The actual meaning of the modulation-transfer function (MTF) and the noise-power spectrum (NPS) is ambiguous in dual-energy images obtained from the single-shot sandwich detector, and their properties for various detector design parameters are also being questioned. In this study, the authors regard the sandwich detector including weighted logarithmic subtraction operation as a single black-box detector, and measure the single-shot dual-energy MTF and NPS performances. Subtraction of two images obtained from the sub-detector layers, which have different thick x-ray converters (hence, different spatial-resolution performances), of the sandwich detector yields a band-pass filter characteristic of the MTF. On the other hand, the NPS is the weighted sum of each NPS obtained from the sub-detector layers. The MTF characteristic is reflected into the DQE, hence the DQE shows a similar band-pass filter characteristics. Therefore, the sandwich detector may lose the contrast performance for large-area objects, but it may emphasize the contrast performance for objects with importance at mid-frequency information.