Institute for Systems Research Technical Reports
Permanent URI for this collectionhttp://hdl.handle.net/1903/4376
This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.
Browse
4 results
Search Results
Item Existence and Construction of Optimal Wavelet Basis for Signal Representation(1994) Zhuang, Y.; Baras, John S.; ISR; CSHCNWe study the problem of choosing the optimal wavelet basis with compact support for signal representation and provide a general algorithm for computing the optimal wavelet basis. We first briefly review the multiresolution property of wavelet decomposition and the conditions for generating a basis of compactly supported discrete wavelets in terms of properties of quadrature mirror filter (QMF) banks. We then parametrize the mother wavelet and scaling function through a set of real coefficients. We further introduce the concept of decomposition entropy as an information measure to describe the distance between the given signal and its projection onto the subspace spanned by the wavelet basis in which the signal is to be reconstructed. The optimal basis for a given signal is obtained through minimizing this information measure. We have obtained explicitly the sensitivity of dilations and shifts of the mother wavelet with respect to the coefficient set. A systematic approach is developed in this paper to derive the information gradient with respect to the parameter set from a given square integrable signal and a discrete basis of wavelets. The existence of the optimal basis for the wavelets has been proven in this paper. a gradient based optimization algorithm is developed for computing the optimal wavelet basis.Item Optimal Wavelet Basis Selection for Signal Representation(1994) Zhuang, Y.; Baras, John S.; ISR; CSHCNWe study the problem of choosing the optimal wavelet basis with compact support for signal representation and provide a general algorithm for computing the optimal wavelet basis. We first briefly review the multiresolution property of wavelet decomposition and the conditions for generating a basis of compactly supported discrete wavelets in terms of properties of quadrature mirror filter (QMF) banks. We then parametrize the mother wavelet and scaling function through a set of real coefficients. We further introduce the concept of information measure as a distance measure between the signal and its projection onto the subspace spanned by the wavelet basis in which the signal is to be reconstructed. The optimal basis for a given signal is obtained through minimizing this information measure. We have obtained explicitly the sensitivity of dilations and shifts of the mother wavelet with respect to the coefficient set. A systematic approach is developed here to derive the information gradient with respect to the parameter set for a given square integrable signal and the optimal wavelet basis. A gradient based optimazation algorithm is developed in this paper for computing the optimal wavelet basis.Item Analysis and Synthesis of Distributed Systems(1994) Zhuang, Y.; Baras, J.S.; ISRWe first model and analyze distributed systems including distributed sensors and actuators. We then consider identification of distributed systems via adaptive wavelet neural networks (AWNNs) by taking advantage of the multiresolution property of wavelet transforms and the parallel computational structure of neural networks. A new systematic approach is developed in this dissertation to construct an optimal discrete orthonormal wavelet basis with compact support for spanning the subspaces employed for system identification and signal representation. We then apply a backpropagation algorithm to train the network to approximate the system. Filter banks for parameterizing wavelet systems are studied. An analog VLSI implementation architecture of the AWNN is also given in this dissertation. This work is applicable to signal representation and compression under optimal orthonormal wavelet bases in addition to progressive system identification and modeling. We anticipate that this work will find future applications in signal processing and intelligent systems.Item Identification of Infinite Dimensional Systems Via Adaptive Wavelet Neural Networks(1993) Zhuang, Y.; Baras, John S.; ISRWe consider identification of distributed systems via adaptive wavelet neural networks (AWNNs). We take advantage of the multiresolution property of wavelet systems and the computational structure of neural networks to approximate the unknown plant successively. A systematic approach is developed in this paper to find the optimal discrete orthonormal wavelet basis with compact support for spanning the subspaces employed for system identification. We then apply backpropagation algorithm to train the network with supervision to emulate the unknown system. This work is applicable to signal representation and compression under the optimal orthonormal wavelet basis in addition to autoregressive system identification and modeling. We anticipate that this work be intuitive for practical applications in the areas of controls and signal processing.