Title

Hubert transform associated with the fractional fourier transform

Keywords

Analytic signals; Fractional fourier transform; Generalized hilbert transform

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, of f. In the time domain, the construction of the analytic part is based on the Hilbert transform f 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.

Publication Date

12-1-1998

Publication Title

IEEE Signal Processing Letters

Volume

5

Issue

8

Number of Pages

206-208

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1109/97.704973

Socpus ID

0032138891 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0032138891

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