On Transformation Noise: Properties and Modeling

In this paper, we study some properties of the class of discrete time transformation noise which is generally non-Gaussian and correlated and is generated by passing another noise process through an invertible memoryless nonlinearity. In general, any discrete time noise process can be considered as transformation noise. The dependency structure of the transformation noise is found to be described by the same set of parameters as the underlying noise, with closely related canonical eigenfunctions. The class of transformation noise generated by multivariate Gaussian underlying noise is proposed to model other second order stationary transformation noise processes. While the nonlinearity is simple to determine, three ad-hoc methods are suggested to obtain the correlation function. One method is found to be simple and reasonable. Oscar Au is with the Department of Electrical and Electronic Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong. John Thomas retired from Princeton University in 1990. He is a IEEE fellow.