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114_1_midterm_2008_Part1

114_1_midterm_2008_Part1 - UCLA Dept of Electrical...

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1 UCLA Dept. of Electrical Engineering EE114 Midterm exam 2/6/2008 This exam consists of five questions. Please show all steps leading to your answers. An answer without explanation will not receive full credit. GOOD LUCK! 1. (20 points) DFT Bold and underlined characters or numbers denote array elements at position zero ( n =0). Be sure to specify the position where n =0 in your results, when applicable. (a) Given the time signal x ( n ) = [ a b c d], what is the 4-point DFT ( X ( k )) as a function of a, b, c, and d? i. Assuming x ( n ) is even and periodic with a period of 4 samples, the result for X ( k ) is simplified. What is the simplified X ( k ) as a function of a, b, c, and d? ii. Assuming x ( n ) is odd and periodic with a period of 4 samples, the result for X ( k ) is simplified. What is the simplified X ( k ) as a function of a, b, c, and d? (b) Assume that the 2-point DFT of x ( n )=[ a b] is X ( k )=[ A B]. Calculate the 4-point DFT of y ( n )=[ a b a b], Y ( k ), as a function of A and B.
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