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-Szegö 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 $\boldsymbol {O(n^{-\frac{1}{2}})}$. 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, ${n\geq 2}$.

中文翻译：

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二维频域系统识别

在本文中，我们提出了两种迭代算法来识别二维 (2-D) 系统的传递函数。所提出的算法是对二维自适应傅立叶分解 (AFD) 和弱预正交自适应傅立叶分解 (W-POAFD) 的修改。二维 AFD 和 W-POAFD 是新建立的多元函数自适应表示理论，分别利用产品-TM 系统和产品-Szegö 字典。所提出的算法产生具有传递函数的实系数的有理近似。由于修改了最大选择原则，算法实现了快速的收敛速度$\boldsymbol {O(n^{-\frac{1}{2}})}$. 使用二维AFD和W-POAFD进行系统辨识，不仅对理论进行了修正，还提供了实用的算法代码。实验示例表明，所提出的算法给出了有希望的结果。本文研究的理论和算法适用于任何${n}$-D 案例， ${n\geq 2}$.