Suppose that an AR(1)-process, has the covariance function Which AR(1)-process is it? What is the variance of the innovations? Find the spectral density, R(f), and the covariance function, r(k), at...

Suppose that an AR(1)-process,

has the covariance function

Which AR(1)-process is it? What is the variance of the innovations?

Find the spectral density, R(f), and the covariance function, r(k), at time lag zero, one and two, of the AR(2)-process

Where

is a white innovation process with variance

The covariance function of a signal, {Yt}, in discrete time, has been well estimated at a few time lags:

Find the innovation variance, the second AR-parameter, and the covariance function at time lag two.