Finite Basic Functions in the Tasks of Sampling Signals of Finite Qxtension

The article deals with the application of systems of the basiс functions, defined on finite argument intervals, in the problem of obtaining discrete signal samples. These mathematical bases allow justifying the size of signal sample lattices for actual situations where their spectra are infinite and are characterized by a certain degree of attenuation at high frequencies. For expressions with finite functions, which do not have the time as argument, the conception “the Nyquist frequency” loses its significance.