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Unformatted text preview: Convolution These overheads were originally developed by Mark Fowler at Binghamton University, State University of New York. HOW? HOW? Convolution LTI System Differential Equation Difference Equation “zero “zero input” state” solution solution “zero “zero input” state” solution solution (solve) (solve) CT DT Use char. poly. roots Use char. poly. roots Notice the parallel between CT and DT systems. We’ll see that they are solved using similar but slightly different tools. Our focus will be on finding the zerostate solution … (we already know how to find the zeroinput solution for CT differential equations and later we’ll learn how to do that for DT difference equations) Our Interest: Finding the output of LTI systems (DT & CT cases) How do we find the ZeroState Response? (Remember … that is the response (i.e., output) of the system to a specific input when the system has zero initial conditions ) y ZS t = ∫ t t h t − λ x λ dλ CT “convolution” Where does this come from? How do we deal with it? We’ll handle DT systems first because they are easier to understand! Recall that in the examples for difference equations we saw: y ZS [ n ]= ∑ i = 1 n h [ n − i ] x [ i ] DT “convolution” Where does this come from?...
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 Fall '10
 DRTERRENCETODD
 Digital Signal Processing, LTI system theory, Impulse response

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