Multidimensional Ramanujan-sum expansions on nonseparable lattices

Abstract

It is well-known that the Ramanujan-sum c_q(n) has applications in the analysis of periodicity in sequences. Recently the author developed a new type of Ramanujan-sum representation especially suited for finite duration sequences x(n): This is based on decomposing x(n) into a sum of signals belonging to so-called Ramanujan subspaces S_(qi). This offers an efficient way to identify periodic components using integer computations and projections, since c_q(n) is integer valued. This paper revisits multidimensional signals with periodicity on possibly nonseparable integer lattices. Multidimensional Ramanujan-sum and Ramanujan-subspaces are developed for this case. A Ramanujan-sum based expansion for multidimensional signals is then proposed, which is useful to identify periodic components on nonseparable lattices.

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