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Image processing device, display device, and image processing method

An image processing device is capable of inhibiting the moire and the false color from occurring in the case of performing color display using four colors of sub-pixels. The image processing device has filter processing sections. The filter processing sections limit frequency bands of signals R, G, B, and W in an X direction and a Y direction in accordance with a positional relationship between the sub-pixels corresponding to each of the colors and the other sub-pixels. Further, the filter processing sections control a frequency response of image signals of the respective colors in accordance with an amplitude of a high frequency component of the image signal corresponding to each of the other colors.