Entropy-based time-varying window width selection for nonlinear-type time–frequency analysis

Abstract

We propose a time-varying optimal window width (TVOWW) and an adaptive optimal window width selection schemes to optimize the performance of several nonlineartype time-frequency analyses, including the reassignment method and its variations. A window rendering the most concentrated distribution in the time-frequency representation is regarded as the optimal window. The TVOWW selection scheme is particularly useful for signals that comprise fastvarying instantaneous frequencies and small spectral gaps. To demonstrate the efficacy of the method, in addition to analyzing synthetic signals, we study an atomic time-varying dipole moment driven by two-color mid-infrared laser fields in attosecond physics and near-threshold harmonics of a hydrogen atom in the strong laser field.

Analysis of adaptive short-time Fourier transform-based synchrosqueezing transform

“…It will be small if α is large. Here we give an estimate of this term when g(t) is the Gaussian function defined by (22). In this case, one can…”

“…For example, when g is the Gaussian function given by (22), then, with g(ξ) = e −2π 2 ξ 2 , the corresponding α is given by…”

“…With the decay conditions of G k (u) and G j,ℓ (t, η), Theorem 2 can be stated in the formulation in Corollary 1. Here instead of giving such a statement for the 2nd-order adaptive FSST as in Corollary 1, we look at the estimate bounds when g(t) is the Gaussian function given by (22).…”

“…When g(t) is given by (22), then G k (u) is given by (67), and α k by solving |G k (u)| = τ 0 for u is given by (69). For (t, η) ∈ O k , we have…”

“…For broadband signals, a narrow window is suitable for the high-frequency parts while a wide window is suitable for the low-frequency parts. Recently the authors in [22] introduced a method to select the time-varying window width for sharp SST representation by minimizing the Rényi entropy. The window width of the signal separation operator algorithm in [6] is also time-varying.…”