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# quiz1 - 2.171 Quiz#1 This quiz is open-book There are four...

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2.171 Quiz #1 October 18, 2006 This quiz is open-book. There are four problems, and each is worth 25 points. Problem 1 (25 points): This problem considers six transfer functions. These are H 1 ( z ) = 20( z 0 . 95) (1) z 1 H 2 ( z ) = z 1 (2) z 0 . 9 H 3 ( z ) = z 0 . 9 (3) 10( z 0 . 99) H 4 ( z ) = 10( z 0 . 99) (4) z 0 . 9 H 5 ( z ) = 1 2 r 1 cos Ω 1 + r 1 2 (5) z 2 z 2 r 1 cos Ω 1 + r 2 1 where r 1 = 0 . 995 and Ω 1 = 0 . 1. (1 2 r 1 cos Ω 1 + r 1 2 )( z 2 z 2 r 2 cos Ω 2 + r 2 2 ) H 6 ( z ) = 2 2 (6) ( z 2 z 2 r 1 cos Ω 1 + r 1 )(1 2 r 2 cos Ω 2 + r 2 ) where r 1 = 0 . 995 and Ω 1 = 0 . 1, as before, and r 2 = 0 . 9995 and Ω 2 = 0 . 01. On two pages attached to the end of this exam are six step responses and six frequency response (Bode) plots. These plots are labeled I, II, III, IV, V, VI; and A, B, C, D, E, F; respectively. For each of the transfer functions above, indicate which are the corresponding step and frequency responses. Your answer should take the form of a number from 1-6 for each transfer function followed by a capital letter indicating the corresponding step response, followed by

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quiz1 - 2.171 Quiz#1 This quiz is open-book There are four...

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