#### Technical Report USC-SIPI-230

“Infinite and Finite Observation Interval Whitening Filters for Certain Fractional Stable Noises”

by George A. Tsihrintzis and Chrysostomos L. Nikias

January 1993

We extend the Mandelbrot-Van Ness models of fractional Gaussian noise to define linear and log fractional symmetric _-stable (S_S) noises. We present both "engineering" definitions, based on certain fractional integrals of white S_S noise, as well as rigorous mathematical definitions via appropriate linear operators acting on subsets of the Banach space L_, 1< _ < 2. For these noises we find a canonical representation and proceed to derive whitening filters for linear and log fractional S_S noises for both infinite and finite observation intervals. The overall style of the report is tutorial complemented with a large number of references which review the relevant literature.

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