IEEE Transactions on Automatic Control, Vol.65, No.2, 577-590, 2020
Two-Dimensional Frequency-Domain System Identification
In this paper, we propose two iterative algorithms to identify transfer functions of two-dimensional (2-D) systems. The proposed algorithms are modifications of the 2-D adaptive Fourier decomposition (AFD) and weak pre-orthogonal adaptive Fourier decomposition (W-POAFD). 2-D AFD and W-POAFD are newly established adaptive representation theories for multivariate functions utilizing, respectively, the product-TM system and the product-Szego dictionary. The proposed algorithms give rise to rational approximations with real coefficients to transfer functions. Owing to the modified maximal selection principles, the algorithms achieve a fast convergence rate O(n(-1/2)). To use 2-D AFD and W-POAFD for system identification not only the theory is revised, but also the practical algorithm codes are provided. Experimental examples show that the proposed algorithms give promising results. The theory and algorithms studied in this paper are valid for any n-D case, n >= 2.
Keywords:Approximation algorithms;Transfer functions;Signal processing algorithms;Barium;Dictionaries;Frequency-domain analysis;Matching pursuit algorithms;Generalized partial backward shift operator;matching pursuit;modified maximal selection principle;multidimensional rational approximation;product-Szego dictionary;product-TM system;two-dimensional (2-D) system identification