Effect of fractional Fourier transformation on time-frequency distributions belonging to the Cohen class

Date
1996-02
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Source Title
IEEE Signal Processing Letters
Print ISSN
1070-9908
Electronic ISSN
1558-2361
Publisher
Institute of Electrical and Electronics Engineers
Volume
3
Issue
2
Pages
40 - 41
Language
English
Type
Article
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Abstract

We consider the Cohen (1989) class of time-frequency distributions, which can be obtained from the Wigner distribution by convolving it with a kernel characterizing that distribution. We show that the time-frequency distribution of the fractional Fourier transform of a function is a rotated version of the distribution of the original function, if the kernel is rotationally symmetric. Thus, the fractional Fourier transform corresponds to rotation of a relatively large class of time-frequency representations (phase-space representations), confirming the important role this transform plays in the study of such representations.

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Keywords
Time frequency analysis, Fourier transforms, Kernel, Optical signal processing, Optical computing, Quantum mechanics, Wavelet transforms, Neural networks, Chirp, Signal processing algorithms
Citation
Published Version (Please cite this version)