We have modeled the signal and noise propagation in a pixelated scintillator detector by using the cascaded linear-systems transfer theory. The main difference from the conventional homogeneous scintillator detector is the additional x-ray quantum sampling process at the beginning stage of the cascaded model. The additional sampling stage is expressed as a multiplication of the fill factor of the pixelated scintillator both in signal and noise. The numerical simulation shows that, while the detective quantum efficiency (DQE) degrades in the low spatial-frequency band due to the x-ray quantum sampling, the DQE maintains high values in the high-frequency band, which is due to the band-limited modulation-transfer function (MTF) property of the pixelated scintillator. The pixelated scintillator design is relatively insensitive to additive electronic noise in the DQE performance compared to the conventional design. As a potential solution to overcome the reduction of DQE in the low-frequency band with the pixelated scintillator design, we propose a partially pixelated scintillator design, which utilizes the concept of pre-filtering before the sampling process of the incident x-ray quanta.