hw4_answers - Homework 4: Answers ECE 220 Spring 2005 1 1....

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Homework 4: Answers ECE 220 Spring 2005 1. (a) ) 1 ( 3 1 ) ( 2 1 + + = z z z H (b) (c) + = + + = 3 ˆ cos 2 1 3 1 3 1 3 1 ) ( ˆ ˆ 2 ˆ ω j j j jw e e e e H or ) 2 / ˆ sin( 3 ) 2 / ˆ 3 sin( ˆ j e (d) (e) ) cos( 3 4 ) cos( 805 . 0 2 ] [ 3 3 4 4 π + = n n n y 2. (a) ) ( ) ( ) ( 1 1 z H z X z Y = ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 2 1 2 1 z H z X z H z H z X z H z Y z Y = = = , where ) ( ) ( ) ( 2 1 z H z H z H =
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(b) For the second system: ) ( ) ( ) ( 2 2 z H z X z Y = ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 1 2 1 2 z H z X z H z H z X z H z Y z Y = = = , where ) ( ) ( ) ( ) ( ) ( 2 1 1 2 z H z H z H z H z H = = (c) ) 2 3 2 1 ( 9 1 ) ( 4 3 2 1 + + + + = z z z z z H (d) (e) = ) 2 / ˆ ( sin 9 ) ( sin ) ( 2 2 ˆ 3 2 ˆ 2 ˆ ω j j e e H (f) (g) ]) 4 [ ] 3 [ 2 ] 2 [ 3 ] 1 [ 2 ] [ ( 9 1 ] [ + + + + = n n n n n n h δ
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3. ) 398 . 0 cos( 5 20 ]) 2 [ 3 ] 1 [ 2 ] [ ( 10 40 ] [ 2 π δ + + = n n n n n y 4. (a) 3 2 1 2 1 1 ) ( ) ( + + + = = z z z z H z H (b) 6 5 4 3 2 1 2 3 4 3 2 1 ) ( + + + + + + = z z z z z z z H (c) ] 6 [ ] 5 [ 2 ] 4 [ 3 ] 3 [ 4 ] 2 [ 3 ] 1 [ 2 ] [ ] [ + + + + + + = n n n n n n n n h (d) ] 6 [ ] 5 [ 2 ] 4 [ 3 ] 3 [ 4 ] 2 [ 3 ] 1 [ 2 ] [ ] [ + + + + + + = n x n x n x n x n x n x n x n y 5. (a) The poles are at
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hw4_answers - Homework 4: Answers ECE 220 Spring 2005 1 1....

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