Electroencephalogram (EEG) analysis consists of locating signal structtures in time and frequency. A detection method based on the Matching Pursuit Algorithms finds the suboptimal solution of the function optimal linear expansion over a redundant waveform dictionary. This paper has put forth a method for the automatic detection and analysis of transient waves during sleep based on the matching pursuit method with a real dictionary og Gabor functions. Each wave peak is described in terms of natural parameters. In this context, there have been confirmed several literature hypotheses regarding the spatial, temporal, and frequency distribution of transient waves during sleep, and their relationships with slow wave brain activity. Mastery and expertise in clinical EEG interpretation is one of the most desirable disgnostic clinical skills in interpreting seizures, epilepsy, sleep disorder, biomarkers for early disgnosis of Parkinson’s and Alzheimer’s disease, and other neurocognitive studies.