General multirate building structures with application to nonuniform filter banks

This paper proposes a general linear dual-rate structure for multirate signal processing, which encompasses the usual multirate building blocks-expanders, LTI filters, decimators, and their cascade combinations-as special cases. Structural properties of such dual-rate systems are studied in detail; in particular, several equivalent implementation structures are proposed: (1) cascade connections of a block expander, a linear periodically time-varying system, and a block decimator; (2) vector sample-rate changers; and (3) cascade connections of an expander, certain linear switching time-varying system, and a decimator. Using such general building blocks in multirate signal processing allows more design freedom and therefore can achieve what is otherwise impossible. This is illustrated in nonuniform multirate filter banks. Using the general building blocks as synthesis systems, the incompatibility for alias cancellation and structural dependency constraint for design, both due to fractional decimation ratios in different channels, are eliminated. Hence optimal design of synthesis systems is possible.