Experiments which 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 fluorescence detectors, which operate with only ~ 10% of duty on dark nights. The radio signals from air showers are caused by coherent emission caused by geomagnetic radiation and charge excess processes. The self-triggers currently used in radio detectors often generate a dense stream of data, which is analyzed afterwards. Large amounts of stored data require significant computing resources for off-line analysis. An improvement of the trigger efficiency would be highly desirable. A wavelet trigger, which investigates the power of radio signals ( ~ V 2 /R) on-line is a promising development of the current designs. In this work, Morlet wavelets with various scaling factors were used for an analysis of real data from the Auger Engineering Radio Array (AERA) 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 was spread over the full band-width sampled by a 200 MHz digitizer with a significant contribution from very high and very low frequencies. These events most probably do not originate from cosmic ray showers but could be human-made contaminations. The engine of a wavelet analysis can be implemented in the modern powerful FPGA and can remove suspicious events on-line to reduce the trigger rate.