Deriving structures of FFT based filter banks by signal flow graphs

Abstract

The design of filter banks, which is a frequently used operator for many practical applications, has been widely reported in the literature. The requirements of using extensive mathematical manipulations for finding computationally efficient structures of filter banks have imposed severe difficulties for those who lack sufficient mathematical background. This paper is to report procedures of deriving computationally efficient filter bank structures by using a few graphic transformations of equivalent multi-rate operations. It is seen that these procedures used in the derivation process are elegantly simple and straight forwards in concept. In particular, these procedures can be flexibly used to find the computationally efficient structures of both maximally decimated (p=1) and non-maximally decimated (p>1) filter banks, where p is the oversampling factor. For the non-maximally decimated filter banks, the computational complexity needed by our derived structure is less than that needed by the structures reported in the literature.