Wavelets for power spectral density estimation of gravitational wave data

TL;DR

This paper introduces a wavelet-based method for fast and robust power spectral density estimation in gravitational wave data, improving accuracy for stationary and non-stationary noise over traditional methods.

Contribution

It presents a novel wavelet-based PSD estimation technique that enhances frequency resolution and robustness in gravitational wave data analysis.

Findings

Wavelet smoothing outperforms Welch PSD in matched filtering.

Wavelet packet median provides greater robustness for non-stationary noise.

The method enables high-resolution PSD estimates with low variance.

Abstract

Power spectral density (PSD) estimation is a critical step in gravitational wave (GW) detectors data analysis. The Welch method is a typical non-parametric spectral estimation approach that estimates the PSD of stationary noise by averaging periodograms of several time segments, or by taking the median of periodograms to adapt to non-stationary noise. In this work, we propose a wavelet-based approach for fast PSD estimation of both stationary and non-stationary noise. For stationary noise, we apply wavelet smoothing to the periodogram, avoiding the segmentation step in the Welch method, and enabling PSD estimates with high frequency resolution and low variance. The wavelet smoothing PSD outperforms Welch PSD in matched filtering and parameter estimation. For non-stationary noise, we estimate the PSD by taking the median of wavelet packet coefficients in each frequency bin, which offers greater robustness than the traditional median periodogram method. This work introduces a new PSD estimation approach for GW data analysis and expands the application of wavelet methods in this field.