  In this work, we examine the application of the wavelet transform to the
X-ray timing analyses of active galactic nuclei (AGN) and quasi-periodic
eruption sources (QPEs). Several scenarios are simulated to test the
effectiveness of the wavelet analysis to stationary and non-stationary data. We
find that the power spectral density (PSD) slope and the nature of the periodic
signal can influence the ability to identify important features in the wavelet
power spectrum. In general, weak and transient features can be discerned, which
make the wavelet spectrum an important tool in examining AGN light curves. We
carried out a wavelet analysis to four unique objects: Ark 120, IRAS
13224-3809, RE J1034+396, and the QPE GSN 069. The well-known quasi-periodic
oscillation (QPO) in RE J1034+396 is significantly detected in the wavelet
power spectrum. In IRAS 13224-3809, significant transient features appear
during a flare at frequencies coincident with previously detected reverberation
signals. Finally, the wavelet power spectrum of the QPE GSN 069 significantly
reveals four persistent signals that exhibit a 3:2 ratio in oscillation
frequencies, consistent with high-frequency QPOs in stellar mass X-ray
binaries, but we cannot rule out the possibility this is an artefact of the
calculation.
