Beamforming on Acoustic Transients in the Discrete Orthonormal Stockwell Basis
Abstract
This paper reports the development of a method for beamforming on transient acoustic signals using a set of basis vectors known as the Discrete Orthonormal Stockwell Basis (DOSB). The DOSB is a set of orthonormal basis vectors in CN that is derived from a specific sampling of the continuous S-transform kernel. The DOSB, and the S-transform as well, is like wavelet bases in that it inherently provides a means to represent a length-N time series at a range of scales and frequencies. However, it provides the additional benefit of retaining an absolute time reference with respect to the beginning of the data record which is like the discrete-time Fourier basis. This feature, along with the sparse nature of the DOSBs frequency-domain representation and the ability to apply the transform in O(N log2 N) operations, enables beamforming in much the same way that is performed in the Fourier domain. The difference being that the beamforming occurs on each Stockwell basis function which has a specific time-frequency localization. Thus, the ability to beamform on multiple short transients or a transient I strong clutter within a single data record is possible, which makes it particularly useful for processing of battlefield events such as gunfire and explosions. Moreover, it is essentially an automatic method for estimating the direction of arrival of transients without the explicit need for a separate transient wave detector. Theory and an example applied to synthetic data are provided.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 31, 2022
- Accession Number
- AD1195729
Entities
People
- William Garth Frazier
Organizations
- University of Mississippi