Experiments that observe coherent radio emission from extensive air showers induced by ultra-high energy cosmic rays are designed for a detailed study of the development of the electromagnetic part of air showers. Radio detectors can operate with 100% up time as e.g. surface detectors based on water-Cherenkov tanks. They are being developed for ground-based experiments (e.g. the Pierre Auger Observatory) as another type of air shower detector in addition to the fluorescence detectors, which operate with only ~10% of duty in dark nights. The radio signals from air showers are caused by the coherent emission due to geomagnetic radiation and charge excess processes. Currently used self-triggers in radio detectors often generate a dense stream of data, which is analyzed afterwards. Huge amounts of registered data requires a significant man-power for the off-line analysis. An improvement of the trigger efficiency becomes a relevant factor. In this work, Morlet wavelets with various scaling factors were used for an analysis of real data from the Auger Engineering Radio Array and for an optimization of the utilization of the resources in an FPGA. The wavelet analysis showed that the power of events is concentrated mostly in a limited range of the frequency spectrum (consistent with a range imposed by the input analog band-pass filter). However, we found several events with suspicious spectral characteristics, where the signal power is spread over the full band-width sampled by a 200 MHz digitizer with significant contribution of very high and very low frequencies. These events may not origin from cosmic ray showers but can be human-made contaminations. The engine of the wavelet analysis can be implemented into the modern powerful FPGA and can remove suspicious events on-line to reduce the trigger rate.