[Authors] V. N. Malozemov and K. Yu. Tsvetkov [Title] A sampling theorem in Vilenkin-Chrestenson basis [AMS Subj-class] 42C10 Fourier series in special orthogonal functions [Abstract] The following statement is proved: if a discrete signal $x$ has zero-valued high-frequency coefficients in its Vilenkin-Chrestenson expansion then $x$ is a step function. [Comments] Russian, 6 pp. [Contact e-mail] malv@gamma.math.spbu.ru wavelet3@mail.ru