Title :
MRA of processes synthesized by fractional integration
Author :
Dabeer, Onkar ; Dasai, U.
Author_Institution :
Dept. of Electr. & Comput. Eng., California Univ., San Diego, La Jolla, CA, USA
fDate :
4/1/2000 12:00:00 AM
Abstract :
In this correspondence, we show that the multiresolution analysis (MRA) of the reproducing kernel Hilbert space, associated with processes synthesized by fractional integration of white processes, leads to an orthogonal, multiresolution decomposition of the process. We show that the decomposition converges almost surely and uniformly on finite intervals. We also show that the random coefficients in the decomposition can be evaluated almost surely
Keywords :
Gaussian processes; Hilbert spaces; integration; signal resolution; convergence; fractional integration; multiresolution analysis; orthogonal decomposition; random coefficients; reproducing kernel Hilbert space; white processes; Brownian motion; Gaussian processes; Hilbert space; Kernel; Multiresolution analysis; Random processes; Random variables; Signal resolution; Stochastic processes; Wavelet transforms;
Journal_Title :
Signal Processing, IEEE Transactions on
