lecture22 - EE313 Linear Systems and Signals Fall 2010...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
EE313 Linear Systems and Signals Fall 2010 Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin Difference Equations
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
22 - 2 Linear Difference Equations Discrete-time LTI systems can be characterized by difference equations y [ n ] = (1/2) y [ n -1] + (1/8) y [ n -2] + f [ n ] Taking z -transform of difference equation gives description of system in z -domain Σ f [ n ] y [ n ] Unit Delay Unit Delay 1/2 1/8 + + + y [ n -1] y [ n -2]
Background image of page 2
22 - 3 Advances and Delays Sometimes differential equations will be presented as unit advances rather than delays y [ n +2] – 5 y [ n +1] + 6 y [ n ] = 3 f [ n +1] + 5 f [ n ] One can make a substitution that reindexes the equation so that it is in terms of delays Substitute n with n -2 to yield y [ n ] – 5 y [ n -1] + 6 y [ n -2] = 3 f [ n -1] + 5 f [ n -2] Before taking the z -transform, recognize that we work with time n 0 so u [ n ] is often implied y [ n -1] → y [ n -1] u [ n ] y [ n -1] u [ n -1]
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 8

lecture22 - EE313 Linear Systems and Signals Fall 2010...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online