hw2 - Boston University Department of Electrical and...

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Boston University Department of Electrical and Computer Engineering ENG EC515 Digital Communication ( Fall 2009 ) Problem set 2 Assigned: Friday 18 Sep Due: Monday 28 Sep Suggested reading: Class-notes, handouts, and Ch. 2 textbook O ce hours: M, W 4:00–5:30pm PHO438 Notation: δ ( t ) , t R denotes the continuous-time Dirac-delta (impulse) function, P ( E ) denotes probabil- ity of event E , E ( · ) denotes the mathematical expectation operator, Q ( x ) denotes the Q-function defined as Q ( x ) = 1 2 π R x exp( - t 2 / 2)d t , pmf is the acronym for probability mass function and cdf the acronym for cumulative distribution function. Problem 2.1 (a) Prove that if s 0 ( t ) and s 1 ( t ) are orthogonal complex baseband signals of bandwidth W , then s 0 ( t ) cos(2 π f 0 t ) and s 1 ( t ) cos(2 π f 0 t ) are also orthogonal signals provided f 0 is larger than W . (b) Give an example for which the statement fails when f 0 is smaller than W . (Hint: Use the fact that orthogonality in time domain has a corresponding expression in the frequency
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hw2 - Boston University Department of Electrical and...

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