1.2(a) Consider a signal plus noise model of the general formxt=st+wt,

wherewtis Gaussian white noise withs2= 1. Simulate and plotn=200 observations from each of the following two models (Save the data generated here for use in Problem 1.21):

(a)xt=st+wt, fort= 1, ...,200, where

( 0, t= 1, ...,100

(t-100)

st=10 exp{-20}cos(2pt/4), t= 101,...,200.

Although the model in problem 1.2(a) is not stationary (why?), the sample ACF can be informative. For the data you generated in that problem, calculate and plot the sample ACF, and then comment.