Practical and efficient implementation of the Levinson algorithm for multichannel sound reproduction

Abstract

This paper addresses the problem of computation of inverse filters in transauralization and multichannel sound reproduction. A huge set of block Toeplitz equations must be usually solved in order to design good filters under the least squares error criterion. A practical and efficient method of main matrix construction and the solution of the set of equations are thoroughly described. An optimal implementation of the Levinson algorithm in two steps that dramatically reduces the computational cost is also presented. The algorithm uses the generalized Levinson recursion for block matrices as a first step and the Gohberg-Semencul formula as the second step. This allows to save about 75% of operations in a typical transauralization problem. A study of the performance of the algorithm in terms of computational cost compared to other algorithms is also carried out.