The Spectrum of a High-Index FM Waveform: Woodward´s Theorem Revisited

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.