ENGG1203_Tutorial_5B - ENGG 1203 Tutorial Systems and...

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1 ENGG 1203 Tutorial Systems and Control 7 November Learning Objectives Difference Equations Z-transform Poles Ack.: MIT OCW 6.01, 6.003
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2 } 1 , 2, 1, , 0, { ] [ : Output 2 7 2 2 3 ) 2 5 3 ( 2 1 ) 2 5 3 ( 2 1 ) ( 0 2 5 3 0 ) ( } 0 , 2 , 5 , 1 , 3 , 0 { ] [ : Input ) ( 2 1 ) ( 2 1 ) ( : transform ] 1 [ 2 1 ] [ 2 1 ] [ : Equations Difference 2 7 2 3 5 4 3 2 1 4 3 2 1 1 4 3 2 1 5 4 3 2 1 0 1 n y z z z z z z z z z z z z z z z Y z z z z z z z X n x z X z z X z Y Z n x n x n y Review 2 1 3
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3 delay (1) 2 input = [0,3,-1,5,2,0] or [1,0,0,0,0,0] output = ? Find the output of the system? Assume: The system has no signal before the input. 0 (0) = 0 3 (3) + 2(0) = 3 -1 (-1) + 2(3) = 5 5 (5) + 2(5) = 15 2 (2) + 2(15) = 32 0 (0) + 2(32) = 64 Hence, output is {0,3,5,15,32,64} 1 (1) = 1 0 (0) + 2(1) = 2 0 (0) + 2(2) = 4 0 (0) + 2(4) = 8 0 (0) + 2(8) =16 0 (0) + 2(16) = 32 Hence, output is {1,2,4,8,16,32} Question 1 (tutorial 4A Q1(b))
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4 delay (1) 2 input = [0,3,- 1,5,2,0,0,0,…] output = ? ? transform - using analyzed but , ] [ output the is What 2 1 2 5 3 ) ( ... 0 2 5 3 0 ) ( } 0,... 0, 0, 2, 5, 1, 3, 0, { ] [ : Input 2 1 ) ( ) ( ) ( ) ( 2 ) ( ] [ ] 1 [ 2 ] [ 1 4 3 2 1 5 4 3 2 1 0 1 1 Z n y z z z z z z Y z z z z z z z X n x z z X z Y z X z Y z z Y n x n y n y
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