The Ramanujan Periodicity Project

Period vs Time Plane for a chirp signal using Ramanujan Filter Banks. [View Larger]

Going Beyond Parallelograms! Bringing more general lattices into DSP. [View Larger]

Detecting repeats in bio-molecules such as Proteins using Nested Periodic Dictionaries. [View Larger]

What's it all about?

The Ramanujan Periodicity Project is a new framework for periodicity analysis. Starting from a novel union of subspaces model for periodic signals, we have developed several techniques to estimate and track periodicities in data. These include dictionary methods, projection techniques and filter banks.

Our techniques offer important advantages over traditional methods such as those based on DFT and MUSIC, such as involving integer operations, requiring smaller data lengths, and producing much cleaner period estimates (see the example below). These features are especially important in the context of mixtures of periodic signals. For example, adding signals with periods 3, 7 and 11 can give rise to a period 231 signal. Our methods can identify these 'hidden periods' 3, 7 and 11 in addition to estimating the period as 231 (see the example below).

We have demonstrated these techniques on several real world applications such as in detecting epileptic seizures, repeats in bio-molecules such as proteins and DNA (relevant in forensics, genealogical tests and many other fields), and ECG signals, apart from computer generated data.

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An example illustrating the advantages