A wavelet-based KL-like expansion for wide-sense stationary random processes

We describe a wavelet-based series expansion for wide-sense stationary processes. The expansion coefficients are uncorrelated random variables, a property similar to that of a Karhunen-Loeve (KL) expansion. Unlike the KL expansion, however, the wavelet-based expansion does not require the solution of the eigen equation and does not require that the process be time-limited. This expansion also has advantages over Fourier series, which is often used as an approximation to the KL expansion, in that it completely eliminates correlation and that the computation for its coefficients are more stable over large time intervals. The basis functions of this expansion can be obtained easily from wavelets of the Lemaire-Meyer (1990) type and the power spectral density of the process. Finally, the expansion can be extended to some nonstationary processes, such as those with wide-sense stationary increments.<
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