Title :
On the continuous wavelet transform of second-order random processes
Author :
Cambanis, Stamatis ; Houdré, Christian
Author_Institution :
Dept. of Stat., North Carolina Univ., Chapel Hill, NC, USA
fDate :
5/1/1995 12:00:00 AM
Abstract :
Some second-order properties of random processes such as periodic correlation, stationarity, harmonizability, self-similarity, are characterized via corresponding properties of their wavelet transform: any one of these properties of the wavelet transform characterizes the corresponding property of the increments of the random process, of order equal to the order of regularity of the analyzing wavelet. These results are then specialized to fractional Brownian motion and other self-similar processes
Keywords :
Brownian motion; correlation theory; random processes; signal processing; wavelet transforms; continuous wavelet transform; fractional Brownian motion; harmonizability; periodic correlation; regularity; second-order random processes; self-similarity; stationarity; Brownian motion; Continuous wavelet transforms; Helium; Nonlinear filters; Random processes; Signal analysis; Signal processing; Statistics; Wavelet analysis; Wavelet transforms;
Journal_Title :
Information Theory, IEEE Transactions on
