Wb. Mikhael et Hp. Yu, ADAPTIVE, FREQUENCY-DOMAIN, 2-D MODELING USING SPATIOTEMPORAL SIGNALS, Journal of circuits, systems, and computers, 6(4), 1996, pp. 351-358
In this paper, an adaptive, frequency domain, steepest descent algorit
hm for two-dimensional (2-D) system modeling is presented. Based on th
e equation error model, the algorithm, which characterizes the 2-D spa
tially linear and invariant unknown system by a 2-D auto-regressive, m
oving-average (ARMA) process, is derived and implemented in the 3-D sp
atiotemporal domain. At each iteration, corresponding to a given pair
of input and output 2-D signals, the algorithm is formulated to minimi
ze the error-function's energy in the frequency domain by adjusting th
e 2-D ARMA model parameters. A signal dependent, optimal convergence f
actor, referred to as the homogeneous convergence factor, is developed
. It is the same for all the coefficients but is updated once per iter
ation. The resulting algorithm is called the Two-Dimensional, Frequenc
y Domain, with Homogeneous mu, Adaptive Algorithm (ZD-FD-HAA). In add
ition, the algorithm is implemented using the 2-D Fast Fourier Transfo
rm (FFT) to enhance the computational efficiency. Computer simulations
demonstrate the algorithm's excellent adaptation accuracy and converg
ence speed. For illustration, the proposed algorithm is successfully a
pplied to modeling a time varying 2-D system.