EE3TP4_8_DTConvolution_1_v3_Lecture 10

EE3TP4_8_DTConvolution_1_v3_Lecture 10 - Convolution These...

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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) C-T D-T Use char. poly. roots Use char. poly. roots Notice the parallel between C-T and D-T systems. We’ll see that they are solved using similar but slightly different tools. Our focus will be on finding the zero-state solution … (we already know how to find the zero-input solution for C-T differential equations and later we’ll learn how to do that for D-T difference equations) Our Interest: Finding the output of LTI systems (D-T & C-T cases) How do we find the Zero-State 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 C-T “convolution” Where does this come from? How do we deal with it? We’ll handle D-T 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 ] D-T “convolution” Where does this come from?...
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EE3TP4_8_DTConvolution_1_v3_Lecture 10 - Convolution These...

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