Stochastic processes evolutionary spectrum estimation via harmonic wavelets

The problem of estimating the power spectrum of non-stationary stochastic processes using dyadic, generalized, and filtered harmonic wavelets is addressed. Explicit relationships between the statistical moments of the coefficients of the wavelets based representation of the process and of its evolving spectral values are given. It is shown that the popular concept of a separable evolutionary spectrum involving a deterministic modulating envelope is subject to interpretation. Further, mathematical expressions elucidating the analogy between the wavelets based spectral representation and the traditional one involving trigonometric functions are derived. Finally, the applicability and the physical soundness of the developed procedure are demonstrated by applying it to records of the Kocaeli, Turkey earthquake (8/17/1999).