Symmetric alpha-stable filter theory

Symmetric α-stable (SαS) processes are used to model infinite-variance impulsive noise. In general, Wiener filter theory is not meaningful in (SαS) environments because the expectations may be unbounded. To develop a theory for linear finite impulse response systems with independent identically distributed (SαS) 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 (SαS) densities, zero-forcing least-mean-squares 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