The spectrogram, method of reassignment, and frequency-domain beamforming - Averbuch, Gil (The Journal of the Acoustical Society of America, 2021)
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.