Multiple discrete orthonormal S-transforms and its application in analyzing, modelling, and simulating random process and field

Abstract

We examine the derivation and characteristics of the basis function employed in the discrete orthonormal S-transform (DOST). The examination is aimed at clarifying the interpretation of the power characteristics associated with the partitions and basis functions employed in DOST. Based on this examination, it is suggested that a one-half shift to the time index of the original DOST basis functions could be considered to facilitate the interpretation of the power distribution in the time–frequency domain. Although the non-redundant DOST is a highly efficient transform, its resolution in the time–frequency space is relatively coarse as compared to some of the continuous time–frequency decomposition techniques. To improve the resolution, and without significantly increasing the computational time, we propose the multiple DOSTs (MDOSTs) approach that uses M DOSTs, each associated with a different partition scheme in the time–frequency domain and a set of corresponding orthogonal basis functions. The redundancy factor of MDOSTs is simply equal to M. In addition, we show that the MDOSTs can be used to model and simulate nonstationary non-Gaussian processes and fields within the framework of the iterative power and amplitude correction algorithm. The use of MDOSTs for analyzing, modelling, and simulating seismic ground motion and corrosion surface is illustrated by numerical examples. The results show that using MDOSTs can effectively improve the time–frequency resolutions while maintaining high computational efficiency.