Random Processes with Applications to Circuits and Communications by Bernard C. Levy

Author:Bernard C. Levy
Language: eng
Format: epub
ISBN: 9783030222970
Publisher: Springer International Publishing

(6.44)

Let τ = RC denote the time constant of the circuit. The expression (6.44) shows that when t exceeds about 5τ, the variance

(6.45)

Furthermore, if the initial variance P(0) is equal to the steady-state variance P ss, P(t) is constant and equal to the steady-state variance for all times.

Consider now expression (6.43) for V (t), where t ≥ s. In this expression V (s) is independent of the second term, since V (s) depends only on V (0) and N(u) over 0 ≤ u ≤ s. Accordingly, the autocorrelation

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