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Unformatted text preview: University of Minnesota Dept. of Electrical and Computer Engineering EE 8581 DETECTION AND ESTIMATION THEORY Spring 2010 April 29, 2010 _________________________________________________________________________ Name:_______________________________________ Student ID:___________________________________ Question 1 /10 Question 2 /10 Question 3 /10 TOTAL /30 Solve the three problems that appear on the next pages. Problem 1: In a certain problem, it is desired to decide which of two hypotheses H and H 1 is true. The observed waveform under each hypothesis is given by H 1 : r(t) = x(t) +n(t), 0 t 1 H : r(t) = n(t), 0 t 1, where ? ( ) = ? ( ) + ( ), ( ) is a zero mean white Gaussian noise process of intensity 1, ? ( ) is a zero mean Gaussian noise process with covariance ( , ) = 1 + cos 2 ( ) , and x(t) is a deterministic ideal lowpass waveform with no frequency content above 2.5 Hz and unit energy over the interval [0,1], i.e., content above 2....
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