The N-dimensional complex delta distribution

The notion of a 1-D complex delta distribution of the form Ψ _δ(t)=δ(t)+j/πt 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