The History of Applications of Analytic Signals in Electrical and Radio Engineering

Analytic signals have been originally described in 1946 by Dennis Gabor. The paper describes briefly the mathematical background created in the past by prominent mathematicians, physicists and engineers, especially the complex notation of functions, the theory of analytic functions and the Fourier spectral analysis and the theory of distributions. Due to the personal experience of the author, the extension of the Gabor's notion of the analytic signal for N-dimensional signals is briefly described As well, problems of analytic spectra of causal signals with extension for N dimensions and 2N-dimensional Wigner distributions are shortly presented.