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Unformatted text preview: a t = ”. This symmetry is is expressed as ) 2 ( ) ( a t w t w += . Note #3. p.1 ) ( t v a t a ) ( t v t ) ( t x t 11 1 t t ) ( t x t 11 1 ) ( ) ( a t x t w= t a +1 a1 1 a 4. Property. Derive the following property. If ) ( ), ( t h t x are even, then the convolution ) ( ) ( ) ( t h t x t y = is even. 5. Example 1. Show that the convolution, ) ( ) ( ) ( t h t x t y = , where t e t x= ) ( and < = else t t h , , 1 ) ( 2 1 , is even. In this case we get, 6. Example 2. In this example, shift the pulse, ) ( t h to the right so that ( 29 2 1 1 ) (= t h t h . Show that the convolution, ) ( ) ( ) ( ) ( ) ( ) ( 2 1 2 1 1 1== = t y t h t x t h t x t y is symmetrical about the line, 2 1 = t , i.e. , Note #3. p.2 ) ( t y 2 1 t 2 1) ( 1 t y 2 1 t...
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 Spring '07
 WOZNY
 Digital Signal Processing, The Signal, 1 W

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