Quote:
Originally Posted by Shiraz
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Hi Ray,
Thanks for the link to the Quanta Magazine article that provides
additional background on the debate.
Quote:
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Originally Posted by Michael Brooks, New Scientist
The best weapon in the arsenal is known as a Fourier transform. This splits a signal into various frequency components and converts it into a power spectrum, which details how much of the signal’s power is contained in each of those components. This can be done with a window function, a mathematical tool that operates on a selected part of the data. Whether or not to use one is at the heart of the disagreement over LIGO’s results (see main story).
Andrew Jackson’s dissenting team at the Niels Bohr Institute in Denmark chose not to use a window function, a decision that LIGO’s Neil Cornish describes as a “basic mistake”. Jackson says they didn’t use one because it subtly alters the Fourier-transformed data in a way that can skew the results of subsequent processing.
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So to window or not to window, that is the question.
As I understand it, even when one doesn't use a window function on
a FFT, if you are just considering some brief time interval then
you are effectively getting a rectangular window function anyway.
I'd speculate it is the nature of a transient - something in the time domain -
to now being analyzed in the frequency domain.
However, the nature of window functions is that they create a mathematical
convolution between themselves and the signal you are sampling.
So I know experts in signal analysis have to be careful when analysing transient
signals,. There are a gamut of window function choices with various
tradeoffs and so on from which one can choose.
Given the wealth of expertise in the world in signal analysis across
multiple disciplines in engineering and science plus the number of
mathematicians and statisticians who are steeped in the
mathematical underpinnings, in some ways it seems a surprise this
debate has dragged on for so long.
Certainly the top graph in the Quanta Magazine paper
looks more correlated with a larger SNR than the lower graph when you
just eyeball it but that falls short of the analytical rigour required.
Alas, I am no expert and my experience is limited to now and then
switching on a benchtop spectrum analyzer, twiddling the knobs and
with luck trying to separate the signal from the noise in obvious
radio signals whose strength is dozens of orders of magnitude stronger than LIGO.
I note the LIGO team have one technology they call the Fast Chirp Transform :-
https://www.advancedligo.mit.edu/fast_chirp.html
They have this patent on it :-
https://patents.google.com/patent/US6509866B2/en