Ive spent some time studying the measurements I previously described having taken, and observing on the computer screen the results of applying various window durations to them. As a result Ive chosen two specific correction filters to evaluate sonically in the coming days. Ive uploaded jpg files depicting those filters, which can be viewed
here. There are ten files, five for each filter, depicting the corrections in terms of frequency response, group delay, impulse response, step response, and phase response. In interpreting them, be sure to take into account the scales marked on the vertical axes. (To see the markings clearly, click on the image thumbnails to expand them). The measurements, window durations, and correction limits that were used in creating these filters are described below.
The ways in which I narrowed down the many possible correction filters to these two are as follows:
As you may recall, I had performed measurements of each speaker at distances of 30, 36, and 42 inches, with the grilles removed, and also at 36 inches with the grilles in place. The grilles appeared to make essentially no difference.
I found that both 36 inch measurements of the right speaker had a huge group delay spike at about 420 Hz, which was not helped significantly by smoothing, and which did not appear in the 30 or 42 inch measurements of that speaker, and which did not appear in any of the measurements of the other speaker. I have no idea why that occurred, as the two speakers and the mic were positioned identically when they were measured, within perhaps 1/8 or less. The only variable that seemed to be present, which in turn seems very unlikely to have anything to do with that spike, is that the design of the speakers is such that their rear surfaces, rather than being parallel to the front baffle, or being otherwise identical between the two speakers, are mirror-imaged at an angle such that the side of each speaker that is closest to the other speaker (in their normal positions) is 1.5 inches shorter than the other side. In any event, due to that spike I eliminated the 36 inch measurements from consideration.
I experimented on the computer with windowing of the 30 and 42 inch measurements at three different points, each of them just prior to what appeared to be significant reflections or increases in reflections, at about 13, 17, and 21 milliseconds. The 21 ms window resulted in significant frequency response wiggles in the 500 Hz to 1000 Hz area, so I eliminated that choice.
The 13 and 17 ms window durations provided results that looked fairly similar, but 13 ms (which terminated just prior to what Im pretty certain was a ceiling reflection, based on its timing) looked slightly more promising. So thats what I went with, for both measurement distances, that also being exactly what Andrew (Drewan77) had suggested the other day after looking at the measurements I had posted.
The (approximately) 13 ms window duration (actually 13.1 ms for the 30 inch measurement and 13.2 ms for the 42 inch measurement) corresponds to 7.4 ms after the initial sound arrival for the 30 inch measurement, and 6.7 ms after the initial sound arrival for the 42 inch measurement.
Regarding the correction limits I set, I used the default amplitude limits, which in turn were not called into play at all within the frequency response limits that I set. For both correction filters, Filter 1 corresponding to the 30 inch measurements and Filter 2 corresponding to the 42 inch measurements, I set frequency response limits such that corrections were only performed between about 400 Hz and 10.5 kHz. Those choices being made taking into account suggestions from both Nyal Mellor of Acoustic Frontiers and Alan Langford of DEQX to be conservative in dealing with the top octave, and to avoid correcting further into the bass region than seems reasonable in relation to the window duration. With the latter determination being made in the manner I described in my post dated 6-22-15. And, also, taking into account a presumption I made that both the high frequency and low frequency limits should be chosen such that abrupt discontinuities in frequency response are not introduced at the limit points.
Finally, in deriving the correction filters all parameters which I havent mentioned were used at their default values, including 100% smoothing.
Best regards,
--Al