Some contributions on the characterization of one-dimensional spatial processes
In spatial signal processing a two-sided impulse response often occurs, i.e. a process y(s) has the representation \[ y(s)=\int^{\infty}_{- \infty}I(u)z(s-u)du, \] where z(s) is a continuous white noise and I(u) is a two-sided impulse response (IR) function. Expressions for two-sided IR functions corresponding to various rational factorizations of the spectral density functions of continuous ARMA(p,q) models are derived in the paper. However, space dependent systems usually require the IR function to be continuous. With the restriction on the continuity of IR at the origin, some models (e.g. continuous AR(1) or ARMA(2,1) models) are found not to be admissible for representation of space series. Possible applications to discern directional properties of surface profiles are mentioned.
directional properties of surface profiles
scientific article; zbMATH DE number 4180420