Symmetric alpha-stable filter theory

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