Polyphase analysis of aliasing effects in enlargements

Typical image processing applications use linear interpolation or piecewise cubic interpolation for resampling of images. However, since the frequency domain characteristics of the interpolation filters are not good, two effects usually appear and cause a noticeable degradation in 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. Enlargement of an image by a rational factor of (L/M) is represented by first interpolating the image on a grid L times finer than the original sampling grid, and then resampling it every M grid points. While the usual treatment of the aliasing is carried out by analyzing the interpolation filter in the frequency domain, this paper suggests analyzing the aliasing effects using a polyphase representation of the interpolation process. It turns out that the aliasing effects are caused by differences between the polyphase filters. We therefore define the average amplitude function and use it to measure the aliasing expected from the interpolation filter.