The Spectral Density of a Sinusoid Phase Modulated by a Gaussian-Filtered Gaussian Process

A simple calculation is made for the power spectral density (psd) of a sinusoid phase modulated by a filtered Gaussian process. The premodulation filter has a Gaussian-shaped frequency response. Design curves are presented for the out-of-band interference, the in-band power, and the psd in terms of the premodulation filter's bandwidth and the rms modulation index.