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Unformatted text preview: ECE 301, Homework #2, due date: 9/07/2011 http://cobweb.ecn.purdue.edu/ ∼ chihw/11ECE301F/11ECE301F.html Question 1: [Basic] Consider two functions f ( t ) and g ( t ) described as follows. f ( t ) = 2 if 2 ≤ t < 1 if 0 ≤ t < 4 0 otherwise (1) g ( t ) = 3 + t if 3 ≤ t < 3 if 0 ≤ t < 2 otherwise . (2) Find the value of R ∞∞ g (1 t ) f ( t ) dt . Question 2: [Basic] Review of Trigonometry: Suppose π/ 2 ≤ α ≤ 0 and π ≤ β ≤ 3 π/ 2, and cos( α ) = 0 . 2 sin( β ) = . 4 . Find the values of cos( α + β ) and sin( α β ). Question 3: [Basic] Review of complex numbers: Let j be the imaginary number, i.e., j 2 = 1. Suppose √ 2 + √ 2 j = e a + bj e 3+ 5 π 3 j = c + dj. Find the values of a , b , c , and d . Question 4: [Basic] Suppose A is a 3 by 3 matrix. Consider a linear system that outputs y = Ax where x ∈ R 3 is the input signal. To be more precise, x is a column vector of dimensional 3, and y ∈ R 3 is the output column vector of dimension 3. Further assumeis the output column vector of dimension 3....
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 Fall '06
 V."Ragu"Balakrishnan
 Complex number

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