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: () ( ) 21 2 A jj =+− ( ) ( ) 1 1 tan 3 /4 0.5 0.5 2 tan 3 /4 2 2 43 4 3 5 j j Aj e e =− = + = ( ) ( ) 11 t a n3 / 4 t a / 4 5cos 5sin 22 −− ⎛⎞ =+ ⎜⎟ ⎝⎠ 1 1 tan 3 / 4 1 tan tan tan 1 / 3 23 == ( ) 35 5 3 1 5cos tan 5sin tan 33 10 10 2 2 j j = = 1 tan 1 /3 0.3218 31 2.121 0.707 5 2.236 j j j e e ≈− −= 2. Express the following number in polar form and Cartesian form: 3/ 4 4 12 B ee ππ 4 4 3 3 2 cos sin 2cos 2 sin 44 4 4 Be e j j π ⎡⎤ = + + + ⎢⎥ ⎣⎦ 1 tan 1 / 3 222 2 3 3 2 2 2 2 2 2 2 j Bj j j e + = + − 1 tan 1 / 3 2.820 32 2 2.121 0.707 5 2.236 j j j e e = 3. Express the following number in polar form and Cartesian form: ( )( ) Ce e ( ) ( ) 1 2s i n1 j j j j e e e e e j = + () () /2 1.571 0 1.683 0 2sin 1 2sin 1 1.683 Cj j e e ≈+ =
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ECE634 Signals and Systems II, Spring 2009 – Homework 1 Solutions Daniel S. Brogan 2 4. Use partial fraction expansion on () 2
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This note was uploaded on 03/05/2009 for the course ECE 651 taught by Professor Messner during the Spring '09 term at New Hampshire.

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ECE634S09_HW1solutions - ECE634 Signals and Systems II,...

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