HW2 - ECE 301 Homework#2 due date...

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ECE 301, Homework #2, due date: 9/11/2008 http://www.ece.purdue.edu/ chihw/ECE301 08.html Question 1: Consider two functions f ( t ) and g ( t ) described as follows. f ( t ) = 1 if - 2 t < 0 3 if 0 t < 4 0 otherwise (1) g ( t ) = 2 if - 2 t < 0 2 - t if 0 t < 2 0 otherwise . (2) Find the value of R -∞ f (2 - t ) g ( t ) dt . Question 2: Review of Trigonometry: Suppose 0 α π/ 2 and π/ 2 β π , and sin( α ) = 0 . 2 sin( β ) = 0 . 3 . Find the values of cos( α + β ) and sin( α - β ). Question 3: Review of complex numbers: Let j be the imaginary number, i.e., j 2 = - 1. Suppose 1 + 3 j = e a + bj e - 2+ π 4 j = c + dj. Find the values of a , b , c , and d . Question 4: 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 assume that we know that When x 1 = (1 , 0 , 0) T , the output is y 1 = (3 , 2 , 1) T .
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When x 2 = (0 , 1 , 2) T , the output is y 2 = (2 , - 1 , 3) T .
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