1. Reminders: random functions and linear filtering

1.1 Random functions and background noise

• The random signalsX (t ), referred to as "background noise", are stationary random signals of order 2, i.e. with at least the first two moments independent of time, i.e. E {X } and E {X ² } (the mathematical expectations).

  Recall that the variance ${\sigma }_X^2$ is 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...