The ubiquitous matched filter: A tutorial and application to radar detection

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In 1946, David Middleton, along with his PhD advisor J.H. Van Vleck (later to be awarded the Nobel prize), published the paper “A Theoretical Comparison of the Visual, Aural, and Meter Reception of Pulsed Signals in the Presence of Noise” in the Journal of Applied Physics [23]. This paper evolved from earlier work of Middleton in 1943. In it, a new type of device was derived and analyzed. It was to be called the matched filter. It allowed filter designers a straightforward method for detecting the presence of a signal that was obscured by additive noise. Coming at a time when radar was being developed and its important role in World War II recognized, the matched filter was to have a lasting impact on humanity. Although principally motivated by the radar application, it has found widespread use in commercial and military applications. From locating blood vessels from retinal images [11], to monitoring water pollution [1], to the design of cell phones [7], this once “military” concept has proven to be a fundamental tool in modern signal processing. A recent Google search produced more than 568,000 hits in response to the input “matched filter”, with application fields that are widely diverse.

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Classical, Semi-Classical and Quantum Noise