Investigation of the Power Spectrum Produced by the Linear Mixing of Frequency Modulated Signals

摘要

A generalized approach to the spectrum analysis of randomly frequency modulated signals is presented and indicates the need for approximate methods and knowledge of their expected accuracy. Sufficient conditions are established for the applicability of Woodward's (adiabatic) Theorem for large modulation index fm spectra and an upper bound is given for the spectral error committed in using the approximation for sinusoidal and/or Gaussian random modulation. The approximate spectra are compared with computed spectra for ideallow pass, ideal band pass and sinusoidal plus idela band pass Gaussian modulation. The computer programs employed are described. Also given is a development of an approximate expression for the spectra of a sinusoid with random phase switching which is compared to results obtained by making some simplifying assumptions and employing an equation given in Lawson and Uhlenbeck, M.I.T. Radiation Laboratories Series, Vol. 24, pg. 45. (Author)