Two-dimensional, frequency domain, adaptive system modeling using three-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´s excellent adaptation accuracy and convergence speed. For illustration, the proposed algorithm is successfully applied to modeling a time varying 2-D system