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# Multivariate Random Signals

Before reading on, it is highly recommended that you review the basics of multivariate probability theory

A real time signal can be considered as a random process and its samples a random vector is the expectation of :

The mean vector of is

The covariance matrix of is

where is the covariance of two random variables and . When , becomes the variance of , . In general, is the data set is complex, the covariance matrix is Hermitian, i.e., . In particular if the data set is real, then is real and symmetric .

The correlation matrix of is defined as

where . Note that as and , both and are symmetric matrices (Hermitian if is complex).

A signal vector can always be easily converted into a zero-mean vector with all of its dynamic energy (representing the information contained) conserved. Without loss of generality for convenience, sometimes we can assume so that .

After a certain orthogonal transform of a given random vector , the resulting vector is still random with the following mean and covariance:

Next: Covariance and Correlation Up: klt Previous: klt
Ruye Wang 2013-04-23