For the observation of ultra high-energy cosmic rays (UHECRs) by the detection of their coherent radio emission an FPGA based trigger and radio frequency interference (RFI) filter was developed. Using radio detection, the electromagnetic part of an air shower in the atmosphere may be studied in detail, thus providing information complementary to that obtained by water Cherenkov detectors which are predominantly sensitive to the muonic content of an air shower at ground. For an extensive radio detector array, due to the limited communication data rate, a sophisticated self trigger is necessary. However, radio signals in the frequency range of 30-80 MHz are significantly contaminated by RFI and human made distortions. The digitized signals are converted from the time to frequency domain by a FFT procedure, then a deconvolution and RFI-filters are applied to correct the frequency response and to suppress the RFI. Finally the filtered data is transformed back into the time domain by an iFFT, also generating an envelope as a base for the final self-trigger. To avoid leakage effect and to create an overlap of successive data blocks, trapezoidal windowing is applied with internal overclocking. The algorithms for two polarization channels have been successfully implemented in a single FPGA and tested in a prototype board with 180 MHz sampling rate, 16-bit dynamic range, and 12-bit resolution.