This paper presents a novel single-channel decomposition approach to facilitate the decomposition of electroencephalography (EEG) signals recorded with limited channels. Our model posits that an EEG signal comprises short, shift-invariant waves, referred to as atoms. We design a decomposer as an artificial neural network aimed at estimating these atoms and detecting their time shifts and amplitude modulations within the input signal. The efficacy of our method was validated across various scenarios in brain--computer interfaces and neuroscience, demonstrating enhanced performance. Additionally, cross-dataset validation indicates the feasibility of a pre-trained model, enabling a plug-and-play signal decomposition module.