# Intuitive definition of ergodicity for random signal

Is it possible to define the ergodicity of the random signal in an intuitive sense without using any statistical reference?

## 1 Answer

When a process or system in which the average, over time, of the physical quantities that describe it coincides with the average calculated over a set of possible states of the process or of the system itself.

I would use an example like the following:

-You would have the similar results after flipping 100 coins as flipping a coin 100 times.

I hope it helps.

• Thanks a million. That example really helps. – thamid adnan Jan 4 at 2:59
• Be a bit careful, though, the definition "ensemble and time average of the mean are the same" is a very narrow definition of ergodicity; I'd call that "ergodic (only) w.r.t. averaging"(it also has the special name of "pointwise ergodicity",iirc); the definition from literature that I find most useful is that "A stochastic process (random signal) $X(t)$ is ergodic with respect to a function $g(\cdot)$ iff the time average $\overline{g(x(t)}$ of every realization converges to the ensemble average $E(g(X(t)))$". For that to exist, the latter must be a constant, so stationarity is a requirement. – Marcus Müller Jan 4 at 8:11