Modeling negative power law noise

This paper discusses the theory behind the generation of practical but rigorous models for integer negative power law (neg-p) noise in both the frequency and time domains. It is shown that both wide-sense stationary (WSS) and non-stationary (NS) representations or pictures are useful in modeling neg-p noise processes and that these pictures are not in conflict, because different assumptions are used for each picture. The WSS picture, where neg-p noise processes can be characterized in the f-domain by a single-frequency PSD L_p(f) prop f^p with p<0 (and which gives neg-p noise its name), is shown to be necessarily divergent in the t-domain. On the other hand, the NS picture, where such neg-p processes cannot be characterized in the f-domain by a single-frequency PSD, is shown to be generally, but not always, convergent in the t- domain. It is then shown that such divergence problems can be resolved by defining each neg-p process as the limit of a related non-divergent sister process and, further, that these sister processes are also useful in generating practical f and t simulation models for neg-p noise. The paper then discusses the practical modeling of flicker of phase (p=-1) and random walk of phase (p=-2) noise in both the f and t domains through the use of Wiener filtered white noise processes. Finally, the paper discussed how models for any integer neg-p can be generated by concatenating these flicker and random walk models.