enough, is to avail yourself of a larger room in which to make the measurement, thereby increasing the time delay before the arrival of the first boundary reflection. A hundred yards or so down the road from where I live is a community hall that, because it meets some badminton regulation, has a ceiling about 9m high. It was while I was giving blood there one time, staring at said lofty ceiling, that it dawned on me: here was an ideal space for loudspeaker measurement.

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Footnote 2: W.R. Stevens, "Loudspeakers—Cabinet effects," Hi-Fi News, September 1976, p.87.

Footnote 3: Since the summer of 2000, I have been measuring loudspeakers outdoors in an enclosed yard, which allows the speaker to be raised around 6' from the ground on a high stand. However, this still doesn't give me more than 6ms or so of true anechoic impulse response.—John Atkinson

Footnote 4: D.B. Keele, "Low-Frequency Loudspeaker Assessment by Nearfield Sound-Pressure Measurements," JAES, Vol.22 No.3, 1974.