difference between time average and ensemble averge ?

hi all,

I want to know what does esemble average and time average mean. I tried many places but all i could find was the expressions for the two, but what is the physical meaning of the two, and which applications prefer which sort of definition.

I would be thankful, if someone could share some materials that draws the line between the two terms in a clear fashion....

Hello,

for analog continous signals, we have time average. Time average is averaged quantity of a single system over a time inetrval directly related to a real experiment.

for discrete signals, we have ensemble average. Ensemble average is averaged quantity of a many identical systems at a certain time.

For further explaination : **broken link removed**

You created two identical topics? So I repeate

Some random processes have a property of ergodicity - it means that the time averaging is equvalent to ensemble averaging. This requires that prosess to be stationary. The vise-versa in general is not true - stationary process might not be ergodic.

To estimate patameters of random process you should have its time observation results. The longer the observation - the better precision. But usually you cannot have the total time realization of process, so you take a part of it - the ensemble. Ensemble is any random sample collection of time realization of random process.

Something about this I retold from book 'The foundation of digital communication. Theory and application' by Berhard Sklar. Try to google term 'ergodicity' also.