Algorithms for Optimal Multirate Filter Bank Design

This paper is concerned with the problem of designing optimal multirate lter banks. Three design criteria are considered for linear phase FIR lter banks: H 2 measure, H 1 and the mixture of them. A closed-form solution is presented for optimal H 2 lter bank design. For optimal H 1 lter bank design, two algorithms are given which involve solving the design problem using positive semi-deenite programming techniques. The mixed H 2 =H 1 design problem is also solved. The results of this paper are excepted to be useful in applications such as speech coding, sampling rate conversion and multi-stage ltering.