Frequently asked questions on filtered noise

This note was made in response to several returning questions on noise and ways to calculate covariance of filtered random signals, where filters could origin from residual generators. Reference is made to stochastic signals treated in appendix 2 of the book Diagnosis and Fault-tolerant Control by Blanke, Kinnaert, Lunze and Staroswiecki, 2003.

The note is aimed at graduate students who follow their first course in diagnosis and fault-tolerant control where design of appropriate filters is an important part of the design of fault diagnosis.