Statistical AM-FM models, extended Kalman filter demodulation, Cramer-Rao bounds, and speech analysis

A stochastic dynamical system model for describing time signals that are jointly amplitude (AM) and frequency (FM) modulated is presented. The signal is assumed to be bandpass, perhaps originating from a filter bank applied to a broadband signal, and includes the constraint that the magnitude of the complex baseband signal is positive. Motivated by speech processing and the desire for narrowband modulating signals, time is divided into frames, and the modulating signals are smoothly interpolated across each frame. The model allows a detailed characterization of the bandwidth of the modulating signals and the statistical character of the measurement noise. An adaptive estimation algorithm based on extended Kalman filtering ideas for extracting the modulating signals from the measured signal is described and demonstrated on both voiced and unvoiced speech signals. The Cramer-Rao bound on the performance of any estimator is computed.