Question
Sinusoid with random phase . Consider the random process X(t )= A cos(0t+ ), where A and 0 are real constants and U (0, 2).
Sinusoid with random phase. Consider the random process X(t )= A cos(0t+
), where A and 0 are real constants and U (0, 2).
(a) Find the mean function E[X(t) ]and the autocorrelation function Rx(t+ , t). Is X (t) wide-sense stationary? Why?
(b) Assume now U(0,/2). Determine the mean-square value E[X2(t)]. Is E[X2(t)] deterministic? time dependent? Is the new random process X(t) wide-sense stationary? Why? If E[X2(t)] is time varying, what is its time average?
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Differential Equations and Linear Algebra
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
2nd edition
131860615, 978-0131860612
