This book is written with the intention of giving a pragmatic reference on statistical signal processing (SSP) to graduate/PhD students and engineers whose primary interest is in mixed theory and applications. It covers both traditional and more advanced SSP topics, including a brief review of algebra, signal theory, and random processes. The aim is to provide a high‐level, yet easily accessible, treatment of SSP fundamental theory with some selected applications.

The book is a non‐axiomatic introduction to statistical processing of signals, while still having all the rigor of SSP books. The non‐axiomatic approach is purposely chosen to capture the interest of a broad audience that would otherwise be afraid to approach an axiomatic textbook due to the perceived inadequacy of their background. The intention is to stimulate the interest of readers by starting from applications from daily life, and from my personal and professional experience, I aim to demonstrate that book theory (still rigorous) is an essential tool for solving many problems. The treatment offers a unique approach to SSP: applications (somewhat simplified, but still realistic) and examples are interdisciplinary with the aim to foster interest toward the theory. The writing style is layered in order to capture the interest of different readers, offering a quick solution for field‐engineers, detailed treatments to challenge the analytical skills of students, and insights for colleagues. Re‐reading the same pages, one can discover more, and have a feeling of growth through seeing something not seen before.

Why a book for engineers? Engineers are pragmatic, are requested to solve problems, and use signals to “infer the world” in a way that can then be compared with the actual ground‐truth. They need to quickly and reliably solve problems, and are accountable for the responsibility they take. Engineers have the attitude of looking for/finding quick‐and‐dirty solutions to problems, but they also need to have the skills to go deeper if necessary. Engineering students are mostly trained in this way, at graduate level up to PhD. To attract graduate/PhD engineering students, and ultimately engineers, to read another new technical book, it should contain some recipes based on solid theory, and it should convince them that the ideas therein help them to do better what they are already doing. This is a strong motivation to deal with a new theory. After delineating the solution, engineering readers can go deeper into the theory up to a level necessary to spot exceptions, limits, malfunctioning, etc. of the current solution and find that doing much better is possible, but perhaps expensive. They can then consciously make cost‐benefit tradeoffs, as in the nature of engineering jobs.

Even if this book is for engineers and engineering students, all scientists can benefit from having the flavor of practical applications where SSP offers powerful problem‐solving tools. The pedagogical structure for school/teachers aims to give a practical vision without losing the rigorous approach. The book is primarily for ICT engineers, these being the most conventional SSP readers, but also for mechanical, remote sensing, civil, environmental, and energy engineers. The focus is to be just deep enough in theory, and to provide the background to enable the reader to pursue books with an axiomatic approach to go deeper on theory exceptions, if necessary, or to read more on applications that are surely fascinating for their exceptions, methods, and even phenomenalism.

Typical readers will be graduate and PhD students in engineering schools at large, or in applied science (physics, geophysics, astronomy), preferably with a basic background in algebra, random processes, and signal analysis. SSP practitioners are heavily involved in software development as this is the tool to achieve solutions to many of the problems. The book contains some exercises in the form of application examples with Matlab kernel‐code that can be easily adapted to solve broader problems.

I have no presumption to get all SSP knowledge into one book; rather, my focus is to give the flavor that SSP theory offers powerful tools to solve problems over broad applications, to stimulate the curiosity of readers at large, and to give guidelines on moving in depth into the SSP discipline when necessary. The book aims to stimulate the interest of readers who already have some basics to move into SSP practice. Every chapter collects into a few pages a specific professionalism, it scratches the surface of the problem and triggers the curiosity of the reader to go deeper through the essential bibliographical references provided therein. Of course, in 2017 (the time I am writing these notes), there is such easy accessibility to a broad literature, software, lecture notes about the literature, and web that my indexing to the bibliographical references would be partial and insufficient anyway. The book aims to give the reader enough critical tools to choose what is best for her/his interest among what is available.

In my professional life I have always been in the middle between applications and theory, and I have had to follow the steps illustrated in the enclosed block diagram. When facing a problem, it is important to interact with the engineers/scientists who have the deepest knowledge of the application problem itself, its approximations and bounds (stage‐A). They are necessary to help to set these limits into a mathematical/statistical framework. At the start, it is preferable if one adopts the jargon of the application in order to find a good match with application people, not only for establishing (useful) personal relations, but also in order to understand the application‐related literature. Once the boundary conditions of the problem have been framed (stage‐A), one has to re‐frame the problem into the SSP discipline. In this second stage (B), one can access the most advanced methods in algebra, statistics, and optimization. The boundary between problem definition and its solution (stage‐C) is much less clearly defined than one might imagine. Except for some simple and common situations (but this happens very rarely, unfortunately!), the process is iterative with refinements, introduction of new theory‐tools, or adaptations of tools developed elsewhere. No question, this stage needs experience on moving between application and theory, but it is the most stimulating one where one is continuously learning from application ‐ experts (stage‐A). Once the algorithm has been developed, it can be transferred back to the application (stage‐D), and this is the concluding interaction with the application‐related people. Tuning and refinement are part of the deal, and adaptation to some of the application jargon is of great help at this stage. Sometimes, in the end, the SSP‐practitioner is seen as part of the application team with solid theory competences and, after many different applications, one has the impression that the SSP‐practitioner knows a little of everything (but this is part of the professional experience). I hope many readers will be lured into this fascinating and diverse problem‐solving loop, spanning multiple and various applications, as I have been myself. The book touches all these fields, and it contains some advice, practical rules, and warnings that stem from my personal experience. My greatest hope is to be of help to readers’ professional lives.

P.S. My teaching experience led to the style of the book, and I made an effort to highlight the intuition in each page and avoid too complex a notation; the price is sometimes an awkward notation. For instance, the use of asymptotic notation that is common in many parts is replaced by “” meaning any convenient limit indicated in the text. Errors and typos are part of the unavoidable noise in the text that all SSPers have to live with! I did my best to keep this noise as small as possible, but surely I failed somewhere.