Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0905.94009
Ninness, Brett
Estimation of $1/f$ noise. (English)
[J] IEEE Trans. Inf. Theory 44, No.1, 32-46 (1998). ISSN 0018-9448

Summary: Several models have emerged for describing $1/f^\gamma$ 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 $1/f^\gamma$ 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 $\gamma$ in the range $\gamma\in (0,1)$. This is in contradiction to the results suggested in previous empirical studies. When $\gamma\in (0,1)$ 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 $\gamma$ 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 $1/f^\gamma$ noise processes.

MSC 2000:: *94A12 Signal theory
93E10 Estimation and detection in stochastic control
42C15 Series and expansions in general function systems
62M05 Markov processes: estimation

Keywords: Brownian motion; maximum-likelihood estimation; wavelet; noise; noise processes

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]