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Lecture#3 - BIM 108 Lecture#3 Convolution Discrete-time...

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1 BIM 108 Lecture #3 Convolution Discrete-time Example Time invariant ?
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2 Discrete-time Convolution 0 2 4 6 8 10 12 14 16 18 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 [ ] [0] [ ] [1] [ 1] [2] [ 2] ... [ ] [ ], 0,1,2,... i x n x n x n x n x i n i n δ δ δ δ = = + + + = = 0 [ ] [0] [ ] [1] [ 1] [2] [ 2] ... [ ] [ ] [ ] [ ], 0,1,2,... i y n x h n x h n x h n x i h n i x n h n n = = + + + = = ± Matlab command: y=conv(x,h); Recall Delta Function Recall impulse function: ) ( t δ = ε ε λ λ δ d ) ( = = τ τ δ τ τ τ δ τ d t x d x ) ( ) ( ) ( ) ( 0 t n x(t)
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