The problem of making an envelope representation of the fluctuating classical wave amplitude of a stationary optical field is investigated. The condition that the envelope function fluctuates as slowly as possible, in a least-squares sense, is shown to lead naturally to the complex analytic signal representation first introduced by Gabor. Besides being in correspondence with the quantum-mechanical description of the optical field, this representation is the only one in accord with intuitive notions about the envelope of a random process.
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