Duffing's equation describes the dynamic behavior of a mildly compressive (soft-clipping) second-order system. It is applicable to a wide variety of practical devices such as, for example, power amplifiers, limiters, transducers, magnetic tape, and photographic film, as well as certain perceptual mechanisms in hearing and vision. The complex modulation transfer function is a means to define a frequency response for such systems at a certain level of compression. In photography, it predicts the resolution at a given contrast.
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