Alpha-stable signals and adaptive filtering

Let {D
_k
,X
_k
} be jointly stationary symmetric α-stable processes with index 1 < α < 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 D
_j
on the basis of the input vector X
_j
. Various convergence results are established for the signal and tap weights estimation errors.