Gauss-legendre sampling on the rotation group

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

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)


    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
    Article number7336509
    Pages (from-to)207-211
    Number of pages5
    JournalIEEE Signal Processing Letters
    Issue number2
    Publication statusPublished - 1 Feb 2016


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