Signals are mathematical functions that describe the variation of a quantity across time or space. Time-dependent signals are often called time series. Examples of time series include share prices, which are typically presented as successive points in time spaced at uniform time intervals. In physics or biology, experimental devices record the evolution of variables such as electromagnetic waves or biological processes.

In signal processing, a general objective consists of extracting meaningful and relevant information from raw, noisy measurements. Signal processing topics include signal acquisition, transformation, compression, filtering, and feature extraction, among others. When dealing with a complex dataset, it can be beneficial to clean it before applying more advanced mathematical analysis methods (such as machine learning, for instance).

In this concise chapter, we will illustrate and explain the main foundations of signal processing. In the next chapter, Chapter 11, Image...