Title :
Wavelets and random processes: optimal matching in the Bhattacharyya sense
Author :
Keshava, Nirmal ; Moura, Jos?© M E
Author_Institution :
Dept. of Electr. & Comput. Eng., Carnegie Mellon Univ., Pittsburgh, PA, USA
Abstract :
The use of wavelet packet bases to represent deterministic signals has led to optimal representations that minimize a desired cost function. In this paper we present an algorithm that uses wavelet packet bases to construct a random process that is matched to an arbitrary correlation matrix. An analytical expression for the Bhattacharyya coefficient gauges the similarity between the two processes and leads to two iterative algorithms that are used jointly to find the desired quantities. Eigen-decompositions for the two processes reduce the problem to finding the best wavelet-based unitary matrix and a set of eigenvalues. Examples illustrates the technique.
Keywords :
correlation theory; eigenvalues and eigenfunctions; iterative methods; matrix algebra; random processes; signal representation; wavelet transforms; Bhattacharyya coefficient; arbitrary correlation matrix; desired cost function; deterministic signals; eigen-decompositions; eigenvalues; iterative algorithms; optimal matching; optimal representations; random processes; similarity; wavelet based correlation matrix; wavelet packet bases; wavelet-based unitary matrix; Algorithm design and analysis; Cost function; Eigenvalues and eigenfunctions; Filter bank; Iterative algorithms; Optimal matching; Random processes; Stochastic processes; Wavelet analysis; Wavelet packets;
Conference_Titel :
Signals, Systems and Computers, 1996. Conference Record of the Thirtieth Asilomar Conference on
Print_ISBN :
0-8186-7646-9
DOI :
10.1109/ACSSC.1996.599093
