This paper demonstrates how elementary convolutional neural networks can be used to classify noise signals of three types: normal, uniform, exponential – where the signals have identical power, which means that a classifier has to rely on their structural properties. A key innovation in our approach, as compared to existing research, is that our networks take raw data as input and automatically generate a selection of informative features. We have also analyzed the structure of trained convolutional networks and their decision-making process. Robustness to contamination of input data (model of channel/sensor cut-off) and the capability to detect prevailing signal in a mixture of signals under the conditions of a priori uncertainty have been evaluated as well. The study has shown that neural networks are effective in applications involving narrowband or broadband stochastic processes, as well as distinct patterns, and can, therefore, be used for signal processing tasks.