2-Dimensional, Frequency-Domain, Adaptive System Modeling Using 3-Dimensional Spatiotemporal Inputs

In this paper, an adaptive, frequency domain, steepest descent algorithm for two-dimensional (2-D) system modeling is presented. The algorithm is derived here for the equation error model, and models the 2-D spatially linear and invariant unknown system by a 2-D auto-regressive, moving-average (ARMA) process. The proposed technique is implemented in the 3-D spatiotemporal domain. At each iteration, corresponding to a given pair of input and output images, the algorithm is formulated to minimize the energy of an error-function in the frequency-domain by adjusting the coefficients of the 2-D ARMA model. Signal dependent, optimal convergence factors, referred to as the homogenous convergence factors, are developed. Computer simulations demonstrate the algorithm\u27s excellent adaptation accuracy and convergence speed. For illustration, the proposed algorithm is successfully applied to modeling a time varying 2-D system