Chapter_2-lecture_3 - Chapter 2 Discrete LTI Systems...

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١ ١ Chapter 2 Discrete LTI Systems Analysis Dr. Ammar AbuHudrouss Spring 2008 ٢ Resolution of A Discrete Signal into Impulses Any discrete signal x(n) can be represented by summation of impulses. Example : the signal in the graph can be represented as ) 4 ( 4 ) 3 ( 4 ) 2 ( 4 ) 1 ( 4 ) ( 4 ) 1 ( 3 ) 2 ( 2 ) 3 ( ) 5 ( ) 1 ( ) ( + + + + + + + + + + + + = n n n n n n n n n n x δ
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٢ ٣ The Convolution Sum Let us define h(n, k) as the output for a system when the input ) ( k n δ As x(n) can be expressed as a summation of impulses, or −∞ = = k k n k x n x ) ( ) ( ) ( ) ) ( ) ( ( )) ( ( ) ( −∞ = Τ = Τ = k k n k x n x n y −∞ = Τ = k k n k x n y )) ( ( ) ( ) ( −∞ = = k k n h k x n y ) ( ) ( ) ( The output can be found by: Convolution sum or y(n) = x(n) * h(n) ٤ The Convolution Sum −∞ = = k k n h k x n y ) ( ) ( ) ( 0 0 The output by calculating at any instant by
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Chapter_2-lecture_3 - Chapter 2 Discrete LTI Systems...

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