1207.5558 (Z. Khalid et al.)

Fast directional spatially localized spherical harmonic transform    [PDF]

Z. Khalid, R. A. Kennedy, S. Durrani, P. Sadeghi, J. D. McEwen

For signals defined on the sphere, we develop a tool to project the signal onto the joint spatio-spectral domain. We revisit the definition of the spatially localized spherical harmonic transform (SLSHT) from the literature, where azimuthally symmetric window functions were used for spatial localization. We propose a directional (i.e., azimuthally asymmetric) window function for spatial localization, which enables the transform to reveal localized directional content in the spatio-spectral domain; hence, we call the proposed transform the directional SLSHT and the spatio-spectral representation as the directional SLSHT distribution. We present a fast algorithm for the efficient computation of the transform, which is required for practical applications. We study the accuracy and speed of our fast algorithm and show that it achieves very good numerical accuracy, with numerical errors at the level of floating point precision. Finally, an example is presented to illustrate the capability of the directional SLSHT to resolve localized directional features in the spatio-spectral domain.

View original: http://arxiv.org/abs/1207.5558