Second-order statistics are fundamental to the definition of wide-sense
stationary (WSS) processes, and this video considers the properties that
a WSS autocorrelation sequence (ACS) must satisfy. Some of properties
primarily derive from the key property that the ACS must be positive
semi-definite, but other basic ones include the symmetrical property of
the ACS, that a random variable cannot be more correlated with another
random variable than itself, and that the second moment must always be
positive. The video then considers a couple of examples, which tests
whether a particular sequence or function is indeed valid.
PGEE11164 Probability, Estimation Theory, and Random Signals Lectures -- School of Engineering, University of Edinburgh. Copyright James R. Hopgood and University of Edinburgh, Scotland, United Kingdom (UK). 2020.
Institute for Digital Communications, Alexander Graham Bell Building, The King's Buildings, Thomas Bayes Road, Edinburgh, EH9 3JL. UK.