Fractional Hilbert transform

Abstract

We have generalized the Hilbert transform by defining the fractional Hilbert transform (FHT) operation. In the first stage, two different approaches for defining the FHT are suggested. One is based on modifying only the spatial filter, and the other proposes using the fractional Fourier plane for filtering. In the second stage, the two definitions are combined into a fractional Hilbert transform, which is characterized by two parameters. Computer simulations are presented.

Design and application of discrete-time fractional Hilbert transformer

“…0 n 0 ): (9) Combine the above results. The analytic signalx (n) is given bŷ x (n) = cos(!0n) 0 e 0j cos(!0n 0 ) = je 0j sin( )e j!…”

Bragg grating based integrated photonic Hilbert transformers

“…Fractional Hilbert transformers (FrHT) offer a new degree of freedom, the fractional order, which can be used for a better characterization of a signal under test, or as an additional encoding parameter [10,11] with an experimental demonstration presented in this work.…”

“…The definition of FrHT was discussed in [10,11]. A devices implementing FrHT would have a fractional order of π phase shift in the frequency response while the amplitude response remains constant.…”

Symbolic analysis of time series signals using generalized Hilbert transform

“…Lohmann et al [8] introduced the concept of a generalized Hilbert transform in the fractional Fourier space instead of the conventional Fourier space; a discrete version of this generalized Hilbert transform was developed later [9]. For geophysical applications, Luo et al [10] proposed another type of generalized Hilbert transform that is essentially the windowed version of traditional Hilbert transform.…”