1. An image processing device comprising: a modulation clock generator configured to generate a modulation clock by modulating a frequency of a reference clock at a predetermined modulation cycle; a line synchronization signal generator configured to generate, on the basis of the modulation clock, a line synchronization signal whose line cycle varies from line to line; a line image sensor configured to sequentially read an image of one line of a document at a timing corresponding to the line synchronization signal and to output image data; and an image processor configured to process the image data on the basis of the modulation clock.