A useful average in the consideration of noise in FM demodulation is the cross-correlation
 where y(t) is assumed stationary.
(a) Show that 

where R_y(Ï„) is the auto correlation function of y(t). (The frequency response function of a differentiate is H(f) = j2Ï€f.)

(b) If y(t) is Gaussian, write down the joint pdf of 

at any time t, assuming the ideal low pass power spectral density 

Express your answer in terms of N₀ and B.

(c) Can one obtain a result for the joint pdf of y and dy(t) / dt if y(t)
is obtained by passing white noise through a low pass RC filter? Why or why not?

Transcribed Image Text:

dy(t + t) |Ry3 (7) = E { y(t) Гуў dt d R, (t) Ryy (t) = "уў dt