Estimation of 1/f noise

Abstract

Several models have emerged for describing 1/f/sup /spl gamma// noise processes. Based on these, various techniques for estimating the properties of such processes have been developed. This paper provides theoretical analysis of a new wavelet-based approach which has the advantages of having low computational complexity and being able to handle the case where the 1/f/sup /spl gamma// noise might be embedded in a further white-noise process. However, the analysis conducted here shows that these advantages are balanced by the fact that the wavelet-based scheme is only consistent for spectral exponents /spl gamma/ in the range /spl gamma//spl isin/(0, 1). This is in contradiction to the results suggested in previous empirical studies. When /spl gamma//spl isin/(0, 1) this paper also establishes that wavelet-based maximum-likelihood methods are asymptotically Gaussian and efficient. Finally, the asymptotic rate of mean-square convergence of the parameter estimates is established and is shown to slow as /spl gamma/ approaches one. Combined with a survey of non-wavelet-based methods, these new results give a perspective on the various tradeoffs to be considered when modeling and estimating 1/f/sup /spl gamma// noise processes.