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Published April 2015 | public
Book Section - Chapter

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.

Additional Information

© 2015 IEEE. This work was supported in parts by the ONR grant N00014-11-1-0676, and the Information Science and Technology (IST) initiative of Caltech.

Additional details

Created:
August 20, 2023
Modified:
October 20, 2023