ABSTRACT
This chapter discusses the auto-correlation functions and analysis of time signals using discrete Fourier transform (DFT). Certainly, significant computational costs required by N2 multiplications were the main reason for the lack of widespread usage of the DFT up to 1965. Nevertheless, there was another reason which delayed computerized applications of the DFT, and that was a lack of awareness of certain of the most critical achievements in the Fourier analysis from the past. In quantum-mechanical signal processing, the term Schrödinger basis is more transparent, since it points directly at the quantum-mechanical origin of the state functions that do stem from the Schrödinger equation. Nevertheless, to avoid potential confusion across interdisciplinary fields, one should always bear in mind that the Schrödinger and Krylov basis are two different nomenclatures for the same set.
