Woodward's theorem asserts that the spectrum of a high-index frequency-modulated (FM) waveform is approximately the probability distribution of its instantaneous frequency, i.e., the univariate distribution of the modulating wave shifted by the carrier frequency. A new proof is presented which for the first time includes an upper bound on the error of this approximation and thus shows under what circumstances it is reliable.
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Blachman et al. (1969) studied this question.