Alpha-stable signals and adaptive filtering

Let {Dk,Xk} be jointly stationary symmetric (alpha)-stable processes with index 1<(alpha)<2. We first consider the problem of optimal FIR linear and regression filters. We then consider the signed-error and sign-sign adaptive filtering algorithms for the estimation of the desired signal Dj on the basis of the input vector Xj. Various convergence results are established for the signal and tap weights estimation errors.