Electrocardiogram is a pictorial representation of the electrical activity of heart beats. Because of the direct relationship between the ECG waveform and interval of the heart beats, it is possible that doctor can diagnose cardiac disease and monitor patient conditions from the unusual ECG waveforms. Based on the wavelet transform, this work introduces an algorithm to detect QRS complex. In particular, the quadratic spline wavelet has been adopted. The thesis first reviews wavelet transform briefly, then develops a QRS detention algorithm, which is then tested by using the MIT-BIH arrhythmia database. It is hoped that the proposed QRS detection algorithm can be a useful tool for medical personnel who are interested in using QRS information to explore their research work.

Fast algorithms for N-point shifted discrete Fourier transform (SDFT) are proposed by efficient matrix factorization¡DThe resulted matrix decomposition is realized by a cascade of several basic computation blocks with each block implemented by a parameterized IP module¡DBy combining these modules with different parameters, it is easy to implement a wide variety of digital transforms, such as DCT/IDCT in image/video coding, and modified DCT (MDCT) in audio coding¡D The transform processors realized using the parameterized IP modules have advantages of locality¡Amodularity¡Aregularity¡Alow-cost¡Aand high-throughput¡D Furthermore ¡Athe computation accuracy can be easily controlled by selecting different numbers of IP modules with proper parameters in the processors.

This project estimates interwell connectivity, a characteristic that is crucial to determine reservoir continuity while developing a waterflooding project. It tests the combination of Fourier transforms (FT’s) of the flow rate data and analytical solutions from analog electrical circuits to infer the inverse diffusivity coefficient (IDC). I solved the transmission line equation analytically for 0D, 1D, and 2D resistance/capacitance (RC) network models and used those solutions to compare with the flow rate FT’s to determine the diffusivity parameters. I used the analogy between the electrical response of RC networks and the fluid response of permeable reservoirs on the basis of the similarities in the governing equations. I conclude that the analogy works accurately in simple reservoirs, where the assumptions of an analytical solution are met, i.e. single-phase fluid and a homogeneous system. For two-phase liquid cases, I determined that the analogy remains applicable because we still could produce accurate interwell connectivity information. When I investigated cases with dissolved-gas production around the wellbore, however, the analogy broke down and the results were not as good as the liquid systems.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 74-76). Also available on the Internet.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (p. 30-31).

Thesis (M.S. in Math.)--School of Mathematics, Georgia Institute of Technology, 2004. Directed by Yang Wang. / Includes bibliographical references (leaves 37-38).

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 74-76). Also available on the Internet.

The ability to efficiently and sparsely represent seismic data is becoming an increasingly important problem in geophysics. Over the last thirty years many transforms such as wavelets, curvelets, contourlets, surfacelets, shearlets, and many other types of ‘x-lets’ have been developed. Such transform were leveraged to resolve this issue of sparse representations. In this work we compare the properties of four of these commonly used transforms, namely the shift-invariant wavelets, complex wavelets, curvelets and surfacelets. We also explore the performance of these transforms for the problem of recovering seismic wavefields from incomplete measurements.

Thesis (Ph. D.)--University of Hawaii at Manoa, 2005. / Includes bibliographical references (leaves 125-129). / Also available by subscription via World Wide Web / xi, 129 leaves, bound ill. 29 cm

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 47-51).