DT Convolution Examples

DT Convolution Examples - EECE 301 Signals &...

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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 + = 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 &...

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