Issues in the Implementation of General Dual-rate systems

General dual-rate systems enhance the design freedom by removing the structural dependencies and hence can be used in the incompatible nonuniform filter banks. Recently it was shown that realising these dual-rate systems using a simple linear time invariant (LTI) system, a conventional sampler and a block sampler, can reduce the circuit layout complexity. The dual-rate system specifications are obtained in the Multi Input Multi Output (MIMO) representation, in the design of the filter bank. This paper address the issue of designing the LTI system for the simple realisations from the MIMO specifications. We obtain the relationship between the polyphase decomposition of the LTI system and the transfer matrix of the MIMO representation. Our analysis show that the simple realisations are obtained from generalising the switching representations of linear periodically time varying (LPTV) systems.