Binary decisions guide our everyday lives in situations both critical and trivial. The choices made by politicians and physicians may have consequential implications on a global or individual scale. Perhaps less consequential is whether or not we choose to carry an umbrella on a cloudy day. Any choice made inherently involves a conscious, subconscious, or formal tradeoff between benefits and detriments.This monograph develops and presents a framework for binary hypothesis testing as it applies to both the classical and quantum mechanical environments. The authors set the scene by first describing separately the operating characteristics associated with classical binary hypothesis testing and those within quantum mechanics. They proceed to describe in detail in subsequent chapters how quantum measurements that employ redundant, or overcomplete, representations of the state of the system being measured can be used.Written in a tutorial style, readers from both classical and quantum backgrounds will find this an enlightening treatise on the topic. Examples and problems are used throughout to enable the reader to readily grasp the new concepts and to further their own understanding. This monograph is a comprehensive and accessible overview of a complex problem for students and researchers in signal processing.

A collection of articles originally intended for use in a graduate course. This collection of papers is the result of a desire to make available reprints of articles on digital signal processing for use in a graduate course offered at MIT. The primary objective was to present reprints in an easily accessible form. At the same time, it appeared that this collection might be useful for a wider audience, and consequently it was decided to reproduce the articles (originally published between 1965 and 1969) in book form. The literature in this area is extensive, as evidenced by the bibliography included at the end of this collection. The articles were selected and the introduction prepared by the editor in collaboration with Bernard Gold and Charles M. Rader. The collection of articles divides roughly into four major categories: z-transform theory and digital filter design, the effects of finite word length, the fast Fourier transform and spectral analysis, and hardware considerations in the implementation of digital filters.