Multidimensional Ramanujan-sum expansions on nonseparable lattices

摘要

It is well-known that the Ramanujan-sum c(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. This offers an efficient way to identify periodic components using integer computations and projections, since c(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.