Gauss-Legendre Sampling on the Rotation Group

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

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We propose a Gauss-Legendre quadrature based sampling on the rotation group for the representation of a band- limited signal such that the Fourier transform (FT) of a signal can be exactly computed from its samples. Our figure of merit is the sampling efficiency, which is defined as a ratio of the degrees of freedom required to represent a band-limited signal in harmonic domain to the number of samples required to accurately compute the FT. The proposed sampling scheme is asymptotically as efficient as the most efficient scheme developed very recently. For the computation of FT and inverse FT, we also develop fast algorithms of complexity similar to the complexity attained by the fast algorithms for the existing sampling schemes. The developed algorithms are stable, accurate and do not have any pre-computation requirements. We also analyse the computation time and numerical accuracy of the proposed algorithms and show, through numerical experiments, that the proposed Fourier transforms are accurate with errors on the order of numerical precision.
Original languageEnglish
Pages (from-to)207-211
Number of pages5
JournalIEEE Signal Processing Letters
Volume23
Issue number2
DOIs
Publication statusPublished - Feb 2016

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