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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク 2D Z-transform ： ウィキペディア英語版 2D Z-transform The 2D Z-transform, similar to the Z-transform, is used in Multidimensional signal processing to relate a two-dimensional discrete-time signal to the complex frequency domain in which the 2D surface in 4D space that the Fourier Transform lies on is known as the unit surface or unit bicircle.〔Siamak Khatibi, “Multidimensional Signal Processing: Lecture 11”, BLEKINGE INSTITUTE OF TECHNOLOGY, PowerPoint Presentation.〕 The 2D Z-transform is defined by :$X\_z(z\_1,z\_2)\; =\; \backslash sum\_^\backslash sum\_^\; x(n\_1,n\_2)\; z\_1^\; z\_2^$ where $n\_1,n\_2$ are integers and $z\_1,z\_2$ are represented by the complex numbers: :$z\_1\; =\; Ae^\; =\; A(\backslash cos+j\backslash sin)\backslash ,$ :$z\_2\; =\; Be^\; =\; B(\backslash cos+j\backslash sin)\backslash ,$ The 2D Z-transform is a generalized version of the 2D Fourier transform. It converges for a much wider class of sequences, and is a helpful tool in allowing one to draw conclusions on system characteristics such as BIBO stability. It is also used to determine the connection between the input and output of a linear Shift-invariant system, such as manipulating a difference equation to determine the system's Transfer function. ==Region of Convergence (ROC)== The Region of Convergence is the set of points in complex space where: : In the 1D case this is represented by an annulus, and the 2D representation of an annulus is known as the Reinhardt domain.〔Dan E. Dudgeon, Russell M. Mersereau, “Multidimensional Digital Signal Processing”, Prentice-Hall Signal Processing Series, ISBN 0136049591, 1983.〕 From this one can conclude that only the magnitude and not the phase of a point at $(z\_1,z\_2)$ will determine whether or not it lies within the ROC. In order for a 2D Z-transform to fully define the system in which it means to describe, the associated ROC must also be know. Conclusions can be drawn on the Region of Convergence based on Region of Support (mathematics) of the original sequence $(n\_1,n\_2)$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「2D Z-transform」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.