A Wiener–Wintner theorem for 1/ f power spectra

Wiener's generalized harmonic analysis (GHA) provides a theory of harmonic analysis for subspaces of tempered functions not accessible to the L 1, L 2, and Fourier series theories; and it does it in a way that is usually more quantitative than that provided by the theory of distributions. On th...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical analysis and applications 2003-03, Vol.279 (2), p.740-755
Main Authors: Benedetto, John J., Scott, Sherry E., Kerby, Rodney
Format: Article
Language:English
Subjects:
1/ f noise
Algebra
Autocorrelation
Exact sciences and technology
Fractional Brownian motion
Mathematics
Number theory
Power spectra
Sciences and techniques of general use
Wiener's generalized harmonic analysis
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Wiener's generalized harmonic analysis (GHA) provides a theory of harmonic analysis for subspaces of tempered functions not accessible to the L 1, L 2, and Fourier series theories; and it does it in a way that is usually more quantitative than that provided by the theory of distributions. On the other hand, GHA does not yield an adequate spectral analysis of large classes of functions, including nonstationary processes and, in particular, 1/ f noise. In this paper we adapt GHA to deal with 1/ f noise by extending the Wiener–Wintner theorem to the case of 1/ f power spectra.
ISSN:0022-247X
1096-0813
DOI:10.1016/S0022-247X(03)00070-2