The stationary process has a spectral density which we assume is constant in the interval and zero for all other values. (a) Which is the smallest sampling frequency that can be chosen if one...

The stationary process

has a spectral density which we assume is constant

in the interval

and zero for all other values.

(a) Which is the smallest sampling frequency that can be chosen if one wants to avoid aliasing?

(b) Sometimes it is easy to forget that in many measurements there might be a strong disturbance at the frequency 50(60) Hz from the electricity current. Suppose that this disturbance process can be described by

where the random variable φ is uniformly distributed in the interval


Our measurement signal consists of

and we choose our sampling frequency to

Hz. What frequency interval is covered by the process

and the disturbance

respectively, after the sampling?