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DT Convolution Examples

# DT Convolution Examples - EECE 301 Signals& Systems Prof...

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Unformatted text preview: EECE 301 Signals & Systems Prof. Mark Fowler Discussion #3b • DT Convolution Examples Convolution Example “Table view” h (-m ) h (1- m ) Discrete-Time Convolution Example: “Sliding Tape View” D-T Convolution Examples ( ) ] 4 [ ] [ ] [ ] [ 2 1 ] [ − − = = n u n u n h n u n x n-3 -2 -1 1 2 3 4 5 6 7 8 9 ] [ i h i …-3 -2 -1 1 2 3 4 5 6 7 8 9 ] [ i x i …-3 -2 -1 1 2 3 4 5 6 7 8 9 ] [ i h − i Choose to flip and slide h [ n ] This shows h [ n- i ] for n = 0 … For n < 0 h [ n- i ] x ( i ) = 0 ∀ i ] [ < = n for n y ⇒ ] [ ] [ i x i h − i For n = 0 ⇒ y [0] = 1-3 -2 -1 1 2 3 4 5 6 7 8 9 ] [ i x i Notice that for n = 0, n = 1, …, n = 3 The general result is: ( ) 3 , 2 , 1 , 2 1 ] [ = = ∑ = n for n y n i i ( ) ) ( 2 1 1 2 1 1 1 Sum Geometric n − − = + ( ) 3 , 2 , 1 , 2 1 1 2 ] [ 1 = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − = + n for n y n-2 -1 1 2 3 4 5 6 7 8 … ] 1 [ ] [ i h i n h − = − i ⇒ y (1) = 1 + ½ = 3/2 For n = 1-3 -2 -1 1 2 3 4 5 6 7 8 9 ] [ i x i n = 4 case...
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DT Convolution Examples - EECE 301 Signals& Systems Prof...

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