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The electroencephalography (EEG) signal contains important information about the electrical activity of the brain, which can reveal many pathologies. This information is transmitted in certain waveforms and events, one of which is the K-complex. Detection of these patterns is essential in sleep studies to diagnose neurophysiological and cognitive disorders. Existing detection methods rely heavily on tedious, time-consuming and error-prone manual inspection of the EEG waveform. Therefore, automatic identification of K-complexes is of great interest. In this paper, adapted wavelets are constructed to detect K-complexes using a variant of the Discrete ÓtextitShapelet Transform II (DST-II). This transform is designed to detect patterns (such as these K-complexes) by localizing them in time and frequency. This is achieved by numerically solving a system of nonlinear equations that estimates a wavelet filter adapted to the pattern. In this research, a numerical strategy for solving the nonlinear system of DST-II is presented. The influence of such a strategy on the detection of K-complexes in different signals and the detection accuracy versus other classical wavelet filters were evaluated. [ABSTRACT FROM AUTHOR]