Re: Is an upsampled Maximum Length Sequence also an MLS?

robert bristow-johnson wrote:

BTW, as i point out in that tutorial, MLS has some truly bizarre
behavior with non-linearities in your device under test.  and
loudspeakers are not known for being the most linear of transducers.
you might want to consider linearly swept frequency measurements.

Interesting!

Farina wrote a paper [1] where he describes how he identifies the
first couple of terms in the Volterra series of the loudspeaker
transfer function using swept sine measurements.

A quick search turned out a paper [2] which compares four standard
excitation signals in acoustic measurements. Sensitivity to non-
linearity is not mentioned in the abstract, but as I read the section
on sine sweeping it mentions exactly that same fact (possiblity to
accomodate non-linearity) as an advantage against MLS.

I think the reason why there exist de facto standard test signals like
impulses, MLS and sine sweeps is because the inverse for these test
signals is well known. In principle, non-parametric identification of
the impulse response of an LTI system under measurement noise is a
linear problem. Any excitation signal can be used, but of course there
are good and bad choices. I tried this approach using a couple of test
signals and it turned out that the swept sine resulted in a highly
instable least-squares inversion (= bad choice). Much better was the
MLS sequence. I also had good results with arbitrary music signals and
uniform or Gaussian white noises.

I used the Matlab "\" operator for inversion. However, the resulting
least-squares problem is highly structured, unfortunately Matlab does
not yet offer an algorithm for solving non-symmetric Toeplitz least-
squares (the main motivation for this would be memory and stability,
not speed). There exist some preconditioners that turn this problem
into one of solving a circulant matrix (which can be inverted in O(n
log n) with the FFT). Lots of variants to try out.

I think a closer inspection on test signals and deconvolution methods
than [2] is warranted. Do you know of any other overview articles?

If all of the advantages of the method described in [1] (robustness to
noise, time-variance and non-linearity of test equipment) are
considered, why has MLS such widespread use in the audio measurement
community?

Regards,
Andor

[1] http://pcfarina.eng.unipr.it/Public/Papers/134-AES00.PDF
[2] http://www.aes.org/e-lib/browse.cfm?elib=11083
.

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