Factorizability of complex signals higher (even) order spectra: a necessary and sufficient condition
نویسندگان
چکیده
This paper presents a necessary and sufficient condition for the factorizability of higher order spectra of complex signals. Such a factorizability condition can be used to test if a complex signal can modelize the output of a linear and time invariant system driven by a stationary non gaussian white input. The condition developped here is based on the symmetries of higher order spectra and on an extension of a formula proposed by Marron et al. to unwrap third order spectrum phases. It is an identity between products of six higher order spectra values (which reduces to four values if only phases are considered). Our factorizability test requires no phase unwrapping, unlike existing methods developped in the cepstral domain. Moreover its extension to the N-th order case is direct. Simulations illustrate the deviation to this factorizability condition in a factorizable case (linear system) and a non factorizable case (non linear system).
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