These short notes contain an introduction to filtering of deterministic
and stochastic signals.
The connection with algorithms from classical complex analysis
(the Schur algorithm) and with the recurrence relation (Szegö) for
polynomials orthogonal with respect to a measure supported on the unit circle
are both given.
The interpretation of these algorithms in terms of linear algebra lead to
fast algorithms for structured matrices.
It is explained how these algorithms can be generalized to situations
where the signal is not stationary. The corresponding notion of matrices
with low displacement rank is introduced.
The notes are organized like lecture notes and contain several exercises
that form an essential part of the text. Solutions are provided at the end.