Fast Periodicity Estimation and Reconstruction of hidden components from noisy periodic signal

Periodicity estimation from an arbitrary length noisy signal is computationally very costly. A recently developed Ramanujan Fat Dictionary is one of the ways to find the hidden components from an arbitrary length (non integral multiple of period) of the signal. This method suffers from high run time due to the lack of information about the period and effect of noise on the signal. We propose a new method that efficiently estimates the period of the signal and finding the hidden components thus becomes easy from it. Our method works well with significantly low SNR values and runs in O(n) time complexity, n being length of the signal. Comparision of run time analysis between our method for period estimation of a given signal and SVD method at various SNR values has been made and the corresponding hidden components are there by extracted by projecting onto the factor-Ramanujan Subspaces.Comment: 10 pages, 29 figure

Minimal Dictionaries For Spanning Periodic Signals

Recently, several high dimensional dictionary representations were proposed for discrete time periodic signals. These dictionaries could span any periodic signal whose period lies in a given range 1 ≤ P ≤ P_(max). Such dictionaries were used in various ways to estimate unknown periods. In this work, we derive some fundamental properties that any such dictionary must satisfy. For example, we derive bounds on the minimum size of such dictionaries, necessary conditions on their composition, and so on. Our results also demonstrate a natural connection between the well-known Euler Totient function (φ-function) from number theory, and periodicity analysis