ABSTRACT
This chapter reviews the principal ideas of sampling theory, reconstruction, and antialiasing. Sampling theory is central to the study of sampled-data systems, e.g., digital image transformations. It lays a firm mathematical foundation for the analysis of sampled signals, offering invaluable insight into the problems and solutions of sampling. It does so by providing an elegant mathematical formulation describing the relationship between a continuous signal and its samples. We use it to resolve the problems of image reconstruction and aliasing. Reconstruction is an interpolation procedure applied to the sampled data. It permits us to evaluate the discrete signal at any desired position, not just the integer lattice upon which the sampled signal is given. This is useful when implementing geometric transformations, or warps, on the image. Aliasing refers to the presence of unreproducibly high frequencies in the image and the resulting artifacts that arise upon undersampling.
