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We report the design and the performance of the engineering model of the digital signal processing system called the Pulse Shape Processor (PSP) for the Soft X-ray Spectrometer (SXS) onboard the ASTRO-H satellite. The SXS employs an X-ray microcalorimeter system, in which X-ray photons are detected as a heat pulse due to photoelectric absorption. The pixelized HgTe absorbers are cooled down to 50 mK. The required energy resolution is 7 eV (FWHM) at 6 keV. Since the data link to the satellite data recorder is limited to 200 kbit s-1, the onboard digital processor PSP plays a critical role in achieving the required resolution. The PSP is also the rate-limiting factor for other performance of the SXS, such as maximum count rate and energy range. In this paper, we show the design of the PSP, and show the performance based on a series of laboratory tests performed with the engineering models of the detector and the analog readout electronics. We found that (1) the PSP can register energy in the 0.07-18 keV band [energy range], (2) the energy resolution of the engineering model system, including the detector, analog electronics, and the PSP, is 4.8-5.7 eV at 5.9 keV [energy resolution], and (3) the PSP has sufficient processing power to handle a point-like source fainter than 0.3 Crab [maximum count rate]. These results are expected to be quite similar to those with the flight model, thus the results will be useful for the observation planning using the SXS.