Quiz1_2011_with_solution

Quiz1_2011_with_solution - Quiz 1 ECE 816 Spring Quarter...

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Unformatted text preview: Quiz 1 ECE 816 Spring Quarter 2011 April 11th, 2011 Problem 1: Consider a random variable X with the exponential probability density function (pdf) , Find the pdf of . Solution: To find the pdf of note: = , we can follow the example in page 13 of the lecture = Problem 2: (a) Find the modified Stokes vector corresponding to the electric field (V/m) that propagates in the direction in free space; note you will need to specify a coordinate system. (b) What type of polarization is this? If your answer is not “linear”, specify the handedness (i.e. left or right) of the polarization. If your answer is “elliptical”, also specify the axial ratio and tilt angle of the ellipse (and the axis from which this tilt angle is measured.) Solution: (a) W ith the coordinate system given in the class, the selection of and gives Thus, the modified Stokes parameters are (b) This is an elliptical polarization, and is right handed since . Using Ishimaru’s formulas: , , to find degrees and degrees. The polarization ellipse is rotated 58.28 degrees with respect to the axis and has an axial ratio ...
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