ON THE SPECTRAL PROPERTIES OF POLYNOMIAL-PHASE SIGNALS

Polynomial-phase signals (PPS's), i.e., signals parameterized as s(t) = A exp(j2 pi Sigma(m=0)(M) a(m)t(m)), have been extensively studied a nd several algorithms have been proposed to estimate their parameters. From both the application and the theoretical points of view, it is p articularly important to know the spectrum of this class of signals, U nfortunately, the spectrum of PPS's of generic order is not known in c losed form, except for first- and second-order PPS's, The aim of this letter is to provide an approximate behavior of the spectrum of PPS's of any order. More specifically, we prove that: i) the spectrum follow s a power law behavior f(-gamma), with gamma = (M - 2)/(M - 1); ii) th e spectrum is symmetric for M even and is strongly asymmetric for M od d; and iii) the maximum of the spectrum has an upper bound proportiona l to T(M-1/M) and a lower bound proportional to T-1/2. These results a re useful to predict the performance of the so-called high order ambig uity function (HAF) and the Product-HAH (PHAF), specifically introduce d to estimate the parameters of PPS's, when applied to multicomponent PPS's.