Random processes
Properties of random processes
- Expected value of signal at time t:
μX(t)=E[X(t)]
- Autocorrelation of signal at times t1 and t2:
RXX(t1,t2)=E[X(t1)X(t2)]
- Autocovariance of signal at times t1 and t2:
CXX(t1,t2)=E[˜X(t1)˜X(t2)]=RXX(t1,t2)−μX(t1)μX(t2)
where ˜X(t)=X(t)−μX(t)
Properties of two random processes
- Cross-correlation of X(t1) and $Y(t_2):
RXY(t1,t2)=E[X(t1)Y(t2)]
- Cross-covariance of X(t1) and $Y(t_2):
CXY(t1,t2)=E[˜X(t1)˜Y(t2)]