Hilbert transform associated with the fractional Fourier transform

    Authors

    A. I. Zayed

    Comments

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    Abbreviated Journal Title

    IEEE Signal Process. Lett.

    Keywords

    analytic signals; fractional Fourier transform; generalized Hilbert; transform; WIGNER; Engineering, Electrical & Electronic

    Abstract

    The analytic part of a signal f (t) is obtained by suppressing the negative frequency content of f, or in other words, by suppressing the negative portion of the Fourier transform, (f) over cap of f. In the time domain, the construction of the analytic part is based on the Hilbert transform (f) over cap of f(t), We generalize the definition of the Hilbert transform in order to obtain the analytic part of a signal that is associated with its fractional Fourier transform, i,e,, that part of the signal f (t) that is obtained by suppressing the negative frequency content of the fractional Fourier transform of f (t), We also show that the generalized Hilbert transform has similar properties to those of the ordinary Hilbert transform, but it lacks the semigroup property of the fractional Fourier transform.

    Journal Title

    Ieee Signal Processing Letters

    Volume

    5

    Issue/Number

    8

    Publication Date

    1-1-1998

    Document Type

    Article

    Language

    English

    First Page

    206

    Last Page

    208

    WOS Identifier

    WOS:000075140300005

    ISSN

    1070-9908

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