The spectrogram, method of reassignment, and frequency-domain beamforming

Abstract

A smeared spectrogram is a result of the smoothing kernel in the short-time Fourier-transform (STFT). Besides the smeared energy, time and frequency phase information is also smeared, i.e., spectral components may contain imprecise phase information. The STFT is also used as the basis for more advanced signal processing techniques such as frequency-domain beamforming and cross correlation (CC). Both methods seek the delay time between signals by exploring phase-shifts in the frequency domain. Due to the inexact phase information in some of the time-frequency elements, their phase shifts are incorrect. This study re-introduces the reassigned spectrogram (RS) as a measure to fix the STFT artifacts. Moreover, it is shown that by using the RS, phase shifts can be optimized and improve beamforming and CC results. Synthetic and recorded data are used to show the advantage of using the RS in time-frequency analysis, CC, and beamforming. Results show that, subject to certain constraints, the RS provides exact time-frequency representation of deterministic signals and significantly improve CC and beamforming results. Array analysis of infrasonic signals shows that better results are obtained by either the RS- or STFT-based analysis depending on the signals' spectral components and noise levels.

Evidence for Short Temporal Atmospheric Variations Observed by Infrasonic Signals: 1. The Troposphere

“…The best beam is the back azimuth and apparent velocity combination that yields the delay‐and‐sum signal with the highest possible SNR. Implementations of the method exist both in time domain (Assink et al., 2016; Smets & Evers, 2014) and frequency domain (Averbuch, 2021; den Ouden et al., 2020; Smart & Flinn, 1971).…”

“…The efficient propagation of infrasound in the atmosphere combined with array processing techniques makes infrasound monitoring useful in two ways. First, infrasound is used to study sources of infrasound such as ocean waves (Arrowsmith, 2018;Averbuch et al, 2019;Brekhovskikh et al, 1973;De Carlo et al, 2021;Posmentier, 1967;Vorobeva et al, 2021;Waxler & Gilbert, 2006), volcanic eruptions (Anderson, Johnson, Steele, et al, 2018;Fee & Garcés, 2007;Smets et al, 2016), earthquakes (Donn & Posmentier, 1964;Evers et al, 2014;Shani-Kadmiel et al, 2018, 2021, sprites (Applbaum et al, 2020), and explosions (Assink et al, 2016(Assink et al, , 2018Pilger et al, 2021). Especially, infrasound is one of four technologies used to verify the comprehensive nuclear-test-ban treaty (Dahlman et al, 2009).…”

“…Therefore, the timescales at which changes in the atmosphere affect infrasound propagation are essential; specifically, when infrasound is used to detect, locate, and study a particular event (Arrowsmith et al, 2021). Then, propagation models are often used to explain the observations by simulating infrasound propagation through realistic atmospheric conditions, that is, temperature and winds (Applbaum et al, 2020;Assink et al, 2016Assink et al, , 2018Evers et al, 2018;Fee et al, 2013;Shani-Kadmiel et al, 2018, 2021. The atmospheric conditions are retrieved from weather prediction models or atmospheric reanalysis models operated by (but not only) the European Centre for Medium-Range Weather Forecasts (ECMWF), North American Mesoscale Model (NAM), and NASA's Global Modeling and Assimilation Office (NASA-GMAO).…”