ϕ-linear canonical analytic signals

In this paper, a ϕ-linear canonical Hilbert transform (ϕ-LCHT) is proposed by a linear combination of a given signal and its parameter Hilbert transform (PHT). Herein, a PHT is a generalized HT based on the linear canonical transform (LCT). Some essential properties of a ϕ-LCHT are also derived. According to the derivation of a ϕ-LCHT, four different versions of ϕ-linear canonical analytic signals (ϕ-LCASs) are defined and analyzed in detail. Furthermore, ϕ-LCASs are discussed and compared by some valuable properties such as the LCT spectrum and ϕ-LCHT eigenfunction property. In terms of application, a multi-key single-sideband (SSB) modulation scheme is investigated using one of the ϕ-LCASs proposed in this paper, and its performance with respect to noise and sensitivity to security key perturbations is analyzed.