Title :
Reciprocal processes on a tree-modeling and estimation issues
Author :
Dijkerman, Robert W. ; Mazumdar, Ravi R. ; Bagchi, Arunabha
Author_Institution :
INRS-Telecommun., Quebec Univ., Verdum, Que., Canada
fDate :
2/1/1995 12:00:00 AM
Abstract :
Motivated by multiresolution decomposition methods such as the discrete wavelet transformation, the authors introduce reciprocal processes on truncated N-ary trees. The authors discuss the relationship between such processes and nearest neighbor models. The authors show that they can derive a recursive description of the process, and that all reciprocal processes on N-ary trees reduce to autoregressive processes in the case of zero-valued boundary values at the bottom of the tree, corresponding to truncation of the tree. The authors then study the smoothing equations associated with such models
Keywords :
autoregressive processes; estimation theory; modelling; smoothing methods; trees (mathematics); wavelet transforms; autoregressive processes; discrete wavelet transformation; estimation issues; multiresolution decomposition methods; nearest neighbor models; reciprocal processes; recursive description; smoothing equations; truncated N-ary trees; zero-valued boundary values; Array signal processing; Autoregressive processes; Discrete wavelet transforms; Equations; Nearest neighbor searches; Signal processing; Signal resolution; Smoothing methods; Time frequency analysis; Wavelet coefficients;
Journal_Title :
Automatic Control, IEEE Transactions on