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

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

γ_xx(m) = P cos2πf₁m + σ²_uδ(m)

Where f1 is the frequency of the sinusoidal, P is its power, and σ²_π 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 function of σ²_ω 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 σ²_ω → 0.