ESTIMATION OF 1 F NOISE

Several models have emerged for describing 1/f(gamma) noise processes. Based on these, various techniques for estimating the properties of s uch processes have been developed. This paper provides theoretical ana lysis of a new wavelet-based approach which has the advantages of havi ng low computational complexity and being able to handle the case wher e the 1/f(gamma) noise might be embedded in a further white-noise proc ess. However, the analysis conducted here shows that these advantages are balanced by the fact that the wavelet-based scheme is only consist ent for spectral exponents gamma in the range gamma is an element of ( 0, 1). This is in contradiction to the results suggested in previous e mpirical studies. When gamma is an element of (0, 1) this paper also e stablishes that wavelet-based maximum-likelihood methods are asymptoti cally Gaussian and efficient. Finally, the asymptotic rate of mean-squ are convergence of the parameter estimates Is established and is shown to slow as gamma approaches one. Combined with a survey of non-wavele t-based methods, these new results give a perspective on the various t radeoffs to be considered when modeling and estimating 1/f(gamma) nois e processes.