Dictionary approaches for identifying periodicities in data

We propose several dictionary representations for periodic signals and use them for estimating their periodicity. This includes estimating concurrent multiple periodicities. These are inspired from the recently proposed DFT based Farey dictionary, where period estimation was cast as a sparse vector recovery problem. We show that this can instead be framed as an l₂ norm based data-fitting problem with closed form solutions and much faster computations. We also generalize the complex valued Farey dictionary to simpler integer valued dictionaries. We find that dictionaries constructed using the recently proposed Ramanujan Periodicity Transforms provide the best trade-off between complexity and noise immunity.