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HW1 - ECE 301 Homework#1 due date...

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ECE 301, Homework #1, due date: 1/20/2010 http://cobweb.ecn.purdue.edu/ chihw/10ECE301S/10ECE301S.html Review of calculus and arithmetics: Question 1: Compute the values of the following integrals. Z 3 π π sin( s + 1 + π/ 3) ds Z 0 . 5 π 0 cos( π/ 2 - 2 u ) du Z 3 . 5 1 Z 5 3 cos( 3 5 + 4 ) dxdy Question 2: Compute the values of the following integrals. Z 2 π - π 3 -| t | e j 3 π 4 t dt Z 3 - 3 ω cos( π 2 ω ) Z 2 - 2 (2 - | z | ) e j 2 πz dz Question 3: Compute the expressions of the following integrals. Z 2 ω 0 ( t - 2 s ) e jωπ (2 t - s ) ds and 1 T ˆ Z T/ 2 - T/ 2 ( T 2 - t ) e - j 2 T t dt + Z 3 T/ 2 T/ 2 ( t - T 2 ) e - j 2 T t dt ! , where k is an integer. Question 4: Suppose f ( t ) = t 2 - 3 t + 2. Define g ( t ) = f (1 - 2 t ). Compute the following
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values. g (3) Z 5 2 g (1 + s ) ds and Z 3 0 g 0 ( s ) e jπs ds, where g 0 ( t ) is the first order derivative of g ( t ). Question 5: Suppose f ( t ) = | t | . Define g ( t ) = Z t +1 t - 2 f ( s ) ds Compute the following values. g (3) Z 5 2 g ( s ) ds and Z 1 - 1 g ( s ) f (1 - s ) ds. Question 6: Consider a discrete series f [ n ] = 2 n - 1. Define g [ n ] = 1 X k = - 2 kf [ n - k ] Compute the following values.
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