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The relation between instantaneous frequencies and Fourier components of a time-dependent signal is examined. Examples are given in which large excursions of the instantaneous frequency do not correspond to any Fourier components, and in which Fourier components are not manifest in the instantaneous frequencies. It is shown that, while the appropriately weighted first moments of the component frequency and the instantaneous frequency coincide, the same is not true of the higher moments. There is no one-to-one relationship between the two frequencies which correspond to different measurements. These considerations may be important in the study of resonant interactions between atoms and electromagnetic fields.
L Mandel (Tue,) studied this question.