This paper verifies the sampling conditions of discharge and net precipitation series, subjects of integral transforms. The time step influence on the discrete numerical integration of the hydrological system input and output signals was analysed. Our approach is based on the sampling theorem and on the basic properties of the Discrete Cosine Transform (DCT) and of the Fourier integral transform. Arguments from conceptual models of river basin rainfall-runoff are considered to underlie our time series sampling. The application of the integral transform methods like DCT in the Instantaneous Unit Hydrograph (IUH) parameters computation needs to fix the summing limits before designing the numerical procedure.