A Novel Wavelet-base Algorithm for Reconstruction of the Time-Domain Impulse Response from Band-limited Scattering Parameters with Applications

TL;DR

This work addresses reconstructing a time-domain impulse response from band-limited frequency-domain S-parameters $S_{ij}(\omega)$ in ship-hull contexts. It introduces a wavelet-Fourier reconstruction framework that maps the frequency-domain data into the continuous wavelet domain, reconstructs a time-domain signal via an inverse wavelet transform, and iteratively restores missing DC and low-frequency content by spectral corrections. The authors prove convergence of the iterative scheme and show compatibility with exponential-sum approximations through simulations, demonstrating accurate impulse responses from band-limited data. The approach enables robust transient analysis for systems described by band-limited S-parameters, improving accuracy of EM signatures and time-domain behavior when DC content is unavailable.

Abstract

In this paper, we introduce a novel waveletbased algorithm for reconstructing time-domain impulse responses from band-limited scattering parameters (frequencydomain data) with a particular focus on ship hull applications. We establish the algorithm and demonstrate its convergence, as well as its efficiency for a class of functions that can be expanded as exponential functions. We provide simulation results to validate our numerical results.

Figures (8)

• Figure 1: Illustration a two-port network and the related S-parameter matrix.
• Figure 2: The schematic diagram of the proposed method
• Figure 3: The flowchart of the proposed recursive algorithm.
• Figure 4: UP: Impulse response, Middle: real part of the spectrum, Down: imaginary part of the spectrum.
• Figure 5: We have the time-domain signal $x(t)$ and a sample mother wavelet. We increase the scales until the mother wavelet covers the entire time-domain signal.