Wavelet analysis is a powerful tool to investigate non-stationary signals such as amplitude modulated sinusoids or single events lasting for a small percentage of the observing time. Wavelet analysis can be used, for example, to reveal oscillations in the light curve of stars during coronal flares. A careful treatment of the background in the wavelet scalogram is necessary to determine robust confidence levels required to distinguish between patterns caused by actual oscillations and noise. This work describes the method using synthetic light curves and investigates the effect of background noise when determining confidence levels in the scalogram. The result of this analysis shows that the wavelet transform is able to reveal oscillatory patterns even when frequency-dependent noise is dominant. However, their significance in the wavelet scalogram may be reduced, depending on the assumed background spectrum. To show the power of wavelet analysis, the light curve of a well-known flaring star is analysed. It shows two oscillations overlapped. The lower-frequency oscillation is not mentioned in previous works in the literature. This result demonstrates the need for correctly characterizing the background noise of the signal. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.