Confidence Estimates in Simulation of Phase Noise or Spectral Density

In this paper, we apply the method of discrete simulation of power-law noise, developed by Timmer and König, Ashby, and Ashby and Patla, to the problem of simulating phase noise for a combination of power-law noises. We derive analytic expressions for the probability of observing a value of phase noise <inline-formula> <tex-math notation="LaTeX">$ {\mathcal{ L}}(f)$ </tex-math></inline-formula> or of any of the one-sided spectral densities <inline-formula> <tex-math notation="LaTeX">$S_{\phi }(f), S_{y}(f)$ </tex-math></inline-formula>, or <inline-formula> <tex-math notation="LaTeX">$S_{x}(f)$ </tex-math></inline-formula>, for arbitrary superpositions of power-law noise.