Fast algorithms for computing full and reduced rank Wiener filters

Wiener filter is an important tool in many signal processing applications. This paper proposes a fast inverse free method based on mean-square-error (MSE) criterion for the design of Wiener filters when both the given signal and the desired signal are widesense stationary random processes. Specifically, we present several approaches for tracking Wiener filter using gradient descent, line search, and adaptive methods. A new framework for computing the full rank Wiener filter and order update for reduced rank Wiener filter serially is presented. Emphasis is placed on methods that require least amount of matrix inversion including Rayleigh Quotient like methods. Simulations are also presented to examine the performance of the proposed methods.