Question: Consider a 2nd-order random process that is generated by the difference equation y[n] = -2 y[n-1] - y[n-2] + w[n] - w[n-2] where w[n] is

Consider a 2nd-order random process that is generated by the difference equation

y[n] = -2 y[n-1] - y[n-2] + w[n] - w[n-2]

where w[n] is zero-mean white noise random process with variance ?w2 .

a) Find the power spectrum of y[n], algebraic expression in terms of " ?w2 , cos(w ) " only ? Py (ejw) = ?

N.B. Algebraic means that "square-root", "square", "log", "exp" (like) (of) functions of w are prohibited.

Consider a 2nd-order random process that is generated by the difference

Consider a 2"d-order random process that is generated by the difference equation y[n] = -2 y[n-1] - y[n-2] + w[n] - w[n-2] where w[n] is zero-mean white noise random process with variance ow- . a) Find the power spectrum of y[n], algebraic expression in terms of " Ow , cos(w ) " only ? Py (eiw) =? N.B. Algebraic means that "square-root", "square", "log", "exp" (like) (of) functions of w are prohibited

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