HW4Soln - ECE 301: Homework 4 SOLUTION Landis Huffman...

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Unformatted text preview: ECE 301: Homework 4 SOLUTION Landis Huffman Purdue University, Summer 2009 Due Thursday July 16, 2009 in class 1. Chapter 4 problems 4.21(a,g), 4.26(a)(i), 4.33(a,b) 4.21 Solution: (a) We have x ( t ) = [ e- t cos t ] u ( t ) = e- t [ e j t + e- j t ) ] / 2 u ( t ) = 1 2 [ e t (- + j ) + e t (- - j ) ] u ( t ) X ( ) = integraldisplay 1 2 [ e t (- + j ) + e t (- - j ) ] e- jt dt = 1 2 integraldisplay e- t ( - j + j ) + e- t ( + j + j ) dt = 1 2( - j + j ) + 1 2( + j + j ) 1 (g) We have X ( j ) = integraldisplay - x ( t ) e- jt dt = integraldisplay - x ( t )(- j sin( t )) dt ( x ( t ) is odd) = 2 integraldisplay x ( t )(- j sin( t )) dt = 2 integraldisplay 1 t (- j sin( t )) dt + 2 integraldisplay 2 1 (- j sin( t )) dt = 2 j bracketleftbigg t cos( t ) bracketrightbigg 1- 2 j integraldisplay 1 cos( t ) dt + 2 j bracketleftbigg cos( t ) bracketrightbigg 2 1 = 2 j cos( ) -...
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This note was uploaded on 01/10/2010 for the course CDFS 21000 taught by Professor Alisone.baroody during the Summer '09 term at Vincennes.

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HW4Soln - ECE 301: Homework 4 SOLUTION Landis Huffman...

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