STATIONARY RANDOM VARIABLE

STATIONARY RANDOM VARIABLE Подпись: (2.6,1)

Consider a random variable u(t), as shown in Fig. 2.4. The average value of «(f) over the interval (tx — T) to (t1 + T) depends on the mid-time tv and

The function is said to have a stationary mean value й if the limit of «(fj, T) as T —*■ oo is independent of t±: i. e.

1 rti+T

it = lim — u(t) dt (2.6,2)

T^oo2Tjh-T

If, in addition, all other statistical properties of «(f) are independent of tv then it is a stationary random variable. We shall be concerned here only with such functions, and, moreover, only with the deviation v(t) from the mean (see Fig. 2.4). The average value of v(t) is zero.

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