Efficient Decimation And Interpolation

In some digital image processing systems, input images may be oversampled or only the low-pass content of the image will be retained due to some processing such as data compression. Therefore, input signals can be decimated to a lower sampling rate, processed at that low rate, and interpolated back to the same input rate or other desired rates. This approach allows performing the required processing on the size-reduced signals and may save significant computation time. In another application, decimation and interpolation are required to enlarge or reduce the size of the digital image to fit that of a display device. For high-ratio decimation and interpolation, the multistage approach is more computationally efficient than the one-stage approach. In this paper, the optimal multistage implementation of decimation and interpolation is derived for digital image processors of various arithmetic environments. The theoretically derived optimal multistage decomposition is then verified by comparing it against numerical results and is found to be valid for a wide range of decimation ratios.