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.

$\overline{\text{P}}$ANDA is a new experiment in hadron physics at the upcoming FAIR facility in Darmstadt, Germany. The combination of $\overline{\text{P}}$ANDA and the antiproton beam, provided by the antiproton storage ring HESR, yields high production rates of strange hyperon-antihyperon pairs. This enables multiple experiments in strangeness nuclear physics which allow to study the interaction of hyperons and antihyperons within nuclear matter. This is essential to understand the composition of neutron star matter and solve the ``hyperon puzzle''. The modularity of $\overline{\text{P}}$ANDA allows to design and integrate a dedicated setup for the high resolution X-ray and $\gamma$ spectroscopy of heavy $\Xi^-$ hyperatoms and double $\Lambda$ hypernuclei. The germanium detector array PANGEA (PANda GErmanium Array) is mandatory for these experiments. Its optimization and integration into the $\overline{\text{P}}$ANDA target spectrometer is discussed in this thesis. During the experiments at $\overline{\text{P}}$ANDA, the HPGe (High Purity Germanium) crystals of PANGEA will suffer from inevitable hadronic background. %during the experiments. Especially fast neutrons will damage the lattice structure of the crystal and deteriorate its resolution. This effect has been experimentally studied in irradiation tests at the COSY accelerator in J\"ulich, Germany, with up to \SI{5.6e9}{neutrons\per\centi\meter\squared}. A large fraction of the performance loss of the detector could be corrected by analyzing the pulse shape of the detector response. The initial crystal performance could be restored by annealing of the crystal in the laboratory after the irradiation. The effects of the irradiation had to be kept in mind when the feasibility of the hyperatom experiment was studied. $\overline{\text{P}}$ANDA is unique in its ability to study the $\Xi^-$ nucleon interaction in the neutron-rich periphery of $\Xi^-$-\ce{^{208}Pb} hyperatoms. Full simulations of the experiment show that multiple experimental observables will allow to measure the real and imaginary part of the $\Xi^-$ optical potential with a precision of \SI{\pm 1}{\mega\eV}.