Rapidly decaying Fourier-like bases

Kevin Liang*, G. W. Forbes, Miguel A. Alonso

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


In many applications it is natural to seek to extract a characteristic scale for a function’s variations by reference to a frequency spectrum. Although the moments of a spectrum appear to promise simple options to make such a connection, standard Fourier methods fail to yield finite moments when the function’s domain is itself finite. We investigate a family of Fourier-like bases with rapidly decaying spectra that yield well-defined moments for such cases. These bases are derived by considering classes of functions for which a normalised mean square derivative is stationary. They are shown to provide precisely the type of spectrum needed to complete a recent investigation of mid-spatial frequency structure on optical surfaces [K. Liang, Opt. Express 27, 3390-3408 (2019)].

Original languageEnglish
Pages (from-to)32263-32276
Number of pages14
JournalOptics Express
Issue number22
Publication statusPublished - 28 Oct 2019


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