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

TL;DR

This paper introduces a fast, efficient method for estimating the period of noisy signals and extracting hidden components, significantly reducing computation time and working effectively at low SNR levels.

Contribution

A novel O(n) time complexity method for period estimation that improves over existing approaches and facilitates hidden component extraction from noisy signals.

Findings

Works well at low SNR values

Runs in linear time complexity

Outperforms SVD in runtime analysis

Abstract

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.