Time-dependent ARMA modeling of nonstationary signals
01 Aug 1983-IEEE Transactions on Acoustics, Speech, and Signal Processing (IEEE)-Vol. 31, Iss: 4, pp 899-911
TL;DR: The Prony-Pisarenko estimator is adapted to this nonstationary context, the signal considered in this case being the output of a zero-input time-varying system corrupted by an additive white noise.
Abstract: Modeling of nonstationary signals can be achieved through time-dependent autoregressive moving-average models and lattices, by the use of a limited series expansion of the time-varying coefficients in the models. This method leads to an extension of several well-known techniques of stationary spectral estimation to the nonstationary case. Time-varying AR models are identified by means of a fast (Levinson) algorithm which is also suitable for the AR part of a mixed ARMA model. An alternative to this method is given by the extension of Cadzow's method. Lattices with time-dependent reflection coefficients are identified through an algorithm which is similar to Burg's. Finally, the Prony-Pisarenko estimator is adapted to this nonstationary context, the signal considered in this case being the output of a zero-input time-varying system corrupted by an additive white noise. In all these methods the estimation is global in the sense that the parameters are estimated over a time interval [0, T], given the observations [y 0 ... y T ]. The maximum likelihood method which falls within the same framework is also briefly studied in this paper. Simulations of these algorithms on chirp signals and on transitions between phonemes in speech conclude the paper.
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TL;DR: In this article, the Boltzmann formula for lower temperatures has been developed for a correction term, which can be developed into a power series of h. The formula is developed for this correction by means of a probability function and the result discussed.
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