Nested Periodic Matrices and Dictionaries: New Signal Representations for Period Estimation

摘要: In this paper, we propose a new class of techniques to identify periodicities in data. We target the period estimation directly rather than inferring from signal’s spectrum. By doing so, obtain several advantages over traditional spectrum such as DFT and MUSIC. Apart estimating unknown signal, search for finer periodic structure within given signal. For instance, it might be possible that signal was actually sum signals with much smaller periods. example, adding periods 3, 7, 11 can give rise 231 methods these “hidden periods” 11. first family square matrices called Nested Periodic Matrices (NPMs), having useful properties context periodicity. These include DFT, Walsh–Hadamard, Ramanujan periodicity transform examples. Based on matrices, develop high dimensional dictionary representations signals. Various optimization problems formulated representations. an approach based finding least $l_{2}$ norm solution under-determined linear system. Alternatively, identification problem also sparse vector recovery show by slight modification usual $l_{1}$ minimization techniques, incorporate number computationally simple dictionaries.