Signal Processing

Signal processing is the mathematical and engineering discipline concerned with the representation, transformation, and manipulation of signals — time-varying quantities that carry information. A signal may be acoustic, electrical, optical, or abstract; the discipline's core insight is that signals from radically different physical substrates obey the same mathematical laws when analyzed in the frequency domain. Norbert Wiener's wartime work on anti-aircraft fire control produced foundational results in statistical signal processing, including the Wiener filter — an optimal linear filter for extracting a signal from noise given statistical knowledge of both. The Wiener filter is mathematically equivalent to Bayesian inference under Gaussian assumptions, a connection that reveals signal processing as a special case of probabilistic inference rather than a separate discipline. Claude Shannon's information theory and Wiener's signal processing were developed in parallel and cross-pollinated extensively; both can be understood as applications of the insight that noise and information are statistical concepts, not physical ones — a distinction that had implications far beyond engineering, reaching into epistemology and the theory of perception.