solutions_test1_s1_f05

solutions_test1_s1_f05 - ECE 220, Sections 001, 002, Test 1...

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Unformatted text preview: ECE 220, Sections 001, 002, Test 1 Solutions 22 September 2005 Problem 1. (15 points) Consider the graph of the signal s ( t ) shown in figure 1. The graph is accurate. Write down a mathematical expression for this signal, using (time-shifted and scaled, if need be) versions of the ( t ) signal.-40-30-20-10 10 20 30 40-1 1 2 3 4 5 6 7 8 9 10 t --> s(t) The signal s(t) Figure 1: The signal s ( t ) in problem 1. Solution: The signal s ( t ) contains 6 ( ) impulses, equally spaced; the time spacing is 10 units. The impulses (from left to right) can then be expressed as ( t + 20) , ( t + 10) , ( t ) , ( t- 10) , ( t- 20) , ( t- 30) , or, more compactly, as: ( t- 10 k ) , k =- 2 ,- 1 , , 1 , 2 , 3 . So, finally, s ( t ) = 8 3 X k =- 2 ( t- 10 k ) 1 Problem 2. (10 points) Determine whether T = 3 is a period of the signal f ( t ) = 3cos(2 100 t + / 4) cos(2 t- / 4) Justify your answer. Guesses will not count! Solution: We need to check whether f ( t + 3) = f ( t ) ....
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solutions_test1_s1_f05 - ECE 220, Sections 001, 002, Test 1...

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