Background noise and measurements : Reminders: Random Functions and Linear Filtering

Reminders: Random Functions and Linear Filtering
Background noise and measurements

Authors : Matteo VALENZA, Fabien PASCAL, Alain HOFFMANN

Publication date: December 10, 2006 | Lire en français

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1. Reminders: Random Functions and Linear Filtering

Random signals X (t), referred to as "background noise," are stationary random signals of order 2, i.e., they have at least the first two moments independent of time, namely E {X } and E {X²} (the mathematical expectations).

Remember that variance is defined as $σ_{X}^{2}$ the mean square of the centered variable X (t ) – E {X }.

Another consequence of stationarity is that the statistical mean of the product X(t)X(t + τ) depends only on the variable τ; this moment is the autocorrelation function, i.e.:

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Reminders: Random Functions and Linear Filtering