Pontrjagin duality and digital signal processing

摘要

All of the Fourier transforms encountered in signal processing can be regarded as instances of a single universal object-the Fourier transform associated with an abstract abelian group. We show how this way of looking at things leads to a natural and simple account of the similarities between the properties of the Fourier transforms associated with different types of signal and how it sheds a new light on the duality between sampling and aliasing.