Multidimensional Ramanujan-sum expansions on nonseparable lattices
Abstract
It is well-known that the Ramanujan-sum c <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> (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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">qi</sub> . This offers an efficient way to identify periodic components using integer computations and projections, since c <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> (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.
BibTeX
@inproceedings{icassp2015_multidimensional,
title = {Multidimensional Ramanujan-sum expansions on nonseparable lattices},
author = {Palghat P. Vaidyanathan},
booktitle = {ICASSP 2015},
year = {2015}
}