Design of Mth-band FIR filters based on generalized polyphase structure

In this paper, a generalized polyphase (GP) structure based design method for Mth-band FIR filters is presented. A few new transform matrices are proposed as seed matrix for generating a GP structure, which overcomes some limitations of the commonly used Hadamard transform. Under the framework of a general GP structure realization, the relationship between the original filter and the interpolator as well as the constituent filter is revealed from the frequency response perspective. This relationship facilitates the design problem of GP structure based FIR filters, since the original large-tap filter is reduced to a number of short-length constituent filters which can easily be designed according to the derived specifications. In particular, a closed-form frequency specification for the design of Mth-band filters is obtained. Design examples are given to illustrate the effectiveness of the proposed method