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The work describes a novel approach to the design of a fast, multichannel measurement system for plasma diagnostics [A. Wojenski et al., Fusion Eng. Des. 123, 727 (2016)]. Its main scope is to provide measurements of soft X-ray (SXR) emission during plasma phenomena at the W-Environment in Steady-state Tokamak (WEST), especially for monitoring and tracing tungsten impurities. This paper describes the vertical Gas Electron Multiplier (GEM) camera installed at the WEST [M. Chernyshova et al., J. Instrument. 10, P10022 (2015)]. The designed GEM detector readout board has more than 100 channels, resulting in high-performance requirements for the data acquisition and processing system. The novel system construction approach is that the unit works on the raw signals providing a high quality of the data, especially in the scope of pileup effect analysis. In the case of doubtful results, the source data can be easily reviewed offline. The data selection and transmission are done in Field-Programmable Gate Arrays (FPGAs) on the custom boards with the custom Peripheral Component Interconnect (PCI)-Express Gen2 switch that allows us to register signals from multiple FPGAs and then process the data by complex algorithms [G. Kasprowicz et al., J. Fusion Energy 38, 480 (2019)]. The firmware is replaceable and different working modes can be applied (some under verification): global trigger mode, high-speed data serialization, and extended signal registration. Low level optimized central processing unit software for data readout was also designed [P. Linczuk et al., J. Instrum. 14, C05001 (2019)]. The installation of the system is described due to complex system components' distribution. The first results of the successful acquisition of the plasma at the WEST are discussed. The corresponding SXR energy and topology spectra were computed. Those are the first technical measurements of the system to ensure verification of data quality. [ABSTRACT FROM AUTHOR]