We propose a new class of kernels to simplify the design of filters for image interpolation and resizing. Their properties are defined according to two parameters, specifying the width of the transition band and the height of a unique sidelobe. By varying these parameters it is possible to efficiently explore the space with only the filters that are suitable for image interpolation and resizing, and identify the filter that is best for a given application. These two parameters are also sufficient to obtain very good approximations of many commonly-used interpolation kernels. We also show that, because the Fourier transforms of these kernels have very fast decay, these filters produce better results when time-stretched for image downsizing.