Some questions of application of trigonometric splines in problems of the spectral analysis are considered. The known effects of overlapping in the frequency and time domains are discussed. For the first time, the effects of deployment in these areas are considered. The relationship between discrete Fourier coefficients and Fourier coefficients of trigonometric splines is obtained. The expediency of taking into account the differential properties of the studied signals, which are lost during the primary sampling, is shown.