On the spectral properties of polynomial-phase signals

Anna Scaglione, Sergio Barbarossa

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Polynomial-phase signals (PPS's), i.e., signals parameterized as s(t) = A exp(j2πΣ m=0 M a mt m), 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 PPS's of generic order is not known in closed 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 follows a power law behavior f , 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-I)/M and a lower bound proportional to T 1/2. 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 PPS's, when applied to multicomponent PPS's.

Original languageEnglish (US)
Pages (from-to)237-340
Number of pages104
JournalIEEE Signal Processing Letters
Volume5
Issue number9
DOIs
StatePublished - 1998
Externally publishedYes

Fingerprint

Spectral Properties
Polynomials
Polynomial
Directly proportional
Ambiguity Function
Estimate
Power Law
Closed-form
Odd
Higher Order
Lower bound
Upper bound
First-order
Predict

Keywords

  • High-order ambiguity function
  • Polynomial-phase signals

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing

Cite this

On the spectral properties of polynomial-phase signals. / Scaglione, Anna; Barbarossa, Sergio.

In: IEEE Signal Processing Letters, Vol. 5, No. 9, 1998, p. 237-340.

Research output: Contribution to journalArticle

Scaglione, Anna ; Barbarossa, Sergio. / On the spectral properties of polynomial-phase signals. In: IEEE Signal Processing Letters. 1998 ; Vol. 5, No. 9. pp. 237-340.
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