ABSTRACT
In planning a chapter for this book celebrating the career achieve-
ments of Professor Tony Constantinides, we spent some time
wondering what might be best liked by Tony. Some reflection
reminded us that throughout his career Tony has conducted his
research based on solid classical roots, while at the same time always
bringing in fresh daisy-like novelty into his work, to suit modern
applications. You will see this combination in all his work, whether
it is on allpass filters or neural networks, adaptive filtering or
video coding. In keeping with this glorious spirit, we have therefore
decided to write about something that is at once old and new. The
topic we have chosen has the charm of good old classical number
theory. At the same time, it offers the excitement of a novel periodic
decomposition to suit the analysis of highly structured signals.
