An Analysis of the Effect of Integral and Sigma Pulse Frequency Modulation on White Noise

Because Pulse Frequency Modulation (PFM) provides a high degree of immunity to noise, it is presently of interest in many modern communication and control systems. This paper presents a quantitative statistical analysis of PFM systems with a noise input (namely, white noise). Some concepts of the Impulse process and the first passage time problems of diffusion process are introduced, which are analogous to the noise transmission of PFM systems. The autocorrelation and spectral density functions are determined for the output of the PFM system with a white noise input. A comparison between the analytical and experimental results is presented.