HYPERCOMPLEX ANALYTIC SIGNALS : EXTENSION OF THE ANALYTICSIGNAL CONCEPT TO COMPLEX SIGNALS

摘要

The analytic signal is a complex signal derived from a realsignal such that its real part is identical to the original realsignal, and its imaginary part is in quadrature (orthogonal) tothe original signal. The analytic signal permits the envelopeof the original signal to be computed, and it also admits thedefinition of an instantaneous frequency and phase.In this paper we present some initial results on extendingthis idea to the case of a complex signal using a hypercomplexanalytic signal. We show that using the hypercomplexanalytic signal it is possible to calculate a complex envelopeof the original complex signal and that the modulus of thiscomplex envelope is the envelope of the modulus of the originalsignal.