Autocorrelation and its Properties
• Autocorrelation function (ACF) of a random process plays a
major role in knowing whether the process is stationary.
• In particular, for a stationary process the ACF is independent
of time and hence it becomes dependent only on time
difference.
• ACF of a stationary process also helps to determine the
average of the process as the time difference becomes
infinite.
• ACF of a stationary process shows something about how
rapidly one can expect a random process to change as a
function of time
, • If the ACF changes slowly then it is an indication that the
corresponding process can be expected to change slowly and
vice versa.
• If ACF function has periodic components, then the
corresponding process is also expected to have periodic
components.
• Therefore there is a clear indication that the ACF contains
information about the expected frequency content of the
random process.
• Autocorrelation function (ACF) of a random process plays a
major role in knowing whether the process is stationary.
• In particular, for a stationary process the ACF is independent
of time and hence it becomes dependent only on time
difference.
• ACF of a stationary process also helps to determine the
average of the process as the time difference becomes
infinite.
• ACF of a stationary process shows something about how
rapidly one can expect a random process to change as a
function of time
, • If the ACF changes slowly then it is an indication that the
corresponding process can be expected to change slowly and
vice versa.
• If ACF function has periodic components, then the
corresponding process is also expected to have periodic
components.
• Therefore there is a clear indication that the ACF contains
information about the expected frequency content of the
random process.
