HW4S - ECE 402 Communications Engineering Homework 4...

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Unformatted text preview: ECE 402: Communications Engineering Homework 4 Solutions (Fall 2009) 1. (a) Student GPA X is Gaussian distributed with μ = 3 . 05 and σ = 0 . 50. The probability that a student graduates Summa Cum Laude is then Pr { X ≥ 3 . 75 } = Pr ‰ X- μ σ ≥ 3 . 75- 3 . 05 . 50 = Q (1 . 4) = 0 . 08076 so about 8.1% of students graduate with this honor. (b) The probability of graduating Magna Cum Laude is Pr { 3 . 5 ≤ X < 3 . 75 } = Pr { X ≥ 3 . 5 } - Pr { X ≥ 3 . 75 } = Pr ‰ X- μ σ ≥ 3 . 5- 3 . 05 . 50- Q (1 . 4) = Q (0 . 9)- Q (1 . 4) = 0 . 18406- . 08076 = 0 . 1033 so about 10.3% of students earn this honor. 2. The PSD is the Fourier Transform of the autocorrelation function: P X ( f ) = F { R ( τ ) } = F { A exp(- 2 λ | τ | ) } = 2 A 2 λ [1 + (2 πf/ 2 λ ) 2 ] = λA λ 2 + π 2 f 2 which follows from F{ exp(-| t | /T ) } = 2 T 1+(2 πfT ) 2 for T = 1 / 2 λ . 3. (a) Y ( t ) is filtered white Gaussian noise, so Y ( t ) is a zero-mean Gaussian process with PSD P Y ( f ) =...
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This note was uploaded on 01/28/2012 for the course ECE 402 taught by Professor Townsend during the Fall '08 term at N.C. State.

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HW4S - ECE 402 Communications Engineering Homework 4...

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