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We propose an overall procedure for measuring and unfolding fast neutron spectra using a trans-stilbene scintillation detector. Detector characterization was described, including the information on energy calibration, detector resolution, and nonproportionality response. The digital charge comparison method was used for the investigation of neutron-gamma Pulse Shape Discrimination (PSD). A pair of values of 600 ns pulse width and 24 ns delay time was found as the optimized conditions for PSD. A fitting technique was introduced to increase the trans-stilbene Proton Response Function (PRF) by 28% based on comparison of the simulated and experimental electron-equivalent distributions by the Cf-252 source. The detector response matrix was constructed by Monte-Carlo simulation and the spectrum unfolding was implemented using the iterative Bayesian method. The unfolding of simulated and measured spectra of Cf-252 and AmBe neutron sources indicates reliable, stable and no-bias results. The unfolding technique was also validated by the measured cosmic-ray induced neutron flux. Our approach is promising for fast neutron detection and spectroscopy.