The N-dimensional complex delta distribution

The notion of a 1-D complex delta distribution of the form /spl Psi//sub /spl delta//(t)=/spl delta/(t)+j//spl pi/t is used in quantum physics from which it has since then proliferated into the theory of signals and systems. This correspondence recalls the definition of the 1-D complex delta distribution using the Gabor's notion of the analytic signal and presents the consequences of its polar notation. The notions of 2-D and 3-D complex delta distributions are illustrated with approximating functions and written in the polar notation. Examples of periodic complex delta distributions are given.