Effectiveness of Stacks in the Stacked Hilbert-Huang Transform

TL;DR

This paper introduces a stacked Hilbert-Huang Transform (sHHT) that enhances detection of nonlinear and transient signals in astronomical data by aggregating multiple Hilbert spectra, outperforming the conventional HHT especially during rapid frequency changes.

Contribution

The paper develops and analytically validates a new stacked HHT method that improves sensitivity and robustness in analyzing complex astronomical signals.

Findings

sHHT provides more accurate instantaneous frequency estimation.

sHHT better detects rapid frequency changes in signals.

Application confirms sHHT's effectiveness in astrophysical data analysis.

Abstract

The Hilbert-Huang transform (HHT) consists of empirical mode decomposition (EMD), which is a template-free method that represents the combination of different intrinsic modes on a time-frequency map (i.e., the Hilbert spectrum). The application of HHT involves introducing trials by imposing white noise on the signal and then calculating the ensemble mean process of the corresponding EMD to demonstrate its significance on the Hilbert spectrum. In this study, we develop a stacked Hilbert-Huang Transform (sHHT) method that generates the Hilbert spectrum for each trial and compiles all results to enhance the strength of the real instantaneous frequency of the main signal on the time-frequency map. This new approach is more sensitive to detecting/tracing the nonlinear and transient features of a signal embedded in astronomical databases than the conventional HHT, particularly when the signal experiences dramatic frequency changes in a short time. We analytically investigate the consistency of HHT and sHHT and perform numerical simulations to examine the dispersion of the instantaneous frequency obtained through sHHT and compare its advantages and effectiveness with those of conventional HHT. To confirm the feasibility of the sHHT, we demonstrate its application in verifying the signal of superorbital modulation in X-ray and binary black hole mergers in gravitational waves.