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) n c (t) cos (2f 0 t ) n s (t) sin (2f 0 t ) If f 0 is chosen as 10 Hz, what is the cross spectral density, S ncn s (f) (c) If f 0 is chosen as 8 Hz, what is the cross spectral density, S ncn s (f) (d) If f 0 is chosen as 12 Hz, what is the cross spectral density, S ncn s (f) (e) What is the cross correlation function corresponding to part (c) (f) What is the cross correlation function corresponding to part (d)

Question: A band pass random process has power spectral density S(f) = II (f - 10/4) + II (f + 10/4). (a) Find its auto correlation

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) = n_c (t) cos (2πf₀t + θ) - n_s (t) sin (2πf₀t + θ). If f₀ is chosen as 10 Hz, what is the cross-spectral density, S_ncn_s(f)?

(d) If f₀ is chosen as 12 Hz, what is the cross-spectral density, S_ncn_s(f)?

(e) What is the cross-correlation function corresponding to part (c)?
(f) What is the cross-correlation function corresponding to part (d)?

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