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.