The 2 Ã 2 matrix is called a rotation matrix because y = QX is the rotation
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is called a rotation matrix because y = QX is the rotation of x by the angle θ. Suppose X = [X1 X2] is a Gaussian (0, CX) vector where CX = diag[σ21, σ22] and Let Y = QX.
(a) Find the covariance of Y1 and Y2. Show that Y1 and Y2 are independent for all θ if σ21 = σ22.
(b) Suppose σ22 > σ21. For what values θ are Y1 and Y2 independent?
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a From Theorem 88 Y has covariance matrix We conclude that Y 1 and Y 2 have covariance Cov Y 1 Y 2 C ...View the full answer
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Related Book For 
Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers
ISBN: 978-1118324561
3rd edition
Authors: Roy D. Yates, David J. Goodman
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