hw-421-s06-01

# hw-421-s06-01 - ECE 421 Spring 2006 HW Assignment#1 Signals...

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ECE 421, Spring 2006, HW Assignment #1 Signals and Systems Review Problems Due Tuesday, January 31 1. Determine the Laplace transform for the following time-domain signal. Express the answer in the normal transfer function format, that is, as a ratio of polynomials. x 1 ( t )= ½ 0 ,t < 0 t 2 4 e 3 t +3 e 2 t 0 ¾ (1) 2. Determine the time-domain expressions for each of the Laplace transforms shown below. X 2 a ( s 1 s (4 s +1) = 0 . 25 s ( s +0 . 25) (2) X 2 b ( s 12 s 2 (4 s = 3 s 2 ( s . 25) (3) X 2 c ( s 13 s ( s 2 +4 s + 13) = 13 s ( s +2+ j 3) ( s +2 j 3) (4) 3. Without computing inverse Laplace transforms, determine the output signals for each of the following three systems for the given sinusoidal inputs. The system transfer functions are given by the G i ( s ) , and the input signals are x i ( t ) . G 3 a ( s 20 ( s +3) ( s . 2) ( s +6)( s + 10) ,x 3 a ( t )=5cos(2 t π/ 6) (5) G 3 b ( s 10 ( s +2) 2 ( s +5)( s +7) 3 b ( t )=2cos(2 t + 3) + 10 cos (6 t + 3) (6) G 3 c ( s 10 ( s . 3) 3 3 c ( t )=4cos(0 . 5 t )+10cos(2 t + 3) (7) 4. For each of the transfer functions below, determine the poles and zeros and indicate whether the system
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## This note was uploaded on 10/25/2010 for the course ECE 421 taught by Professor Cook,g during the Spring '08 term at George Mason.

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