Representations of Linear Dual-Rate System Via Single SISO LTI Filter, Conventional Sampler and Block Sampler

In this brief, it is proved that a linear dual-rate system can be represented via a series cascade of: 1) a conventional expander, a single-input single-output (SISO) linear time-invariant (LTI) filter and a block decimator, or 2) a block expander, an SISO LTI filter and a conventional decimator. Hence, incompatible nonuniform filter banks could achieve perfect reconstruction via LTI filters, conventional samplers and block samplers without expanding the input-output dimension of a subsystem of linear dual-rate systems or converting the nonuniform filter banks to uniform filter banks. The main advantage of the proposed representations is to avoid complicated design of the circuit layout caused by connecting subsystems with large input-output dimension or a lot of subsystems together.