1. A method for enhancing the sharpness of a color image, comprising the steps of: generating three color separation signals Di (i=1, 2, 3) from a color image, wherein each of the color separation signals represents a different color component of the color image; selecting one of the color separation signals to be a sharp signal So; generating an unsharp signal Uo from the color image, wherein the unsharp signal represents the same color component of the color image as the color separation signal selected to be the sharp signal; subtracting the unsharp signal from the sharp signal to form a difference signal So-Uo; multiplying the difference signal by three multiplier coefficients k which are functions of the form k(Di, Do) to form three sharpness-enhancement signals k(Di, Do).multidot.(So-Uo), wherein Di is a corresponding one of the three color separation signals and Do is the color separation signal selected to be the sharp signal; and adding the sharpness-enhancement signals to the corresponding color separation signals to obtain shaprness-enhanced color separation signals representing a sharpness-enhanced color image.