The weakly stationary process is differentiable and has the spectral density Compute the covariance function and the spectral density of its derivative, Prove that defined by can be a covariance...

The weakly stationary process

is differentiable and has the spectral density

Compute the covariance function and the spectral density of its derivative,

Prove that

defined by

can be a covariance function of a stationary process. Determine the spectral density and prove that the process is differentiable.