On 04/10/2018 12:17 PM, Fons Adriaensen wrote:
On Tue, Apr 10, 2018 at 10:13:17AM -0700, Fernando Lopez-Lezcano wrote:
I actually should go back to my original approach (more complicated) for 1st
order, which was to derive a 4x4 matrix of filters (which would be 8x8 for
the 2nd order mic).
Not necessarily a good idea.
Thanks for chiming in! Yes, agreed, not necessarily a good idea.
The problem with blindly inverting a matrix (in the F-domain, for each
bin of an FFT) is that it will produce some result no matter what you
throw at it. And of course, convolving the measurements with the
resulting matrix will always produce a result that looks perfect.
When I was doing the 4x4 matrix (at low and mid frequencies, this was
for a different reason which turned out to be unnecessary, IMHO) I was
not actually inverting the FFT bins. I was deriving frequency response
curves for each capsule and Ambisonics component by calculating an A to
B matrix for logarithmically spaced frequency bands. And then creating
FIR filters from those curves (and those filters would converge into one
common filter for each component at high frequencies).
This was not a blind bin by bin inversion, but still "blind" in a sense.
For example, I did not do a frequency dependent selection of the width
of the frequency bands, which presumably could be used to do a better
job by ignoring regions or features of the spectrum for which correction
is irrelevant, and concentrating the effort in the places where
corrections are actually needed (after all the filters should not be a
surprise for a given capsule configuration).
So you basically have no sanity checks at all.
Hmmm, I wonder (for my old approach). After I derive the filters I look
at the polar patterns of the recovered B format components. They look
just fine at low and mid frequencies, but I can also see the effect of
the degradation of the polar pattern of the capsules at high
frequencies. Or crosstalk between orders, also at high frequencies. A
test I did was to synthesize a cardioid in an arbitrary direction, and
see if it was actually a cardioid (or second order lobe in the case of
the Octathingy). Does it remain a cardioid (within reason) and keeps
pointing in the same direction? (within reason, again). The answer has
been normally yes, which means that to some degree the phase
relationship between components is correct, and tracks over frequency.
Anything else I could be looking for in terms of sanity? (other than
moving to a place where there is NO chance of having internet access, ha
ha :-).
(and then of course there is recording concerts and doing field
recordings... so far better ears than mine have been happy with the
results in terms of tonal color of the resulting microphone and spatial
characteristics of the recording, but this was definitely not a
scientific study).
It goes without saying that the results are heavily dependent on the
measurements themselves, GIGO (garbage in garbage out...). So easy to
make mistakes.
Of the tens of calibrations I've seen that were done that way (for
tetrahedrals, eigenmics and others) there has been only *one* that
actually made sense. All the others were just inverting measurement
errors, or trying to correct things for which there is no sensible
remedy, like the Zoom's built-in mic array.
Regularisation can help, if it's done correctly. That means doing
the inversion using SVD with careful adjustment of the singular
values (depending on frequency), and not by just adding an arbitrary
constant to the denominator of 1/x for very low or high frequencies
as advocated in some publications.
Noted, thanks for the advice!
I did a few tests again a while back and verified that at low and mid
frequencies the response from the different capsules was slightly
different (and maybe would benefit from a matrix of filters). High
frequencies, I do not know yet. I have to revisit this again...
Best,
-- Fernando
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