Discrete simulation of power law noise

Power law noise plays an important role in the description of high performance oscillators. Commonly, five types of noise are considered to affect clocks and clock measurements: white phase, flicker phase, white frequency, flicker frequency and random walk frequency. These noise types are distinguished by the slopes of their spectral densities, S_y(f) ∝ f^α (on a log-log scale). The noise is inherent both to the oscillators and to the measurement systems and defines the limits of stability of the clocks. Accurate simulation of the noise can be important for testing the measurement system and the characterization software. This paper presents a new algorithm and computer code for simulating power law noises with arbitrary α (it is not restricted to the integer values mentioned above). The general theory of noise simulation is investigated to determine the criteria for evaluating and deriving simulation methods. Past techniques are evaluated and the new method is shown to provide improvements, particularly because it results in non-stationary noise sequences that are also scale-invariant and causal and have the proper autospectral densities and Allan variances.