# inverse 2-D z transform for 2-D recursive discrete system (Scripts) 1.0

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## inverse 2-D z transform for 2-D recursive discrete system (Scripts) Publisher's description

### The program can get the 2-D impulse response of a 2-D recursive discrete system in 2-D digital domain

The program can get the 2-D impulse response of a 2-D recursive discrete system in 2-D digital domain. For a 2-D recursive discrete system, the inverse 2-D z transform can be implemented by a 2-D IIR filter [1-3].
Copyright (C) Yang XIAO, Beijing Jiaotong University, Aug.1, 2007, E-Mail: yxiao@bjtu.edu.cn.
Resort to the theorems in Ref. [1-3], we can get a stable 2-D recursive discrete system, with stable transfer function H(z1,z2)=A(z1,z2)/B(z1,z2) in 2-D z-domain. Since the transfer function is stable, the 2-D impulse response h(n1,n2) of the system equals the solution of a 2-D IIR filter to process a unit impulse in 2-D digital domain [3]. Then this program can get the 2-D impulse response of a given 2-D recursive discrete system in 2-D digital domain if the system is stable.
The stability test for the two examples is provided in Ref [1-3]. In the two examples, the program verifies the convergence of the 2-D impulse response, here, one is of stable denominator polynomial, and the other is of an unstable one. According to the theorems in [1-3], the stability of the systems is depended on that of the denominator polynomial B(z1,z2), the program let us to observe the stability from the 2-D impulse responses of the two systems.
[1] XIAO Yang, Unbehauen R. вЂњNew stability test algorithm for two-dimensional digital filtersвЂќ, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Volume 45, Issue 7, July 1998 Page(s):739 - 741
[2] Yang XIAO, Unbehauen R. вЂњSchur stability of polytopes of bivariate polynomialsвЂќ, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Volume 49, Issue 7, July 2002 Page(s):1020 вЂ“ 1023.
[3] XIAO Yang, Stability Analysis of Multidimensional Systems, Shanghai Science and Technology Press, Shanghai, 2003.
The papers [1] and [2] can be downloaded from Web site of IEEE Explore.

#### System Requirements:

MATLAB 6.5.1 (R13SP1)
Program Release Status: New Release
Program Install Support: Install and Uninstall

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