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Multidimensional Signal, Image, and Video Processing and Coding, 2nd Edition by John W. Woods

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Chapter 3

Two-Dimensional Systems and Z-Transforms

In this chapter we look at the 2-D Z-transform. It is a generalization of the 1-D Z-transform used in the analysis and synthesis of 1-D linear constant coefficient difference equation-based systems. In two and higher dimensions, the corresponding linear systems are partial difference equations. The analogous continuous parameter systems are partial differential equations. In fact, one big application of partial difference equations is in the numerical or computer solution of the partial differential equations of physics. We also look at LSI stability in terms of its Z-transform system function and present several stability conditions in terms of the zero-root locations of the system function. ...

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