Polynomial phase demodulation in multitaper analysis

This paper describes multitaper methods to estimate polynomial frequency modulation (FM) in low signal-to-noise environments. In the intended application, the frequency modulation occurs within the multitaper local bandwidth, the signal-to-noise ratio is low, and the raw data is non-Gaussian. This estimate uses the eigencoefficients as data and reconstructs the narrow band analytic signal and its time derivative from them. A set of polynomials, orthogonal with respect to inner products on the Slepian sequences, allows construction of a sequence of inverses with variable smoothness properties. These extend the standard multitaper F-test for line components to polynomial FM. With quadratic FM (cubic phase) the performance approaches the Cramer-Rao bound.