A#05 - Due Fri 3(15 In this problem we would like to demonstrate that if t h t x t y ∗ = then 2 1 t h t x t y ∗ − = equals In words if 2 1

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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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Assignment #5 – p.2 ECSE-2410 Signals & Systems - Spring 2007
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Unformatted text preview: Due Fri 02/02/07 3(15). In this problem we would like to demonstrate that if ) ( ) ( ) ( t h t x t y ∗ = , then ) ( ) 2 ( ) ( 1 t h t x t y ∗ − = , equals . In words, if ) 2 ( ) ( 1 − = t y t y one of the signals in a convolution is shifted, then the resulting convolution is also shifted in the same way. (a)(7) Find and sketch the output ) ( ) ( ) ( t h t x t y ∗ = of the system whose impulse response and input are shown below. x ( t ) h ( t ) 2 1 t 1 0 1 t 0 1 2 (b)(7) Using convolution, find and sketch the output ) ( ) 2 ( ) ( 1 t h t x t y ∗ + = . (c)(1) From your sketches is it true that ) 2 ( ) ( 1 + = t y t y ? 4(10). 5(15). 6(15)....
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This note was uploaded on 04/10/2008 for the course ECSE 2410 taught by Professor Wozny during the Spring '07 term at Rensselaer Polytechnic Institute.

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A#05 - Due Fri 3(15 In this problem we would like to demonstrate that if t h t x t y ∗ = then 2 1 t h t x t y ∗ − = equals In words if 2 1

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