(1) Using the result of Problem 3 for Chapter 3 and the definition of the power spectrum, show that the power spectrum of MA model with order 1 can be expressed as p(f) = |1−be−2πi f | 2 , where the...

(1) Using the result of Problem 3 for Chapter 3 and the definition of the power spectrum, show that the power spectrum of MA model with order 1 can be expressed as p(f) = |1−be−2πi f | 2 , where the right-hand side can be expressed as 1+b 2 −2bcos(2π f). (2) Using the fact that if σ 2 = 1, the spectrum of an AR model of order 1, yn = ayn−1 + vn, can be expressed as p(f) = (1 − 2acos(2π f) +a 2 ) −1 , show that the maximum and the minimum of the spectrum occurs at f = 0 or f = 0.5. Also, consider where the spectrum p(f) attains its maximum.