Algorithms for Optimal Multirate Filter Bank Design

This paper is concerned with the problem of designing optimal multirate filter banks. Three design criteria are considered for linear phase FIR filter banks: H 2 measure, H1 and the mixture of them. A closed-form solution is presented for optimal H 2 filter bank design. For optimal H1 filter bank design, two algorithms are given which involve solving the design problem using positive semi-definite programming techniques. The mixed H 2 =H1 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 filtering. 1. INTRODUCTION The technique of multirate filtering has been studied by many researchers in recent years. The application of this technique in digital signal processing is wide spread, including filter banks for coding, sampling rate changers, and multi-stage filtering; see, e.g., [?, ?]. Using the standard polyphase representation, most multirate filter bank design problems c..