The article develops the authors’ previous work and examines the sequence of problems that form an approach to solving the problem of detecting a signal in noise, including cases with a low signal-to-noise ratio. The sequence of mathematical problems needed to be solved is determined. For the case of proximity of two hypotheses, analytical constructions are used to obtain test statistics, observational statistics, and decision rules based on frequency, time, and time-frequency distributions. In this paper, the possibility of increasing the signal-to-noise ratio is established when distinguishing between two hypotheses for d-signals. The theoretical results are established by the proof of the corresponding lemmas.