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shadmitcorr.doc
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/
shadmitcorr.doc
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Calculate the admittance and correlation spectra of two real functions.
Usage
-----
admit, error, corr = SHAdmitCorr (gilm, tilm, [lmax])
Returns
-------
admit : float, dimension (lmax+1)
The admittance function, which is equal to Sgt/Stt.
error : float, dimension (lmax+1)
The uncertainty of the admittance function, assuming that gilm and tilm are
related by a linear isotropic transfer function, and that the lack of
correlation is a result of uncorrelated noise.
corr : float, dimension (lmax+1)
The degree correlation function, which is equal to Sgt/sqrt(Sgg Stt).
Parameters
----------
gilm : float, dimension (2, lmaxg+1, lmaxg+1)
The real spherical harmonic coefficients of the function G.
tilm : float, dimension (2, lmaxt+1, lmaxt+1)
The real spherical harmonic coefficients of the function T.
lmax : optional, integer, default = min(lmaxg, lmaxt)
The maximum spherical harmonic degree that will be calculated for the
admittance and correlation spectra. This must be less than or equal to the
minimum of lmaxg and lmaxt.
Description
-----------
SHAdmitCorr will calculate the admittance, admittance error, and correlation
spectra associated with two real functions expressed in real spherical
harmonics. The admittance is defined as Sgt/Stt, where Sgt is the cross-power
spectrum of two functions G and T. The degree-correlation spectrum is defined as
Sgt/sqrt(Sgg Stt), which can possess values between -1 and 1. The error of the
admittance is calculated assuming that G and T are related by a linear isotropic
transfer function: Gilm = Ql Tilm + Nilm, where N is noise that is uncorrelated
with the topography. It is important to note that the relationship between two
fields is often not described by such an isotropic expression.