Quadratic-filter theory is appropriate whenever a system to be studied includes an energy-flux measurement, or has available as the input signal only a second moment of the observed process, a class of problems in which optical systems include perhaps the most important examples.
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A more precise development of Eq. (16) is available in Ref. 11.
G is not bilinear in (u,v). The terminology "dilinear" is introduced to represent the specific two-variable extension of a single variable function that allows the quadratically nonlinear filter of this discussion to be analyzed and synthesized by linear-transfer-function techniques.
The linearity of Eq. (20) is not dependent on the infinite-limit assumption.
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