The average power P of a signal x ( t ) over all time is therefore given by the following time average, where the period T is centered about some arbitrary time t = t 0 : P = lim T → → ∞ ∞ 1 T ∫ ∫ t 0 − − T / 2 t 0 + T / 2 | x ( t ) | 2 d t