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

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ECE 301, Homework #1, due date: 9/4/2008 http://www.ece.purdue.edu/ chihw/ECE301 08F.html Review of calculus and arithmetics: Question 1: Compute the values of the following integrals. Z 2 π 0 cos( s + 2 π/ 3) ds Z π 0 sin( π/ 2 - u ) du Z 2 0 Z 5 3 cos( 3 4 + 3 ) dxdy Question 2: Compute the values of the following integrals. Z 2 π - π 2 | t | e j 3 π 2 t dt Z 3 - 3 ω sin( π 3 ω ) Z 2 0 (2 - 3 z ) e j 3 πz dz Question 3: Compute the expressions of the following integrals. Z 3 ω 0 ( t - s ) e jωπ ( t - s ) ds 1 T ˆ Z T/ 2 0 ( T 2 - t ) e - j 2 T t dt + Z T T/ 2 ( t - T 2 ) e - j 2 T t dt ! , where k is an integer. Question 4: Suppose f ( t ) = 2 t 2 - 3 t + 1. Define g ( t ) = f (1 - t ). Compute the following

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values. g (3) Z 5 3 g (1 + s ) ds Z 2 0 g 0 ( s ) e jπs ds, where g 0 ( t ) is the first order derivative of g ( t ). Question 5: Suppose f ( t ) = 1 - t 2 . Define g ( t ) = Z t +1 t - 2 f ( s ) ds Compute the following values. g (3) Z 5 2 g ( s ) ds Z 1 - 1 g ( s ) f (1 - s ) ds. Question 6: Consider a discrete series f [ n ] = n - 3. Define g [ n ] = 2 X k = - 1 kf [ n - k ] Compute the following values. g [3] 3 X k =1 0 . 9 k g [ k ] X k =3 0 . 9 k g [ k ] Hint: If | r | < 1, then X k =1 ar k - 1 = a 1 - r X k =1 kar k - 1 = a (1 - r ) 2 .
Question 7: Consider a discrete series f [ n ] = n + 1. Define g [ n ] = 1 2 ( f [ n ] - f [ - n ]) . (1) Compute the following values. g [3] 3 X k =1 g [ k ] Question 8: Consider a discrete series such that f [ n ] = 1 if - 1 n 2 and f [ n ] = 0 otherwise. Define g [ n ] = X k = -∞ f [ n - k ]0 . 5 | k | . Compute

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

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