Positive Time Alignment

This past Saturday, I intended to do a "final" (for now) measurement of the actual frequency response resulting from the latest time alignment in the left channel, and then check if the right channel was up to speed now also (which hasn't actually been tested in awhile, I just apply a known correction to the left vs right subs, the other speakers are sufficiently physically centered according to previous measurements).

One look at the results, however, left me wanting to do another check.

Remember that I had adjusted the subwoofer alignment using only out-of-phase "impulse response" sweeps that get converted to frequency response by ARTA.  When the alignment is correct, so the theory goes, there should be maximum cancellation at the acoustic crossover frequency.

There are several problems with this in practice, however.  The first is that the acoustic crossover frequency will likely differ from what was dialed in electrically.  (The acoustic crossover function may differ as well!  It surely won't be a perfect LR8 or whatever, unless all other influences, including room modes and driver resonances, are compensated for.)

OK, I thought I had a handle on that last time.

The other problems are that the resolution of ARTA even with 256k samples, is that the bass resolution appears to be quite poor.   I seem to get much better bass resolution using the 1/6 octave mode of my iPhone RTA app.

I would have thought the samples corresponds to bins of the FFT analysis, but as writing this report, I discovered that there is a separate Bins parameter in the Analysis Parameters setup page.  I'll have to explore that later.  I have just now discovered that the Bins parameter was set to a mere 64k.  However that should still be better than the RTA app which only uses 16k bins, even if possibly covering half as many frequencies.  I noticed some other possibly relevant settings on the Analysis Parameters page, including the Window Function, which strangely defaults to the least selective Hann function.  It seems to me that even at that, I'm seeing less than I should.  64k bins over 48k frequencies is still more than one bin per Hz.

Anyway, for now just take it that the low frequency resolution is poor, and add to that there is a lot of acoustic noise.  I have never shut down my air conditioner (because I don't want to be shortening its life due to my audio madness) and though it is very quiet, it may still be noticeable (especially for morning and afternoon measurements, it is generally quieter in the evenings).  And various other background noises.  The noise level is such that making the same measurement over and over may result in as much as 1dB variation in a particular frequency.  So if you're seeking the deepest dip, and steering your search based on differences smaller than 1dB, there's not much assurance you are going to be steered correctly.

There seems to be a third phenomenon, but it may just be the effect of the first two I've just described.  That is, when there is a deep acoustic notch, caused by room modes or something like that, near the crossover frequency, sometimes the cancellation notch "merges" with the acoustic notch, in a sort of blob-like fashion.  I worry that in these cases the cancellation measurement cannot be assumed to only correlate with the crossover frequency time alignment.

Anyway, all those factors were in play, I now believe, when I did the time alignment in the days just before August 3.

The bottom line is that merely measuring for the best cancellation, either at the nominal crossover frequency or what appears to be (by maximum notch depth) the acoustic crossover frequency, can be misleading.

I'm not believing the reverse, that looking for the best summation is better.  And the best summation is not merely at the crossover frequency, but in an affected range around the crossover frequency, which may extend down to 1/2 of the crossover frequency on the downside, and 2x the crossover frequency on the upside.  That is the range that should be looked at in evaluating how well the crossover is working, and therefore how good the time alignment is (if that is the independent variable).

This was the starting measurement which got me worried:

In my then-way of thinking, the acoustic crossover is around 120 Hz, and that's where this shows a notch centered (though 125 is about half way up to a peak).  But what disturbed me more than that was the dip at 60 Hz.  Back in an earlier measurement (well, it was the one where the midrange was out of polarity) that 60 Hz dip had gone away, so I thought I had fixed it, and now it's back.

I wasn't thinking correctly, maybe.  That 60 Hz dip had gone away possibly because rather than in spite of the fact that the midrange was out of polarity in the bass.  So maybe I should have been ignoring that.  But anyway, if you draw a line between the peaks and dips, what you see isn't pretty, the bass is way down around 60 Hz, peaks about 135 Hz which is significantly above the crossover frequency, then goes generally downward all the way to 500.  I thought it should be much more level than that, on average.  I remembered it being much more level than that.  This looked wrong.  And maybe it was.

This time, I decided to be very systematic about measuring on a grid to get the overall picture of change over the range of interest, before searching to optimize between what appear to be the best grid points.  That way, I figured, I would not be steered in the wrong direction by the randomness of the measurements, which appears to result from noise and possibly other factors.

And by now I had figured out that there is not just one delay time that yields a maximum or minimum, but a series of points, separated by the cycle time of the acoustic crossover frequency.  So if the crossover frequency were 100 Hz, optimal points would appear every 10 ms, where you would get either maximum summation or maximum cancellation.  If my acoustic crossover is identical to my nominal crossover at 125 Hz, I would see repeats about every 8ms, which appears to be the case.

So the best way to keep from going off track is to restrict measurements to a 10ms interval.  I'm not entirely sure I have found the correct 10ms interval, but it can't be too far off, given my initial alignment of the "driver start time," modified by the fact that the bass apparently starts out-of-polarity with a phase lead.  So last time I started from the point where the bass response to a transient starts going in the in-phase direction, and lined that up with the positive phase of the panel response, before optimizing around the crossover frequency.

Then, since there is a known interval, we can set grid points at some considerable distance, but still within that interval, and not worry about being cast far astray because of lack of convexity in the "delay time" vs "peak response" function.  Within every 8ms range there should be one optimal point, and everything else should be worse than that one point, unless the optimal point is at one end of the interval, and then the second optimal point should be at the other end.  This regularity makes gridding a useful method.  If the function were non-convex, in the presense of noise we'd have to sample every single possibility.

The previous adjustment was 3.32 ms delay (relative to 10 ms delay for the panels) so I started just below that at 1.32ms delay, which gave this curve:

1.32 ms subwoofer delay, note crossover suckout

Here the likely acoustic crossover has nearly been sucked into a depression, so I think this is wrong.  Magnitude at 125 Hz is 119.48 db.  (Note these numbers are way too big because my Focusrite level settings are not calibrated in ARTA.  But the numbers from successive tests will be comparable because I did not adjust the levels between them, because I knew that would throw everything off.)

Next I tried 3.32 ms, a repeat of the test I had done earlier in the day

125 Hz nominal crossover frequency is now halfway up a peak, with a magnitude of 125.37 dB.  Progress is being made!  Onward to 5.32.

5.32ms subwoofer delay

I noticed that 60-300 Hz appears now appears more level to my averaging eye than anything seen before.  The dip at 60 Hz is now pretty small, with the dip at 90 Hz larger (which IIRC is the way the sub measures by itself).  Even the reflection cancellation around 300 Hz is diminished considerably.  Overall a pretty nice looking response, with the worst feature being the dip at 500 Hz which has nothing to do with the crossover.  The magnitude at crossover frequency was 126.34, the best yet!

7.32 ms subwoofer delay

Things went from best at 5.32 ms to second worst at 7.32 ms, with a magnitude of 121.80 dB.  Only 1.32 ms so far was even worse, and the drop is so big it could not have been caused by noise.  Everything else looks bad also.  A large dip has opened up just above the nominal crossover frequency (is that the real acoustic crossover?).  Distortion in those frequencies has risen above 1% !   This is what  bad time alignment looks like, and just 2ms or so off the ideal.

It is now pretty certain that 3.32ms - 5.32ms is the optimal range, as those are bracketed by far worse performance at 1.32ms and 7.32ms.  But just to be sure, I kept on going.

9.31ms subwoofer delay

A corner has clearly been turned, and things are headed up again, but no where near another optimal range, with magnitude at 122.05dB.  However, otherwise, the bass looks on a fairly smooth downward tilt from 30 Hz to 300 Hz.

11.32ms delay

At 11.32ms I measured the actual highest magnitude I measured on Saturday night.  I could just barely complain about the response 200-400 Hz being somewhat weaker than usual, with the response from 60-100 Hz being their best, but considering the former more important.

But it should be remembered that 11.32ms is 8ms longer than 3.32ms.  What has happened is exactly as predicted, we have reached another optimal point 8ms longer than the first because 8ms is the cycle time of 125 Hz, the nominal crossover, which is probably very close to the actual acoustic crossover frequency.  It may be this measures slightly better because of noise, or perhaps because it is closer to the  local optimum it is closest to than 3.32.  That makes sense because it appears the acoustic crossover may be above 125 Hz, which would correspond to the cycle time less than 8 ms, which would mean the local optimum which corresponds to this one at 11.32 but nearest 3.32 is higher than 3.32.

There could be better points around these points, the real question is where those better points are, which may not be exactly 3.32 or 11.32 ms.

There has to be different method of choosing between the local optimum close to 3.32 and the local optimum near 11.32.  And that other method, so far, has been described, but should probably be doubled checked, and cross checked by other methods, and so on, in the future.  And so far, I've thrown in my lot with the true alignment point being in the range 3.32 to 5.32, because that fits closest to the aligning the initial upswings in transient response, which occurs around 2ms delay, and I had simply continued up to 11.32 to verify the cyclical nature of the local pseudo-alignment points by the maximum-output method.

But there might be a much better value between 3.32 and 5.32 than I had measured so far, so I proceeded to search for the optimum in that range.  I started with the obvious choice of 4.32 ms.

4.32 ms subwoofer delay

This is clearly better than 3.32 ms, and only slightly worse than 5.52.  Following general searching principles, I should then look between 4.32 and 5.32.  But instead, I was troubled by the possibility that it should be lower, because of the apparent optimum around 11.32.  So, instead, I checked 4ms.

4.0 ms subwoofer delay

I should have followed the general search principles.  This is obviously worse at 126.11dB, so it seems we need to look above 4.32 and not below.

5.0 ms subwoofer delay

Now this is better, the second best magnitude so far at 126.43dB, second only to the other maximum at 11.32 ms which is not in the correct zone by my reasoning.  The more logical place to look now would be between 5 and 5.32, but instead I looked lower again, at 4.7.

4.7 ms subwoofer delay

Lucky guess maybe, not we're up to 126.5dB, highest value so far in this region, and the bass is holding pretty tight tolerances from 50-300 Hz.

4.86 ms subwoofer delay

4.86 ms delay measured better at 126.51dB.  But that's a mere 0.01dB better.  What about in between?

4.78 ms delay

Weird, the point in between two high points is lower than either one.  But we're talking 0.11dB lower.  Remembers there's a lot of noise going on.  Clearly without getting rid of the noise, we can't zero in on the true optimum better than we are doing.  But also, this is pretty close.  The highest point yet is 4.86 ms delay, which is a mere 0.06 ms more.  And another lower point, at 5.0 ms, is only 0.14 ms higher.

I decided that the search has reached a sufficiently good point at 4.86 ms, though I suppose it could be very slightly better at 4.92 ms or something like that, it would be hard to know given the noise level.  I then re-measured 4.86 again.

2nd measurement of 4.86 ms subwoofer delay

Oops, the value at 4.86ms delay has fallen from 126.51dB to 126.44dB, illustrating the "noise" problem perfectly.  But I already decided this was good enough, it's seems within about 0.2dB of the optimum, and 0.2ms of the optimum adjustment, and it's hard to do much better without much more careful measurements, like shutting off everything else in the house, that I'm not willing to do.

You may also notice all the spectra from 4.7ms to 5.0ms look pretty similar and quite good in all respects, the bass response slopes downward from 20 Hz to 400 Hz quite nicely, with just a bit too much of a dip at 500.  The 300 Hz cancellation from rear wall reflection is hardly visible.

The time record, with polarity corrected, of a 2 ms pulse looks like this:

2 ms pulse

The first two ms look fairly pulse-like, with with everything pretty much in alignment.  I'm not sure why there appears to be a negative refection about 3 ms delayed, that could be the chair or some acoustic reflection.  I generally do not move the chair when doing measurements.