Recursive lattice filters - A brief overview

Recently lattice filters structures have been employed in numerous adaptive filtering applications such as noise cancelling; speech processing; and data equalization. In this paper we will be concerned with the algorithms that have been proposed to update the lattice filter coefficients. These algorithms typically fall into one of two classes, those based on stochastic (gradient) formulations and those founded on a least squares criterion. The latter are more complex; however, they provide for a faster response to sudden changes in the input data (e.g., a rapid initial convergence). It is the purpose of this paper to provide a brief exposition of the algorithms and to point out their various parallels. In particular, it is hoped that the simpler structure of the stochastic algorithms will shed some light on the more complex least squares procedures.