Fractional Fourier domains

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Date Issued
1995Author
Ozaktas, H., M.
Aytür O.
Please cite this item using this persistent URL
http://hdl.handle.net/11693/25909Journal
Signal Processing
Published as
http://dx.doi.org/10.1016/0165-1684(95)00076-PCollections
- Research Paper [7145]
Abstract
It is customary to define the time-frequency plane such that time and frequency are mutually orthogonal coordinates. Representations of a signal in these domains are related by the Fourier transform. We consider a continuum of "fractional" domains making arbitrary angles with the time and frequency domains. Representations in these domains are related by the fractional Fourier transform. We derive transformation, commutation, and uncertainty relations among coordinate multiplication, differentiation, translation, and phase shift operators between domains making arbitrary angles with each other. These results have a simple geometric interpretation in time-frequency space. © 1995.