Next-generation DIRC detectors, like the PANDA Barrel DIRC, with improved optical designs and better spatial and timing resolution, require correspondingly advanced reconstruction and PID methods. The investigation of the PID performance of two DIRC counters and the evaluation of the reconstruction and PID algorithms form the core of this thesis. Several reconstruction and PID approaches were developed, optimized, and tested using hadronic beam particles, experimental physics events, and Geant simulations. The near-final design of the PANDA Barrel DIRC was evaluated with a prototype in the T9 beamline at CERN in 2018. The analysis finds excellent agreement between the experimental data and the Geant simulations for all reconstruction algorithms. The best PID performance of up to $5.2 \pm 0.2$ s.d. $\pi$/K separation at 3.5 GeV/c, was obtained with a time imaging PID method. The PANDA Barrel DIRC simulation, as well as the reconstruction and PID algorithms, were evaluated using experimental data from the GlueX DIRC as part of the FAIR Phase-0 program. The performance validation was carried out using physics events of the GlueX experiment and simulations. The initial analysis results of the commissioning dataset show a $\pi$/K separation power of up to 3 s.d. at a momentum of 3.0-3.5 GeV/c, obtained using a geometric reconstruction algorithm.

In recent decades, the quantum field theory of strong interaction (QCD) has been impressively demonstrated in the area of high energies and momentum transfers. Nowadays, novel experiments allow for challenging the methods for the calculation of QCD also in the non-perturbative regime by the continuous improvement of measurement accuracy. PANDA at the upcoming FAIR accelerator facility is one of such experiments. At PANDA, antiprotons with momenta of up to15 GeV/c will be annihilated at a fixed proton target under high luminosities. Among a variety of detector systems, PANDA stands out with its lead tungstate electromagnetic calorimeter (EMC), which is designed to have a wide dynamic range (10 MeVto14.6 GeV) and a relative energy resolution of better than 2.5 % at 1 GeV. The development of the backward part of the PANDA EMC is the first scientific goal of this thesis. Since the development of the backward EMC has progressed so far, it is foreseen for an experiment within the FAIRPhase-0 research programme. It is proposed to measure the double-virtual electromagnetic transition form factor (TFF) of the pion in the Primakoff π0 electroproduction at the Mainz Microtron facility (MAMI). The pion TFF is related via the hadronic light-by-light scattering to the g_μ−2 puzzle. Consequently, the second scientific goal of this thesis are preparatory studies for FAIR Phase-0. The developments of this work resulted in a fully functional prototype calorimeter, which operated stably in numerous tests at MAMI. However, the focus of this work is digital signal processing (DSP) for the PANDA EMC. A specially developed software framework allowed for testing and optimising signal filtering algorithms and parameter extraction methods on realistically simulated signals. Thus, the algorithms are well-adapted to the time structure of the ̄PANDA calorimeter preamplifier (APFEL) signals. Furthermore, the DSP methods were implemented on the Field Programmable Gate Arrays (FPGAs) of the PANDA digitisation board. The developed FPGA firmware provides a self-triggering readout for all calorimeter channels, an efficient implementation of a high order filter with a finite impulse response (FIR), noise hit suppression and pileup handling.Together with the calorimeter prototype, the digital signal processing was tested at MAMI. Thanks to the use of the DSP methods, an energy detection threshold (single-crystal) of less than 2.5 MeV was achieved. This allowed for a measured relative energy resolution of 2.190(2) % at 1 GeV. Moreover, the non-linearity of the calorimeter is in the order of a few per mill. Due to the self-triggering concept of the FPGA firmware,measurements under high detector rates were possible. Thus, a dead time of 464(13) ns and a pileup probability of 4.53(12) % at 100 kHz was determined. For the measurement of the pion TFF, a high flux of low energy electrons and photons is expected. Thus, test beams with the prototype were performed to determine the impact of the low energetic background on the measurement. By utilising both experiment data and simulations, an upper limit for the relative energy resolution (2.75(4) % to 6.57(2) % at 1 GeV) as a function of the luminosity (2.77μb−1/s to 55.34μb−1/s) was found. The study allows an estimation of the FAIR Phase-0 measuring time.