Asymptotic aliasing index of interpolation filters [image scaling applications]

Scaling images by interpolation is a common operation in image processing. The interpolation kernels used are sampled versions of continuous time signals. Since those are not bandlimited, we have aliasing effects. Those aliasing effects result from the sampling of the continuous time kernels. Two effects usually appear and cause a noticeable degradation in the quality of the image. The first is jagged edges and the second is low frequency modulation of high frequency components such as the sampling noise. Both effects result from aliasing. We use a polyphase analysis of interpolation to explain the aliasing effects and define the normalize aliasing index for measuring the aliasing expected from an interpolation filter. That index is defined for a grid that is L times finer than the original image grid. In this paper we find the normalized aliasing index for an infinitesimally fine grid, i.e., when L goes to infinity.