Reminders: Random Functions and Linear Filtering
Background noise and measurements - Theoretical aspects
Article REF: R310 V1
Reminders: Random Functions and Linear Filtering
Background noise and measurements - Theoretical aspects

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

1.1 Random functions and background noise

  • 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 {X 2 } (the mathematical expectations).

    Remember that variance is defined as σX2 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...

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