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This paper studies a class of filter banks called the Ramanujan filter banks which are based on Ramanujan-sums. It is shown that these filter banks have some important mathematical properties which allow them to reveal localized hidden periodicities in real-time data. These are also compared with traditional comb filters which are sometimes used to identify periodicities. It is shown that non-adaptive...
In this paper, we propose a new class of techniques to identify periodicities in data. We target the period estimation directly rather than inferring the period from the signal’s spectrum. By doing so, we obtain several advantages over the traditional spectrum estimation techniques such as DFT and MUSIC. Apart from estimating the unknown period of a signal, we search for finer periodic structure within...
Ramanujan sums have in the past been used to represent arithmetic sequences. It is shown here that for finite duration (FIR) sequences with length N, the traditional representation is not suitable. Two new types of Ramanujan-sum expansions are proposed here for the FIR case, each offering an integer basis. One of these is particularly suited to identify periodicities in the FIR sequence. This representation...
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