Fractal estimation from noisy data via discrete fractional Gaussian noise (DFGN) and the Haar basis

Author

Kaplan, Lance M. ; Kuo, C-C Jay

Author_Institution

Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA

Volume

41

Issue

12

fYear

1993

fDate

12/1/1993 12:00:00 AM

Firstpage

3554

Lastpage

3562

Abstract

The authors show that the application of the discrete wavelet transform (DWT) using the Haar basis to the increments of fractional Brownian motion (fBm), also known as discrete fractional Gaussian noise (DFGN), yields coefficients which are weakly correlated and have a variance that is exponentially related to scale. Similar results were derived by Flandrin (1989), Tewfik, and Kim for a continuous-time fBm going through a continuous wavelet transform (CWT). The new theoretical results justify an improvement to a fractal estimation algorithm recently proposed by Wornell and Oppenheim. The performance of the new algorithm is compared with that of Wornell and Oppenheim´s (see IEEE Trans. Signal Processing, vol. 40, p. 611-623, Mar. 1992) algorithm in numerical simulation

Keywords

estimation theory; filtering and prediction theory; fractals; random noise; signal processing; wavelet transforms; DFGN; DWT; Haar basis; coefficients; continuous wavelet transform; correlation; discrete fractional Gaussian noise; discrete wavelet transform; fractal estimation algorithm; fractional Brownian motion; noisy data; numerical simulation; variance; wavelet filters; 1f noise; Brownian motion; Continuous wavelet transforms; Discrete wavelet transforms; Fractals; Frequency estimation; Gaussian noise; Reactive power; Shape control; Wavelet transforms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.258096

Filename

258096