Nuclear spectroscopy is an interdisciplinary subject of physics and electronics, which adopts state-of-the-art digital electronic technology and computer technology to analyze the information in ionizing radiation. The use of FPGAs shortens the development cycles of the digital circuit design and reduces system noise with compact electronics size. As a result, digital spectrometers with FPGAs are gaining popularity in research and industrial markets. The motivation behind this work was to replace conventional analog electronics with modern digital technology to provide an excellent energy resolution for different kinds of nuclear detectors and experiments. In this thesis, a SiPM-based scintillation detector is first designed based on the basic principles of ionizing radiation. The readout circuit of the detector is given in detail. Subsequently, a real-time DPP module is designed using the FPGA of Lattice. The system noise of the DPP is measured, compared, and analyzed after the hardware verification and implementation of digital algorithms to assess the capability of the DPP module. Afterward, digital pulse processing algorithms are investigated in detail to improve the performance of the designed digital module. The design and implementation of multipass moving average and trapezoidal filter are presented. The PZC and BLR are designed and implemented according to the analysis of the trapezoidal filter’s weakness to have a better energy resolution of the digital system. Algorithms are designed and implemented on a Simulink platform. Experimental results and analyses are provided at the end of this thesis. The acquired data are analyzed in real-time or by offline software. Spectra and resolutions are demonstrated of different detectors to evaluate the performance of digital module and algorithms implementation. The resolution of the scintillation detector can be obtained to 4.2%, which is almost the optimal value based on their datasheet. The implementations of digital algorithms are verified. Other applications are provided, such as coincidence and cosmic muons measurements.