A band pass random process has power spectral density S(f) = II (f – 10/4) + II (f + 10/4).
(a) Find its auto correlation function.
(b) It is to be represented in in phase quadrature form; that is, x(t) = nc (t) cos (2πf0t + θ) – ns (t) sin (2πf0t + θ). If f0 is chosen as 10 Hz, what is the cross-spectral density, Sncns (f)?
(c) If f0 is chosen as 8 Hz, what is the cross-spectral density, Sncns (f)?
(d) If f0 is chosen as 12 Hz, what is the cross-spectral density, Sncns (f)?
(e) What is the cross-correlation function corresponding to part (c)?
(f) What is the cross-correlation function corresponding to part (d)?
