Multidimensional transform: Difference between revisions

Revision as of 18:15, 3 July 2016

Revision as of 12:01, 13 August 2016

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<math display="block">F(x,y)=\textstyle \int\limits_{0}^{\infty}\int\limits_{0}^{\infty}\ f(x,y) e^{-s_1x-s_2y}\, dxdy</math>

F(x,y) is called the image of f(x,y) and f(x,y) is known as the original of F(x,y).<ref name=":1">{{Cite journal|url = |title = Multi-Dimensional Laplace Transforms and Systems of Partial Differential Equations |last = Aghili and Moghaddam|first = |journal = International Mathematical Forum |volume=1 |year=2006 |issue=21 |pages=1043-10501043–1050|doi = |pmid = |access-date = }}</ref> This special case can be used to solve the [[Telegrapher's equations]].<ref name=":1" />

== Multidimensional Z Transform<ref>{{Cite web|url = http://dsp-book.narod.ru/HFTSP/8579ch08.pdf|title = Narod Book|date = |accessdate = |website = |publisher = |last = |first = }}</ref> ==

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<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.

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

ln|z1|≥ln|z01| and ln|z2|≥L*ln|z1|+{ln|z02|-L*ln|z01|} where L is the slope.