Separable two-dimensional discrete Hartley transform | Zendy

Andrew B. Watson | Zendy; Allen Poirson | Zendy

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Separable two-dimensional discrete Hartley transform

Author(s) -

Andrew B. Watson,

Allen Poirson

Publication year - 1986

Publication title -

journal of the optical society of america a

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.803

H-Index - 158

eISSN - 1520-8532

pISSN - 1084-7529

DOI - 10.1364/josaa.3.002001

Subject(s) - discrete hartley transform , hartley transform , separable space , convolution (computer science) , discrete fourier transform (general) , convolution theorem , mathematics , extension (predicate logic) , circular convolution , fourier transform , discrete time fourier transform , fractional fourier transform , pure mathematics , mathematical analysis , computer science , fourier analysis , artificial intelligence , artificial neural network , programming language

Bracewell has proposed the discrete Hartley transform (DHT) as a substitute for the discrete Fourier transform (DFT), particularly as a means of convolution [ J. Opt. Soc. Am.73, 1832 ( 1983)]. Here we show that the most natural extension of the DHT to two dimensions fails to be separable in the two dimensions and is therefore inefficient. We consider an alternative separable form and derive a corresponding convolution theorem. We also argue that the DHT is unlikely to provide faster convolution than the DFT.

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