Conversion of the harmonic signal of limited duration by the sampling theorem for all permitted values of the band index

The paper is devoted to the study of Whittaker-Kotelnikov-Shannon sampling theorem as a tool for transforming the basic object of Fourier analysis ? a harmonic signal of limited duration which a priori does not satisfy the theorem conditions. Ambiguity of the transform result is shown, effects of shifting and overlapping in frequency domain are analyzed, and formulas that determine the limits of theorem applicability are obtained.