Exercise 6.9.16. Apply the relationship in Exercise 6.9.15a on the sine of a sum to the process in Exercise 6.9.2 to show that the process can be rewritten as yt = Asin(2πνt +φ ), where A is the random amplitude and φ is the random phase of the sine curve.

Find the relationship between (A,φ ) and (α,β ). How does this relate to the basic spectral approximation in (6.3.1)? If, instead, we write yt = A∗ cos(2πνt+φ∗), how do (A∗,φ∗) differ from (A,φ )?