  Generalized analytic signal associated with the linear canonical transform
(LCT) was proposed recently by Fu and Li ["Generalized Analytic Signal
Associated With Linear Canonical Transform," Opt. Commun., vol. 281, pp.
1468-1472, 2008]. However, most real signals, especially for baseband real
signals, cannot be perfectly recovered from their generalized analytic signals.
Therefore, in this paper, the conventional Hilbert transform (HT) and analytic
signal associated with the LCT are concerned. To transform a real signal into
the LCT of its HT, two integral transforms (i.e., the HT and LCT) are required.
The goal of this paper is to simplify cascades of multiple integral transforms,
which may be the HT, analytic signal, LCT or inverse LCT. The proposed
transforms can reduce the complexity when realizing the relationships among the
following six kinds of signals: a real signal, its HT and analytic signal, and
the LCT of these three signals. Most importantly, all the proposed transforms
are reversible and undistorted. Using the proposed transforms, several signal
processing applications are discussed and show the advantages and flexibility
over simply using the analytic signal or the LCT.
