I am trying to reconstruct the brand
of Fourier transform proposed by
Foster (Cleanest Fourier Transform) and
Ferraz-Mello. There are a lot of expressions
using inner products. Ferraz-Mello uses
statistical fit to find the coefficients
of the Fourier transform. He gives a statistical
interpretation of the power spectrum as
a variate. With hypothesis test, he can
eliminate noise in data, for instance.
The technique became standard in astronomy
and astrophysics. I suggested to physicist
of Utah State University to use it to
correct GPS and WAAS to meet the specification
of equipament necessary to land airplanes.
I understand that there is an error of
about 1.5m in the location of the plane,
and the specifications require 0.6m. If one
is going to use Ferraz-Mello transform in
the kind of problem, it will be necessary to
perform a lot of Graham-Schmidt
orthogonalizations. I could not figure out
how to define inner products in Maxima
and make the system simplify the expressions.
Of course, I am new in Maxima... Could anyone
give me a hint?
Eduardo Costa
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