Fast algorithms for discrete-time Wiener filters with optimum lag

In many applications, including geophysical signal processing and system identification, the computation of a FIR Wiener filter, corresponding to the optimum lag between the input signal and the desired response, or of an optimum prediction distance predictor are often required. These problems lead to the solution of a family of Toeplitz systems of equations having the same associated matrix but right-hand side vectors which are shifted versions of each other. A very efficient method for the solution of the optimum lag problem is the well known Simpson´s sideways recursions. The purpose of this paper is to introduce two new algorithms for the efficient computation of the optimum lag Wiener filter as well as the optimum prediction distance predictor. Their main characteristic is a coupled step-down step-up recursion which takes full advantage of both the Toeplitz nature of the matrix and the shifted structure of the right-hand side vectors. The proposed algorithms are featured by increased speed (they are about twice as fast as Simpson´s scheme) and computational simplicity. In addition, they provide recursive error computation capability and give further insight into the problem.