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ESE Electronics 2010 Paper 1: Official Paper

Option 2 : and time averages are same

CT 3: Building Materials

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10 Questions
20 Marks
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Ergodic random process:

A stationary process X(t) is called ergodic (or ergodic in mean) if the time average is the same as ensemble average, i.e.

<x(t)> = E[X(t)] = m.

It is called ergodic in autocorrelation if <x(t)x(t + τ)> E[X(t)X(t + τ)] = RXX(τ).

An ergodic process is always stationary but a stationary process may or may not be ergodic.

__Important Points__

Different random processes:

__Strict sense stationary random process__:

If ensemble averages are independent of time then called a strict sense stationary random process.

Every ergodic random process will be strict sense stationary, but the reverse is not true.

__Wide sense stationary random process: __

If mean and autocorrelation functions are independent of time then called a WSS random process.

Every strict sense stationary random process is a wide sense stationary random process, but the reverse is not true.