**Mumbai University > Electronics and Telecommunication Engineering > Sem 5 > Random Signal Analysis

Marks: 10M

Year: May 2016

Definition: If two random processes {X(t)} and {Y(t)} are jointly wide sense stationary then E[X(t).Y(t+τ)] is a function of τ and is denoted by $R_{XY}$ (τ). This function $R_{(X,Y} $(τ) is called the cross correlation function of the processes X(t) and Y(t).

Properties:

• R_(X,Y) (τ)=R_(Y,X) (-τ)
• R_(X,Y) (τ)≤√(R_(X,X) (0).R_(Y,Y) (0))
• R_(X,Y) (τ)≤1/2[R_X (0)+R_Y (0)]
• If the processes X(t) and Y(t) are independent and jointly stationary then R_(X,Y) (τ)=μ_x.μ_y