Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Digital processing of random signals: theory and methods
Digital processing of random signals: theory and methods
Comments on “The Cramer-Rao lower bounds for signals withconstant amplitude and polynomial phase”
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Product high-order ambiguity function for multicomponentpolynomial-phase signal modeling
IEEE Transactions on Signal Processing
Generalized High-Order Phase Function for Parameter Estimation of Polynomial Phase Signal
IEEE Transactions on Signal Processing - Part I
A fast algorithm for estimating the parameters of a quadratic FM signal
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
Nonparametric estimation of instantaneous frequency
IEEE Transactions on Information Theory
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The high-order phase function (HPF) is a useful tool to estimate the instantaneous frequency rate (IFR) of a signal with a polynomial phase. In this paper, the asymptotic bias and variance of the IFR estimate using the HPF are derived in closed-forms for the polynomial phase signal with an arbitrary order. The Cramér-Rao bounds (CRBs) for IFR estimation, in both exact and asymptotic forms, are obtained and compared with the asymptotic mean-square error (MSE) of the HPF-based IFR estimator. Simulations are provided to verify our theoretical results.