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Unformatted text preview: ( t ) sin(2 πt ) dt. Explain why the knowledge of l 1 and l 2 is su²cient to form the optimum decision rule (i.e., explain why l 1 and l 2 are su²cient statistics for the hypothesis testing problem). Also determine the pdf of [ l 1 l 2 ] T under each hypothesis. (b) Specify the decision regions ( l 1 , l 2 ) space for the minimum probability of error decision rule. (c) Show that α 6 P (error) 6 2 α, where α = 1-Φ( A/ 2). ( Hint: Examine the decision regions determined in part (b). What is the region corresponding to an error if, say, H is true? Can you represent this region as a union of two half spaces?) 1 Problem 4 (Poor, Ch. 3, Pr. 13) Problem 5 (Poor, Ch. 3, Pr. 14) Problem 6 (Poor, Ch. 3, Pr. 17) 2...
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- Spring '08
- Phase-shift keying, Gaussian noise, Estimation Theory OSU