Power spectrum of a phase-modulated wave by a Gaussian noise. I - An approximation of spectrum in the case of small phase deviation

This paper derives the calculation formula for the power spectrum of a wave phase-modulated by a band-limited Gaussian signal by using the expansion of the convolution terms of the baseband spectrum. The power spectrum is calculated by using the finite series approximation, and the calculation error of the power spectrum is also calculated. In order to clarify the applicable area of this calculation formula, this paper investigates the calculation error characteristic, which depends on some parameters, such as the effective phase deviation, term number of approximation, baseband spectrum shape, and frequency distance from center frequency. This paper also investigates the application of this calculation formula to the power spectrum of frequency-modulaed wave.