Abstract
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> 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. </para>
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