ANU Open Research Repository has been upgraded. We are still working out a few issues, and there may be periodic outages throughout the day. Please get in touch with if you experience any issues.

An optimal-dimensionality sampling scheme on the sphere with fast spherical harmonic transforms




Khalid, Zubair
Kennedy, Rodney
McEwen, Jason

Journal Title

Journal ISSN

Volume Title


Institute of Electrical and Electronics Engineers (IEEE Inc)


We develop a sampling scheme on the sphere that permits accurate computation of the spherical harmonic transform and its inverse for signals band-limited at L using only L2 samples. We obtain the optimal number of samples given by the degrees of freedom of the signal in harmonic space. The number of samples required in our scheme is a factor of two or four fewer than existing techniques, which require either 2L2 or 4L2 samples. We note, however, that we do not recover a sampling theorem on the sphere, where spherical harmonic transforms are theoretically exact. Nevertheless, we achieve high accuracy even for very large band-limits. For our optimal-dimensionality sampling scheme, we develop a fast and accurate algorithm to compute the spherical harmonic transform (and inverse), with computational complexity comparable with existing schemes in practice. We conduct numerical experiments to study in detail the stability, accuracy and computational complexity of the proposed transforms. We also highlight the advantages of the proposed sampling scheme and associated transforms in the context of potential applications.





IEEE Transactions on Signal Processing


Journal article

Book Title

Entity type

Access Statement

License Rights



Restricted until