A method of realization of two-dimensional transfer functions

✍ Scribed by Atsushi Kawakami

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 265 KB
• Volume: 83
• Category: Article
• ISSN: 1042-0967
• DOI: 10.1002/(sici)1520-6440(200011)83:11<63::aid-ecjc7>3.0.co;2-i

✦ Synopsis

This paper proposes a method for realizing the twodimensional transfer functions based on the state-space method. As the first step, the separable denominator twodimensional transfer function is considered, for which the minimal realization can always be obtained. The unknown is included in the denominator polynomial, and a statical feedback containing the unknown is performed on the state-space realization form. Then, the unknown is determined so that the given two-dimensional transfer function can be realized. The proposed method includes the conventional methods, and all of the minimal realizations that can be obtained by the conventional methods are obtained by the proposed method. In addition, the range of obtainable minimal realizations is expanded by the proposed method using the unknown, compared to the conventional methods not using the unknown. For the case where the minimal realization cannot be obtained by the above method, a method is also proposed where a dynamic feedback containing the rational function of the variable z 1 or z 2 containing the unknown as the coefficient is performed. This method is an extension of the previously proposed minimal realization method based on the static feedback. By the use of the unknown, the dimension of the realization can be reduced compared to the conventional method not using the unknown. Lastly, application examples for the two realization methods proposed in this paper are shown demonstrating their availability.