Symmetric alpha-stable filter theory

Symmetric -Stable (S S) processes are used to model impulsive noise. Wiener lter theory is generally not meaningful in S S environments because the expectations may be unbounded. To develop a lter theory for linear nite impulse response systems with independent identically distributed S S inputs, we propose median orthogonality as a linear lter criterion, present a generalized Wiener-Hopf solution equation, and show a necessary condition for a lter to achieve the criterion. For non-Gaussian S S densities, zero-forcing least-mean-square is the only well-known lter that satis es the criterion, but others can easily be designed. We present a second algorithm and simulations showing that both converge to the generalized Wiener-Hopf solution.