The concept of the characteristic function for scalar random variables
is extended to multivariate densities of random vectors. This is defined
as the multi-dimensional Fourier transform, or the multi-dimensional
Laplace transform for moment generating function (MGF). There is a
discussion that the multi-dimensional transforms are perhaps more useful
as a conceptual rather than practical tool. The video then considers an
example of finding the characteristic function of the multivariate
Gaussian. As an Appendix to this Topic, a derivation of a key integral
identify used in the example is provided.
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.
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