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 ${\sigma }_X^2$ 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...