Signals In The Noise

"One of the more momentous books of the decade." —The New York Times Book Review Nate Silver built an innovative system for predicting baseball performance, predicted the 2008 election within a hair’s breadth, and became a national sensation as a blogger—all by the time he was thirty. He solidified his standing as the nation's foremost political forecaster with his near perfect prediction of the 2012 election. Silver is the founder and editor in chief of the website FiveThirtyEight. Drawing on his own groundbreaking work, Silver examines the world of prediction, investigating how we can distinguish a true signal from a universe of noisy data. Most predictions fail, often at great cost to society, because most of us have a poor understanding of probability and uncertainty. Both experts and laypeople mistake more confident predictions for more accurate ones. But overconfidence is often the reason for failure. If our appreciation of uncertainty improves, our predictions can get better too. This is the “prediction paradox”: The more humility we have about our ability to make predictions, the more successful we can be in planning for the future. In keeping with his own aim to seek truth from data, Silver visits the most successful forecasters in a range of areas, from hurricanes to baseball to global pandemics, from the poker table to the stock market, from Capitol Hill to the NBA. He explains and evaluates how these forecasters think and what bonds they share. What lies behind their success? Are they good—or just lucky? What patterns have they unraveled? And are their forecasts really right? He explores unanticipated commonalities and exposes unexpected juxtapositions. And sometimes, it is not so much how good a prediction is in an absolute sense that matters but how good it is relative to the competition. In other cases, prediction is still a very rudimentary—and dangerous—science. Silver observes that the most accurate forecasters tend to have a superior command of probability, and they tend to be both humble and hardworking. They distinguish the predictable from the unpredictable, and they notice a thousand little details that lead them closer to the truth. Because of their appreciation of probability, they can distinguish the signal from the noise. With everything from the health of the global economy to our ability to fight terrorism dependent on the quality of our predictions, Nate Silver’s insights are an essential read.

Detection of Signals in Noise serves as an introduction to the principles and applications of the statistical theory of signal detection. The book discusses probability and random processes; narrowband signals, their complex representation, and their properties described with the aid of the Hilbert transform; and Gaussian-derived processes. The text also describes the application of hypothesis testing for the detection of signals and the fundamentals required for statistical detection of signals in noise. Problem exercises, references, and a supplementary bibliography are included after each chapter. Students taking a graduate course in signal detection theory.

Random signals and noise are present in many engineering systems and networks. Signal processing techniques allow engineers to distinguish between useful signals in audio, video or communication equipment, and interference, which disturbs the desired signal. With a strong mathematical grounding, this text provides a clear introduction to the fundamentals of stochastic processes and their practical applications to random signals and noise. With worked examples, problems, and detailed appendices, Introduction to Random Signals and Noise gives the reader the knowledge to design optimum systems for effectively coping with unwanted signals. Key features: Considers a wide range of signals and noise, including analogue, discrete-time and bandpass signals in both time and frequency domains. Analyses the basics of digital signal detection using matched filtering, signal space representation and correlation receiver. Examines optimal filtering methods and their consequences. Presents a detailed discussion of the topic of Poisson processes and shot noise. An excellent resource for professional engineers developing communication systems, semiconductor devices, and audio and video equipment, this book is also ideal for senior undergraduate and graduate students in Electronic and Electrical Engineering.

Understanding the nature of random signals and noise is critically important for detecting signals and for reducing and minimizing the effects of noise in applications such as communications and control systems. Outlining a variety of techniques and explaining when and how to use them, Random Signals and Noise: A Mathematical Introduction focuses on applications and practical problem solving rather than probability theory. A Firm Foundation Before launching into the particulars of random signals and noise, the author outlines the elements of probability that are used throughout the book and includes an appendix on the relevant aspects of linear algebra. He offers a careful treatment of Lagrange multipliers and the Fourier transform, as well as the basics of stochastic processes, estimation, matched filtering, the Wiener-Khinchin theorem and its applications, the Schottky and Nyquist formulas, and physical sources of noise. Practical Tools for Modern Problems Along with these traditional topics, the book includes a chapter devoted to spread spectrum techniques. It also demonstrates the use of MATLAB® for solving complicated problems in a short amount of time while still building a sound knowledge of the underlying principles. A self-contained primer for solving real problems, Random Signals and Noise presents a complete set of tools and offers guidance on their effective application.

Designed to follow an introductory text on psychoacoustics, this book takes readers through the mathematics of signal processing from its beginnings in the Fourier transform to advanced topics in modulation, dispersion relations, minimum phase systems, sampled data, and nonlinear distortion. While organised like an introductory engineering text on signals, the examples and exercises come from research on the perception of sound. A unique feature of this book is its consistent application of the Fourier transform, which unifies topics as diverse as cochlear filtering and digital recording. More than 250 exercises are included, many of them devoted to practical research in perception, while others explore surprising auditory illusions generated by special signals. Periodic signals, aperiodic signals, and noise -- along with their linear and nonlinear transformations -- are covered in detail. More advanced mathematical topics are treated in the appendices. A working knowledge of elementary calculus is the only prerequisite. Indispensable for researchers and advanced students in the psychology of auditory perception.

This textbook introduces methods of geoscientific data acquisition using MATLAB in combination with inexpensive data acquisition hardware such as sensors in smartphones, sensors that come with the LEGO MINDSTORMS set, webcams with stereo microphones, and affordable spectral and thermal cameras. The text includes 35 exercises in data acquisition, such as using a smartphone to acquire stereo images of rock specimens from which to calculate point clouds, using visible and near-infrared spectral cameras to classify the minerals in rocks, using thermal cameras to differentiate between different types of surface such as between soil and vegetation, localizing a sound source using travel time differences between pairs of microphones to localize a sound source, quantifying the total harmonic distortion and signal-to-noise ratio of acoustic and elastic signals, acquiring and streaming meteorological data using application programming interfaces, wireless networks, and internet of things platforms, determining the spatial resolution of ultrasonic and optical sensors, and detecting magnetic anomalies using a smartphone magnetometer mounted on a LEGO MINDSTORMS scanner. The book’s electronic supplementary material (available online through Springer Link) contains recipes that include all the MATLAB commands featured in the book, the example data, the LEGO construction plans, photos and videos of the measurement procedures.

This book contains a unified treatment of a class of problems of signal detection theory. This is the detection of signals in addi tive noise which is not required to have Gaussian probability den sity functions in its statistical description. For the most part the material developed here can be classified as belonging to the gen eral body of results of parametric theory. Thus the probability density functions of the observations are assumed to be known, at least to within a finite number of unknown parameters in a known functional form. Of course the focus is on noise which is not Gaussian; results for Gaussian noise in the problems treated here become special cases. The contents also form a bridge between the classical results of signal detection in Gaussian noise and those of nonparametric and robust signal detection, which are not con sidered in this book. Three canonical problems of signal detection in additive noise are covered here. These allow between them formulation of a range of specific detection problems arising in applications such as radar and sonar, binary signaling, and pattern recognition and classification. The simplest to state and perhaps the most widely studied of all is the problem of detecting a completely known deterministic signal in noise. Also considered here is the detection random non-deterministic signal in noise. Both of these situa of a tions may arise for observation processes of the low-pass type and also for processes of the band-pass type.