Adaptive window selection and smoothing of Lomb periodogram for time-frequency analysis of time series

Abstract

This article introduces a new adaptive Lomb periodogram for time-frequency analysis of time series, which are possibly non-uniformly sampled. It extends the conventional Lomb spectrum by windowing the observations and adaptively selects the window length by the intersection of confidence intervals (ICI) rule. To further reduce the variance of the Lomb periodogram due to time smoothing alone, time-frequency smoothing using local polynomial regression (LPR) is proposed. An orientation analysis is performed in order to derive a directional kernel in the time-frequency plane for adaptive smoothing of the periodogram. The support of this directional kernel is also adaptively selected using the ICI rule. Simulation results show that the proposed adaptive Lomb periodogram with time-frequency smoothing offers better time and frequency resolutions as well as lower variance than the conventional Lomb periodogram.