Compute the latitudinal weights used in the Driscoll and Healy (1994) spherical harmonic transform.

Usage

aj = DHaj (n)

Returns

aj : float, dimension (n)
The latitudinal weights used in the spherical harmonic transform.

Parameters

n : integer
The number of samples in latitude used in the spherical harmonic transform. This must be even.

Description

DHaj will calculate the latitudinal weights used in the spherical harmonic transform of Driscoll and Healy (1994; equation 9). The number of samples n must be even, and the transform and its inverse are implemented as SHExpandDH and MakeGridDH, respectively. It is noted that the first element, corresponding to the north pole, is always zero. The element corresponding to the south pole is not included.

Reference

Driscoll, J.R. and D.M. Healy, Computing Fourier transforms and convolutions on the 2-sphere, Adv. Appl. Math., 15, 202-250, 1994.