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We study discrete-time $(m,n)$-multirate systems on separable Hilbert spaces,solving the problem of approximating such a system by one which has a shortermultirate period $(m/q,n/q)$, optimally in the Hilbert-Schmidt norm. We work inthe state-space setting, providing two state-space representations of theoptimal approximant which are expressed in terms of a state-spacerepresentation of the original system.

Optimal approximation of discrete-time multirate systems on Hilbert spaces