Quasi-analytic multidimensional signals

In a recent paper, the authors have presented the unified theory of n-dimensional (n-D) complex and hypercomplex analytic signals with single-orthant spectra. This paper describes a specific form of these signals called quasi-analytic. A quasi-analytic signal is a product of a n-D low-pass (base-band) real (in general non-separable) signal and a n-D complex or hypercomplex carrier. By a suitable choice of the carrier frequency, the spectrum of a low-pass signal is shifted into a single orthant of the Fourier frequency space with a negligible leakage into other orthants. A measure of this leakage is defined. Properties of quasi-analytic signals are studied. Problems of polar representation of quasi-analytic signals and of its lower rank representation are discussed.