Symmetric alpha-stable filter theory

Symmetric α-stable (SαS) processes are used to model impulsive noise. Wiener filter theory is generally not meaningful in SαS environments because the expectations may be unbounded. To develop a filter theory for linear finite impulse response systems with independent identically distributed SαS inputs, we propose median orthogonality as a linear filter criterion, present a generalized Wiener-Hopf solution equation, and show a necessary condition for a filter to achieve the criterion. For non-Gaussian SαS densities, zero-forcing least-mean-square is the only well-known filter that satisfies 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