Angle-Modulation Power Spectra

Exact expressions are obtained for the autocorrelation function of a sinusoidal carrier phase- or frequency-modulated by Butterworth-filtered white Gaussian noise. The corresponding power spectra are obtained numerically, together with bounds on the error resulting from truncation of the Fourier integrals. The spectra are relatively inaccurate in the tail regions, where other methods of calculation are more appropriate. The results are compared with estimates based on Woodward's approximation, and it is concluded that, while the latter are valuable for frequency modulation under a wide range of conditions, their usefulness for phase modulation is limited to wide-deviation modulation by high-order spectra.