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Unformatted text preview: 6.450 Principles of Digital Communication Monday, November 25, 2002 MIT, Fall 2002 Handout #35 Due: Wednesday, December 4, 2002 Problem Set 11 Problem 11.1 The following problem relates to a digital modulation scheme often referred to as minimum shift keying (MSK). Let 2 T E cos(2 πf t ) if 0 ≤ t ≤ T otherwise s ( t ) = , 2 T E cos(2 πf 1 t ) if 0 ≤ t ≤ T otherwise s 1 ( t ) = . (a) Compute the energy of the signals s ( t ) ,s 1 ( t ). You may assume that f 1 T 1 and f 2 T 1. (b) Find conditions on the frequencies f ,f 1 and the duration T to ensure both that the signals s ( t ) and s 1 ( t ) are orthogonal and that s (0) = s ( T ) = s 1 (0) = s 1 ( T ). Why do you think a system with these parameters is called minimum shift keying? (c) Assume that the parameters are chosen as in (b). Suppose that, under H =0, the signal s ( t ) is transmitted, and under H =1, the signal s 1 ( t ) is transmitted. Assume that the hypotheses are equally likely. Let the observed signal be equal to the sum of the transmitted signal and a White...
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