EE3TP4_7_DTSystemRecursion_v2_Lecture 9

EE3TP4_7_DTSystemRecursion_v2_Lecture 9 - D-T System Models...

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D-T System Models We saw that Differential Equations model C-T systems… D-T systems are modeled by Difference Equations. y [ n ] a 1 y [ n 1 ] ... a N y [ n N ]= b 0 x [ n ] b 1 x [ n 1 ] ... b M x [ n M ] A general N th order Difference Equations looks like this: Most “Advanced” Output Sample Least “Advanced” Output Sample The difference between these two index values is the “order” of the difference eq. Here we have: n – ( n N) = N D-T LTI System x [ n ] y [ n ]
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Although Difference Equations are quite different from Differential Equations, the methods for solving them are remarkably similar. We’ll study such analytic methods later. Here we’ll look at a numerical way to solve Difference Equations. This method is called Recursion … and it is actually used to implement (or build) many D-T systems, which is the main advantage of the recursive method. Solving Difference Equations The disadvantage of the recursive method is that it doesn’t provide a closed-form solution … in other words, you don’t get an equation that describes the output (you get a finite-duration sequence of numbers that shows part of the output). Later we’ll see how to get closed-form solutions…
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Solution by Recursion y [ n ]=− i = 1 N a i y [ n i ] i = 0 M b i x [ n i ] Some “past output values , with values already known current & past input values already “received” “current output value to be computed But, for computer processing it is possible to recursively solve (i.e. compute) a numerical solution. In fact, this is how D-T systems are implemented (i.e. built!)
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This note was uploaded on 02/01/2011 for the course ECE 3TP4 taught by Professor Drterrencetodd during the Fall '10 term at McMaster University.

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EE3TP4_7_DTSystemRecursion_v2_Lecture 9 - D-T System Models...

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