On the spectral properties of polynomial-phase signals
Scaglione, A.; Barbarossa, S.
Signal Processing Letters, IEEE
Volume 5, Issue 9, Sep 1998 Page(s):237 - 240
Digital Object Identifier 10.1109/97.712109
Summary:Polynomial-phase signals (PPSs), i.e., signals parameterized as
s(t)=A exp(j2πΣm=0M amtm
), have been extensively studied and several algorithms have been
proposed to estimate their parameters. From both the application and the
theoretical points of view, it is particularly important to know the
spectrum of this class of signals. Unfortunately, the spectrum of PPSs
of generic order is not known in closed form, except for first- and
second-order PPSs. The aim of this letter is to provide an approximate
behavior of the spectrum of PPSs of any order. More specifically, we
prove that: (i) the spectrum follows a power law behavior f-γ
, with γ=(M-2)/(M-1); (ii) the spectrum is symmetric for M
even and is strongly asymmetric for M odd; and (iii) the maximum of the
spectrum has an upper bound proportional to T(m-1)M/ and,
lower bound proportional to T1/2. These results are useful to
predict the performance of the so-called high order ambiguity function
(HAF) and the Product-HAH (PHAF), specifically introduced to estimate
the parameters of PPSs, when applied to multicomponent PPSs
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