Digital Signal Processing with Kernel Methods

1 From Signal Processing to Machine Learning

Signal processing is a field at the intersection of systems engineering, electrical engineering, and applied mathematics. The field analyzes both analog and digitized signals that represent physical quantities. Signals include sound, electromagnetic radiation, images and videos, electrical signals acquired by a diversity of sensors, or waveforms generated by biological, control, or telecommunication systems, just to name a few. It is, nevertheless, the subject of this book to focus on digital signal processing (DSP), which deals with the analysis of digitized and discrete sampled signals. The word “digital” derives from the Latin word digitus for “finger,” hence indicating everything ultimately related to a representation as integer countable numbers. DSP technologies are today pervasive in many fields of science and engineering, including communications, control, computing and economics, biology, or instrumentation. After all, signals are everywhere and can be processed in many ways: filtering, coding, estimation, detection, recognition, synthesis, or transmission, are some of the main tasks in DSP.

In the following sections we review the main landmarks of signal processing in the 20th century from the perspective of algorithmic developments. We will also pay attention to the cross‐fertilization with the field of statistical (machine) learning in the last decades. In the 21st century, model and data assumptions as well as ...