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File filtered-pole.tab
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Author: christian.bizouard@obspm.fr
Started on December 6 2017
The filtered pole coordinates xf and yf are obtained by Gaussian filter of the IERS C01 pole
coordinates computed at 0.05 year interval from 1900. They constitute one of the two realisations of the "low-frequency pole",
replacing in updated IERS Conventions the misleading term of "mean pole" (the other realisation is a linear expression of time,
giving the pure secular polar motion).
The file filtered-pole.tab is updated once per month from December 2017. All successive files are stored in the repertory
filteredpole under the name
filtered-pole.tab.mm.yy
where mm and yyyy are the digits corresponding to the month and year of production respectively.
Between successive files, edge effects of the filter can cause difference of about 3 mas over the last 4 years.
At date T, the filtered values (xf, yf) of the samples (x_i, y_i) at date T_i ( i=1,...,n) are given by
xf(T) = Sum w_i x_i / Sum w_i
yf(T) = Sum w_i y_i / Sum w_i
where the weights are determined by the Gaussian function
w_i = exp[-0.5* ((T(i)-T)/a)^2]
with a = 3.40 years.
This procedure is also a low pass frequency filter having the frequency transfer function
T(f) = exp[-2*pi^2 (a f)^2].
For a =3.4, we have:
T(f=1/25 cycle/year) = 70%
T(f=1/50 cycle/year) = 91%
T(f=1/100 cycle/year) = 98%
However, before to apply this filter, seasonal and Chandler wobble are removed by pass-band filter
in order to avoid any leakage of these large oscillation in low-frequency band.