In the definition of (4.70) for the power spectral density of a weakly stationary process X(t), it is not permissible to interchange the order of expectation and limiting operations. Justify the validity of this statement.
In the next four problems we explore the application of the Wiener-Khintchine theorem of (4.60) to see whether a given function r , expressed in terms of the time shift t, is a legitimate normalized autocorrelation function or not.