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We describe a new statistical approach based on nonlinear filtering ideas for decomposing signals that are modeled as a sum of jointly amplitude- and frequency-modulated cosines, where each cosine has a slowly varying center frequency and the sum of terms is observed in additive noise. This is an alternative approach to methods based on deterministic models such as the Kaiser-Teager (see Proc. IEEE ICASSP-93, vol.III, p.149 and IEEE Trans. Acoust., Speech, Signal Processing, vol.28, no.5, pp. 599, 1980) energy operator. The Cramer-Rao bound for the resulting statistical estimation problem is computed. A practical nonlinear filter, an extended Kalman filter, is described. We demonstrate the ideas on a variety of speech problems