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

•Examined the basis functions used in the discrete orthonormal S-transform (DOST) and proposed a modification to facilitate its power interpretation;•Proposed new multiple transforms (i.e., MDOSTs) to analyze and simulate a process or field for improved efficiency and resolution;•Use of multiple transforms to simulate a random signal is novel, as each transform employs a system of lenses, enabling a focused time–frequency interpretation of the signal from different perspectives;•Numerical examples are employed to show the effectiveness and efficiency of MDOSTs in simulating nonstationary non-Gaussian processes and fields.