It is clear that a continuous periodic signal always takes at some point $x_m$ the absolute mean value. Then we could define the absolute mean value of the signal as the value that it takes at $x_m$.
My question is: What are the conditions necessary in order to define the mean value in the same form in the discrete case?
For example, the mean of a sin function could be defined as the value that the function takes at zero.
I think some time ago i found a formula to calculate the mean value of a discrete periodic signal from the values it takes but i can remember neither the formula nor the reference.
Can you help me?