Sharpening a texture involves a convolution kernel akin to a blur, it is one of the most expensive type of operations one can perform on 2D data. I would certainly not recommend that you render that in real time. If you really want to do it, Unreal has the spiral-blur shader that you could adapt to your needs, then an Unsharp Mask is computed as follows:
RGB - blur(RGB) + RGB
Using also the spiral blur example, you could also implement directly a sharpening kernel, a 2D sharpening convolution could use a kernel as follows: