Median method for robust and accurate power spectral density estimation of stochastic oscillators

A method is proposed for estimating the power spectral density (PSD) of time series that uses median smoothing in the frequency domain. The "Median method" for PSD estimation rejects deterministic noise peaks in the PSD while preserving stochastic signals and noise sources. For a PSD averaging factor M, deterministic noise sources are suppressed by a factor of ∼M in power when applying the Median method. In addition, the Median method leads to a reduction of spectral leakage by a factor of ∼M relative to traditional methods. An increase of up to 44% in the standard deviation in the PSD estimate from the Median method is the trade-off for these advantages. In the context of a stochastically driven simple harmonic oscillator, the estimation of its parameters (stiffness, Q factor, and resonance frequency) using the Median method is much more robust against the presence of deterministic noise peaks and more accurate than linear PSD estimation methods.