Efficient adaptive filtering for smooth linear FIR models

This paper proposes the Smooth Gradient Descent (SGD) algorithm for recursively identifying a linear Finite Impulse Response (FIR) model with a large set of parameters (`long impulse response´). The main thesis is that a successful design of such adaptive filter must hinge on (i) the choice of a proper loss function, and (ii) the choice of a proper norm for the impulse response vector. Theoretical backup for this statement is found in slightly improving and interpreting the regret bound of the Gradient Descent (GD) algorithm presented in [3]. In practice, if the impulse response vector is known to be smooth in some apriori defined sense, the proposed algorithm will converge faster.