ABSTRACT
This chapter summarizes sampling and reconstruction using the concrete one-dimensional example of digital audio. It aims to present the basic mathematics and algorithms that underlie sampling and reconstruction in one and two dimensions. The digital audio recording chain can serve as a concrete model for the sampling and reconstruction processes that happen in graphics. The same kind of under-sampling and reconstruction artifacts also happens with images or other sampled signals in graphics, and the solution is the same: filtering before sampling and filtering again during reconstruction. There is a deeper mathematical theory of sampling with a history reaching back to the first uses of sampled representations in telecommunications. Sampling theory answers many questions that are difficult to answer with reasoning based strictly on scale arguments. Following the frequency domain analysis to its logical conclusion, a filter that is exactly a box in the frequency domain is ideal for both sampling and reconstruction.
