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Cyclic LTI Systems and the Paraunitary Interpolation Problem

机译：循环LTI系统与超幺正插值问题

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Cyclic signal processing refers to situations where all the time indices areinterpreted modulo some integer L. Since the frequency domain is a uniform discrete grid, there is more freedom in theoretical and design aspects. The basics of cyclic L miltirate systems and filter banks have already appeared in the literature, and important differences between the cyclic and noncyclic cases are known. Since there is a strong connection between paraunitary filter banks and orthonormal wavelets, some deeper questions pertaining to cyclic L paraunitary matrices are addressed in this paper. It is shown that cyclic L paraunitary matrices do not in general have noncyclic paraunitary FIR. interpolants, though IIR interpolants can always be constructed. It is shown, as a consequence, that cyclic paraunitary systems cannot in general be factored into degree one nonrecursive paraunitary building blocks. The connection to unitarians of the cyclic state space realization is also addressed.

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