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Linear systems theory is used for the numerical assessment of the detective quantum efficiency (DQE) of the hybrid semiconductor pixel detector DIXI. The Monte Carlo based code GEANT is used to simulate the photon transport in the sensor, charge transport modeling is treated analytically and the readout chip is simulated using PSPICE. The DQE for two differently shaped X-ray spectra of the same quality and for different operational conditions of the readout chip regarding the discrimination level are computed in order to validate the model. The model described in this paper can be adopted for optimizing the detector.