hw2 - ECE 301 Homework#2 due date...

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Unformatted text preview: ECE 301, Homework #2, due date: 1/25/2012 https://engineering.purdue.edu/ ∼ chihw/12ECE301S/12ECE301S.html Question 1: [Basic] Consider two functions f ( t ) and g ( t ) described as follows. f ( t ) = 2 if- 1 ≤ t < 1 if 0 ≤ t < 2 otherwise (1) g ( t ) = 3 + t if- 2 ≤ t < 3 if 0 ≤ t < 1 otherwise . (2) Find the value of ∫ ∞-∞ g (1- t ) f ( t ) dt . Question 2: [Basic] Review of Trigonometry: Suppose- π/ 2 ≤ α ≤ 0 and 3 π/ 2 ≤ β ≤ 2 π , 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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hw2 - ECE 301 Homework#2 due date...

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