# Question: Consider a random process Z t X t

Consider a random process Z (t) = X (t) + Y (t).

(a) Find an expression for SZZ (f) in terms of SXX (f), SYY (f) and SXY (f).

(b) Under what conditions does SZZ (f) = SXX (f) + SYY (f)?

(a) Find an expression for SZZ (f) in terms of SXX (f), SYY (f) and SXY (f).

(b) Under what conditions does SZZ (f) = SXX (f) + SYY (f)?

**View Solution:**## Answer to relevant Questions

Develop a formula to compute the RMS bandwidth of a random process, X (t), directly from its autocorrelation function, RXX (τ). Consider an AR (2) process which is described by the recursion Y [n] = a1Y [n– 1] + a2Y [n– 2] + X [n] Where is an IID random process with zero- mean and variance σ2X. (a) Show that the autocorrelation function of the ...Suppose we form a smoothed periodogram of the PSD, As defined in Equation (10.35), using a rectangular smoothing function, Where fΔ is the width of the rectangle. If we want to form the same estimator using a windowed ...Let be a random process, where An and Bn are random variables such that , E[An]= E[Bn]= 0 E[AnBm] = 0 E[AnAm] dn, mE An = [ 2] E[BnBm] δn, mE [ Bn 2], , and for all and , where is the Kronecker delta function. This process ...A discrete random sequence is the input to a discrete linear filter h [n]. The output is Y [n]. Let Z [n] = X [n+ i] – Y [n]. Find E [Z2 [n]], in terms of the autocorrelation functions for X [n] and Y [n].and the cross- ...Post your question