In this chapter we explore signal processing, which is a subject with applications in diverse branches of science and engineering. A signal in this context can be a quantity that varies in time (temporal signal), or as a function of space coordinates (spatial signal). For example, an audio signal is a typical example of a temporal signal, while an image is a typical example of a spatial signal in two dimensions. In reality, signals are often continuous functions, but in computational applications it is common to work with discretized signals, where the original continuous signal is sampled at discrete points with uniform distances. The sampling theorem gives rigorous and quantitative conditions for when a continuous signal can be accurately represented by a discrete sequence of samples.