This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: EE313 Linear Systems and Signals Spring 2009 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 9  2 Iterative Solutions Example: y [ n ]  y [ n1] = x [ n ] How many initial conditions do we need? For x [ n ] = n 2 u [ n ] and y [1] = 16 , causal system, y [ n ] = y [ n1] + x [ n ] Compute answer iteratively: y [0] , y [1] , y [0] = y [1] + x [0] = (16) + 0 = 8 y [1] = (8) + (1) 2 = 5 y [2] = 6.5 y [3] = 12.25 y [4] = 22.125 9  3 Stability Is the system boundedinput boundedoutput (BIBO) stable? y [ n ]  y [ n1] = x [ n ] Impulse response occurs when x [ n ] = [ n ] Zerostate response y s [ n ] to input [ n ] is 1, 0.5, 0.25, , for n = 0, 1, 2, System appears to be BIBO stable. x [ n ] = n 2 u [ n ] is unbounded in amplitude as n goes to infinity 9  4 ZeroInput, ZeroState Solutions Example: y [ n ]  y [ n1] = x [ n ] with y [1] = 16 Zeroinput solution y [ n ]  y [ n1] = 0 y [ n ] = y [ n1] y [ n ] = 8 () n u [ n ] 8, 4, 2, 1, , [ ] = = n m m n s m n y 2 2 1...
View
Full
Document
This note was uploaded on 01/22/2012 for the course EE 313 taught by Professor Cardwell during the Spring '07 term at University of Texas at Austin.
 Spring '07
 Cardwell

Click to edit the document details