ECE
ECE634S09_HW1solutions

ECE634S09_HW1solutions - ECE634 Signals and Systems II...

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ECE634 Signals and Systems II, Spring 2009 – Homework 1 Solutions Daniel S. Brogan 1 Show all work and write legibly for full credit. 1. Express the following number in polar form and Cartesian form: ( )( ) 2 1 2 A j j = + ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 tan 3 /4 0.5 0.5 2 tan 3 /4 2 2 4 3 4 3 5 j j A j e e = = + − = ( ) ( ) ( ) ( ) 1 1 tan 3 / 4 tan 3 / 4 5 cos 5sin 2 2 A j = + ( ) ( ) ( ) ( ) ( ) 1 1 tan 3 / 4 1 tan tan tan 1 / 3 2 3 = = ( ) ( ) 1 1 1 1 3 5 5 3 1 5 cos tan 5sin tan 3 3 10 10 2 2 A j j j = + = = ( ) ( ) 1 tan 1 /3 0.3218 3 1 2.121 0.707 5 2.236 2 2 j j A j j e e = 2. Express the following number in polar form and Cartesian form: 3 /4 3 /4 1 2 j j B e e π π = + 3 /4 3 /4 3 3 3 3 2 cos sin 2cos 2 sin 4 4 4 4 j j B e e j j π π π π π π = + = + + + ( ) ( ) ( ) 1 2 2 tan 1 / 3 2 2 2 2 3 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 j B j j j e = − + = − = + − ( ) ( ) ( ) 1 tan 1 / 3 2.820 3 2 2 2.121 0.707 5 2.236
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  • Spring '09
  • messner
  • Complex number, Partial fractions in complex analysis, Daniel S. Brogan

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