Fast spin ±2 spherical harmonics transforms and application in cosmology

Yves Wiaux*, L. Jacques, Pierre Vandergheynst

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


A fast and exact algorithm is developed for the spin ±2 spherical harmonics transforms on equi-angular pixelizations on the sphere. It is based on the Driscoll and Healy fast scalar spherical harmonics transform. The theoretical exactness of the transform relies on a sampling theorem. The associated asymptotic complexity is of order O (L2 log22 L), where 2L stands for the square-root of the number of sampling points on the sphere, also setting a band limit L for the spin ±2 functions considered. The algorithm is presented as an alternative to existing fast algorithms with an asymptotic complexity of order O (L3) on other pixelizations. We also illustrate these generic developments through their application in cosmology, for the analysis of the cosmic microwave background (CMB) polarization data.

Original languageEnglish
Pages (from-to)2359-2371
Number of pages13
JournalJournal of Computational Physics
Issue number2
Publication statusPublished - 1 Oct 2007


  • Computational methods
  • Cosmic microwave background
  • Cosmology
  • Data analysis

ASJC Scopus subject areas

  • Computer Science Applications
  • General Physics and Astronomy


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