This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View Full
Document
 Spring '07
 WOZNY

Click to edit the document details