FPGA implementation of the 32-point DFT for a wavelet trigger in cosmic rays experiments

For the observation of ultra high-energy cosmic rays (UHECRs) by the detection of their coherent radio emission an FPGA based wavelet trigger is being 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. The wavelet trigger investigating online a power of signals is promising, however its implementation requires some optimizations. The digitized signals are converted from the time to frequency domain by a standard Altera^® library based FFT procedure, then multiplied by wavelet transforms and finally converted to the time-domain again. Altera^® FFT routines convert ADC data as blocks of 2^N samples. FFT coefficients are provided in a serial stream in 2^N time bins. An estimated signals power strongly depends on relatively positions of the FFT(data) and the wavelet transforms in a frequency domain. Additional procedure has to calculate a most efficient selection of the sample block to reach a response corresponding to a maximal signal power. If a set of FFT coefficients were available in each clock cycle, the signal power could be estimated also in each clock cycle and additional tuning procedure would not be necessary. The paper describes an implementation of the 32-point FFT algorithm into Altera^® FPGA providing all 32 complex DFT coefficients for the wavelet trigger.