Ramanujan filter banks for estimation and tracking of periodicities

Abstract

We propose a new filter-bank structure for the estimation and tracking of periodicities in time series data. These filter-banks are inspired from recent techniques on period estimation using high-dimensional dictionary representations for periodic signals. Apart from inheriting the numerous advantages of the dictionary based techniques over conventional period-estimation methods such as those using the DFT, the filter-banks proposed here expand the domain of problems that can be addressed to a much richer set. For instance, we can now characterize the behavior of signals whose periodic nature changes with time. This includes signals that are periodic only for a short duration and signals such as chirps. For such signals, we use a time vs period plane analogous to the traditional time vs frequency plane. We will show that such filter banks have a fundamental connection to Ramanujan Sums and the Ramanujan Periodicity Transform.