Efficient computation of joint fractional Fourier domain signal representation

Date
2008
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Source Title
Optical Society of America. Journal A: Optics, Image Science, and Vision
Print ISSN
1084-7529
Electronic ISSN
1520-8532
Publisher
Optical Society of America
Volume
25
Issue
3
Pages
765 - 772
Language
English
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Abstract

A joint fractional domain signal representation is proposed based on an intuitive understanding from a time-frequency distribution of signals that designates the joint time and frequency energy content. The joint fractional signal representation (JFSR) of a signal is so designed that its projections onto the defining joint fractional Fourier domains give the modulus square of the fractional Fourier transform of the signal at the corresponding orders. We derive properties of the JFSR, including its relations to quadratic time-frequency representations and fractional Fourier transformations, which include the oblique projections of the JFSR. We present a fast algorithm to compute radial slices of the JFSR and the results are shown for various signals at different fractionally ordered domains.

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Published Version (Please cite this version)