kb:random_processes

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)

  • 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)]

  • kb/random_processes.txt
  • Last modified: 2024-04-30 04:03
  • by 127.0.0.1