A#05 - Due Fri 3(15 In this problem we would like to...

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Assignment #5 – p.1 ECSE-2410 Signals & Systems - Spring 2007 Due Fri 02/02/07 1(20). Carry out the convolution, ) ( ) ( ) ( t w t v t y = , of the signals shown, and sketch your result. Study the relationships between these examples to determine the general principles involved. (a) (b) (c) (d) 2(25). This example illustrates the distributive property of convolution, namely, that convolution distributes over addition: ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) ( 2 1 2 1 t h t x t h t x t h t h t x + = + . For the system shown, let ) 1 ( ) ( ) ( ) ( 2 1 = = t u t u t h t h . Determine and sketch (a) (b) ) ( ) ( 2 1 t h t h + ( ) ) ( ) ( ) ( 2 1 t h t h t x + Now find and sketch (c) (d) ) ( ) ( 1 t h t x ) ( ) ( 2 t h t x (e) ) ( ) ( ) ( ) ( 2 1 t h t x t h t x + You should be able to show that the sketches in (b) and (e) are the same. 0 2 t ) ( 1 t v ) ( 1 t w t 0 2 1 1 4 0 2 t ) ( 2 t v ) ( 2 t w 1 1 t 0 2 4 0 2 t ) ( 3 t v ) ( 3 t w 1 1 t 4 0 2 4 0 2 t ) ( 4 t v ) ( 4 t w 1 1 t 0 2 ) ( 1 t h ) ( 2 t h + + ) ( ) ( t u t x = ) ( t y
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