Title :
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
fDate :
12/1/1993 12:00:00 AM
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;
Journal_Title :
Signal Processing, IEEE Transactions on
