soln7

# soln7 - 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 7 Assigned: Wed 3 Dec Due: Fri 11 Dec Suggested reading: Class-notes, handouts, and Ch. 7 textbook O ce hours: M, W 4:00–6:00pm PHO438 Problem 7.1 Problem 7.1 Solution: (a) The channel, h ( t ), ﬁlters the waveforms, s i ( t ), and leads to modiﬁed waveforms given by: ˜ s i ( t ) = p E s h ( t ) * ψ i ( t ) , i = 1 , 2 To simplify these expressions we denote by, v ( t ) = t for t 0 . 5 1 for 0 . 5 t 1 1 . 5 - t for 1 t 1 . 5 Then, v 1 ( t ) = h ( t ) * ψ 1 ( t ) = v ( t ) + v ( t - 4) , v 2 ( t ) = h ( t ) * ψ 2 ( t ) = v ( t - 1) + v ( t - 5) The corresponding energies of these waveforms are k v i ( t ) k = r 5 12 , i = 1 , 2 Denote by, φ i ( t ), the corresponding unit energy pulses, i.e., φ i ( t ) = r 12 5 v i ( t ) Then the new waveforms are given by, ˜ s i ( t ) = p E s v i ( t ) = p E s k v i

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soln7 - Boston University Department of Electrical and...

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