Search

An innovative tree-like detector is described for dealing with the problem of code division multiple access (CDMA) multiuser detection. Complexity and performance can be traded off by changing the size of the tree.

Two approaches for identifying sparsest representations of given signals in terms of given overcomplete dictionaries are proposed. The first approach is algebraic, and the second, which can be used in circumstances where an algebraic technique is not appropriate, is iterative.

The generalized ULV algorithm for extracting subspaces corresponding to clusters of singular values of the same order of magnitude was developed. A new heuristic was also used for deflation in the ULV decomposition. A new bound on the distance was obtained between the subspaces by applying a ULV algorithm on a perturbed data matrix and those derived using the singular value decomposition on an exact data matrix.

Two new wavelet transform domain least mean square (LMS) algorithms are shown. The algorithms take advantage of the special sparse structures of the wavelet transform of wide classes of correlation matrices and their Cholesky factors to calculate a whitening transformation of the input data. Both algorithms have a convergence rate that is faster than that of time-domain LMS and discrete Fourier transform or discrete cosine transform-based LMS methods. The two methods are compared and their mean and mean square performance are investigated.

A study on the sampling of discrete time wavelet transforms provides necessary conditions for the completeness of an arbitrarily sampled dyadic transform of a periodic signal. It also produces the sufficient conditions for completeness of the sampled wavelet transform for lowpass filters without any unit circle zeros except for z = -1. The test provides only necessary conditions for filters with arbitrary unit circle zeros.

The multiscale difference equation (MSDE) models for 1-D and M-D signals provides solution to signals that are of interest. Both the signal characterization and the number of its higher derivatives are obtained by this technique. Conditions for the existence of L(sub 1) solutions to an MSDE are obtained. The modeling advantages of MSDE signal are discussed.

A novel wavelet based audio synthesis and coding process utilizes optimal adaptive wavelet selection and wavelet coefficients quantization procedures integrated with a dynamic dictionary encoding procedure. The method takes into account the perceptual masking in human hearing and minimizes the number of representative bits for each audio frame.

The parameters of discrete fractionally differentiated Gaussian noise are estimated from the observation of a group of finite size by the construction of a maximum likelihood estimation procedure, which does not involve the calculation of any determinant or matrix inverse. A unique maximum with allowable range values of d is found in the log-likelihood function for the estimation of the parameter d, a fractionally differentiated Gaussian noise. The largest value occurs only at the true value of d.

The study of fractionally differenced Gaussian noise (fdGn) processes indicates that fdGn is a discrete time equivalent of fractional Brownian motion. Signals which have different short-term and long-term correlation structures can be perfectly modelled by the filtered versions of such fdGn processes. The parameters of filtered fdGn processes are estimated by two different iterative algorithms. One of the algorithms is based on the process of expectation maximization and the other follows computationally efficient approximate approach.

An analysis of the parametrization of perfect reconstruction finite impulse response filter banks is outlined in terms of the characterization of dyadic orthonormal wavelets with arbitrary supports and vanishing moments. Results show that characterization is possible with an extension of the parametrization of perfect reconstruction quadrature mirror filter banks. Thus, a compactly supported orthonormal wavelet of 2N - 1 can be parametrized by N - 1 free parameters with values in the (0, 2pi) interval.

We employ the concepts and tools of the discrete wavelet transform (DWT) to encapsulate a body of previous research on efficiently analyzable phase-coded waveforms for use in ranging applications. This DWT perspective enables the direct synthesis of half-rate implementations which are suitable for high-speed applications. We introduce and study a set of sequences, based on a classical Welti construction, which are both DWT-decomposable and exhibit a zero autocorrelation zone property under cyclic extension. We propose a general extension technique which extends the zero correlation width while retaining the same simple receiver filter, and show that this technique is appropriate for many of the sequences in our construction. Finally, we propose a transmit waveform construction which allows a further reduction of two in the receiver hardware complexity. We discuss the resulting tradeoffs between receiver complexity and transmit power. [ABSTRACT FROM AUTHOR]

Finding clusters of genes with expression levels that evolve coherently under subsets of conditions can help uncover genetic pathways. This can be done by applying a biclustering procedure to gene expression data. Given a microarray data set with M genes and N conditions, we define a bicluster with coherent evolution as a subset of genes with expression levels that are nondecreasing as a function of a particular ordered subset of conditions. We propose a new biclustering procedure that identifies all biclusters with a specified number of K conditions in parallel with O(MK) complexity. Unlike almost all prior biclustering techniques, the proposed approach is guaranteed to find all biclusters with a specified minimum numbers of genes and conditions in the data set. All of the biclusters it identifies have no imperfection, i.e., the evolutions of the genes in each bicluster will be coherent across all conditions in the bicluster. Furthermore, the complexity of the proposed approach is lower than that of prior approaches. [ABSTRACT FROM AUTHOR]