Note #01 Discrete-Time Delta and Step Functions

# Note #01 Discrete-Time Delta and Step Functions - ∑-∞ =...

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Note #1. Discrete-Time δ [ n ] and u [ n ] Fall 2006 Definition. Unit impulse function (sample pulse). = = 0 , 0 0 , 1 ] [ n n n A shifted impulse Definition. Unit step function. < = 0 , 0 0 , 1 ] [ n n n u Thus, = - = + - + - + - + = 0 ] [ ... ] [ ... ] 2 [ ] 1 [ ] [ ] [ k k n k n n n n n u . Now express this sum in a more useful form. Change dummy variable. Let k n m - = , so that -∞ = = n m m n u ] [ ] [ . Since the dummy variable is arbitrary, let’s change it back to k , i.e. , let m k = , and reverse the order of the summation so that
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Unformatted text preview: ∑-∞ = = n k n n u ] [ ] [ . Thus the step function is express as a “running sum”. How to interpret this sum? Summary of relationship between [ n ] and u [ n ]: n [ n ] 1 n n 1 [ n-n ] n u [ n ] 1 … …-1 k 1 2 … … … … k k ] 1 [ ] [ ] [--= n u n u n ∑-∞ = = n k k n u ] [ ] [ backward difference running sum...
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## This note was uploaded on 04/10/2008 for the course ECSE 2410 taught by Professor Wozny during the Spring '07 term at Rensselaer Polytechnic Institute.

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