Problem

The autocorrelation of a sequence consisting of a sinusoid with random phase in noise is...

The autocorrelation of a sequence consisting of a sinusoid with random phase in noise is

where f1 is the frequency of the sinusoidal, P is its power, and is the variance of the noise. Suppose that we attempt to fit an AR(2) model to the data.

(a) Determine the optimum coefficients of the AR(2) model as a function of , and f1.

(b) Determine the reflection coefficients K1 and K2 corresponding to the AR(2) model parameters.

(c). Determine the limiting values of the AR(2) parameters and (K1, K2) as .

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Solutions For Problems in Chapter 12