Calculate the eigenfunctions of the spherical-cap concentration problem for a single angular order.

Usage

tapers, eigenvalues = SHReturnTapersM (theta0, lmax, m)

Returns

tapers : float, dimension (lmax+1, lmax+1)
The spherical harmonic coefficients of the lmax+1 localization windows, arranged in columns. The first and last rows of each column correspond to spherical harmonic degrees 0 and lmax, respectively, and the columns are arranged from best to worst concentrated.
eigenvalues : float, dimension (lmax+1)
The concentration factors of the localization windows.

Parameters

theta0 : float
lmax : integer
The spherical harmonic bandwidth of the localization windows.
m : integer
The angular order of the localization windows.

Description

SHReturnTapersM will calculate the eigenfunctions (i.e., localization windows) of the spherical-cap concentration problem for a singular angular order. The spherical harmonic coefficients of each window are given in the columns of tapers, and the corresponding concentration factors are given in eigenvaules. The columns of tapers are ordered from best to worst concentrated, and the first and last rows of each column correspond to spherical harmonic degrees 0 and lmax, respectively. The localization windows are normalized such that they have unit power.

References

Wieczorek, M. A. and F. J. Simons, Localized spectral analysis on the sphere, Geophys. J. Int., 162, 655-675, 2005.

Simons, F.J., F.A. Dahlen, and M.A. Wieczorek, Spatiospectral concentration on a sphere, SIAM Review, 48, 504-536, 2006.