Fast directional spatially localized spherical harmonic transform

Zubair Khalid*, Rodney A. Kennedy, Salman Durrani, Parastoo Sadeghi, Yves Wiaux, Jason D McEwen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


We propose a transform for signals defined on the sphere that reveals their localized directional content in the spatio-spectral domain when used in conjunction with an asymmetric window function. We call this transform the directional spatially localized spherical harmonic transform (directional SLSHT) which extends the SLSHT from the literature whose usefulness is limited to symmetric windows. We present an inversion relation to synthesize the original signal from its directional-SLSHT distribution for an arbitrary window function. As an example of an asymmetric window, the most concentrated band-limited eigenfunction in an elliptical region on the sphere is proposed for directional spatio-spectral analysis and its effectiveness is illustrated on the synthetic and Mars topographic data-sets. Finally, since such typical data-sets on the sphere are of considerable size and the directional SLSHT is intrinsically computationally demanding depending on the band-limits of the signal and window, a fast algorithm for the efficient computation of the transform is developed. The floating point precision numerical accuracy of the fast algorithm is demonstrated and a full numerical complexity analysis is presented.

Original languageEnglish
Article number6463461
Pages (from-to)2192-2203
Number of pages12
JournalIEEE Transactions on Signal Processing
Issue number9
Publication statusPublished - 1 May 2013


  • 2-sphere
  • Signal analysis
  • spherical harmonics

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing


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