Multidimensional transform: Difference between revisions

Revision as of 21:32, 15 November 2016

Revision as of 21:37, 15 November 2016

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=== Region of convergence ===

[[File:Region of Convergence for figure 1.1a.png|thumb|201x201px|Figure 1.1b]]

Points (z1''z''₁,z2''z''₂) for which <math>F(z_1,z_2)=\sum_{n_1=-\infty}^\infty \sum_{n_2=-\infty}^\infty |f(n_1,n_2)| |z_1|^{-n_1} |z_2|^{-n_2}</math> <math><\infty</math> are located in the ROC.

An example:

If a sequence has a support as shown in Figure 1.1a, then its ROC is shown in Figure 1.1b. This follows that |''F''(z1''z''₁,z2''z''₂)| < '''∞''' .

<math>(z_{01},z_{02})</math> lies in the ROC, then all points<math>(z_1,z_2)</math>that satisfy |z1|≥|z01| and |z2|≥|z02 lie in the ROC.

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Therefore, for figure 1.1a and 1.1b, the ROC would be

: <math> \ln|z1z_1|≥ln \ge \ln|z01z_{01}| \text{ and } \ln|z2z_2|≥L* \ge L \ln|z1z_1| + \{ \ln|z02z_{02}| - L*\ln|z01|z_{01}| where L is the\} slope.</math>

where ''L'' is the slope. </math>

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.

The [[2D Z-transform]], similar to the Z-transform, is used in Multidimensionalmultidimensional 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 Transformtransform lies on is known as the unit surface or unit bicircle.

== Applications ==