Thesis (Ph. D.)--Mississippi State University. Department of Electrical and Computer Engineering. / Title from title screen. Includes bibliographical references.

The research was directed toward the viability of an O(n) algorithm which could decompose an arbitrary signal (sound, vibration etc.) into its time-frequency space. The well known Fourier Transform uses sine and cosine functions (having infinite support on t) as orthonormal basis functions to decompose a signal i(t) in the time domain to F(w) in the frequency . domain, where the Fourier coefficients F(w) are the contributions of each frequency in the original signal. Due to the non-local support of these basis functions, a signal containing a sharp localised transient does not have localised coefficients, but rather coefficients that decay slowly. Another problem is that the coefficients F(w) do not convey any time information. The windowed Fourier Transform, or short-time Fourier Transform, does attempt to resolve the latter, but has had limited success. Wavelets are basis functions, usually mutually orthonormal, having finite support in t and are therefore spatially local. Using non-orthogonal wavelets, the Dominant Scale Transform (DST) designed by the author, decomposes a signal into its approximate time-frequency space. The associated Dominant Scale Algorithm (DSA) has O(n) complexity and is integer-based. These two characteristics make the DSA extremely efficient. The thesis also investigates the problem of converting a music signal into it's equivalent music score. The old problem of speech recognition is also examined. The results obtained from the DST are shown to be consistent with those of other authors who have utilised other methods. The resulting DST coefficients are shown to render the DST particularly useful in speech segmentation (silence regions, voiced speech regions, and frication). Moreover, the Spectrogram Dominant Scale Transform (SDST), formulated from the DST, was shown to approximate the Fourier coefficients over fixed time intervals within vowel regions of human speech. / Thesis (Ph.D.)-University of Natal, Durban, 1994.

Increase in technological advancements in fields of telecommunications, computers and television have prompted the need to exchange video, image and audio files between people. Transmission of such files finds numerous multimedia applications such as, internet multimedia, video conferencing, videophone, etc. However, the transmission and rece-ption of these files are limited by the available bandwidth as well as storage capacities of systems. Thus there is a need to develop compression systems, such that required multimedia applications can operate within these limited capacities. This dissertation presents two well established coding approaches that are used in modern' image and video compression systems. These are the wavelet and fractal methods. The wavelet based coder, which adopts the transform coding paradigm, performs the discrete wavelet transform on an image before any compression algorithms are implemented. The wavelet transform provides good energy compaction and decorrelating properties that make it suited for compression. Fractal compression systems on the other hand differ from the traditional transform coders. These algorithms are based on the theory of iterated function systems and take advantage of local self-similarities present in images. In this dissertation, we first review the theoretical foundations of both wavelet and fractal coders. Thereafter we evaluate different wavelet and fractal based compression algorithms, and assess the strengths and weakness in each case. Due to the short-comings of fractal based compression schemes, such as the tiling effect appearing in reconstructed images, a wavelet based analysis of fractal image compression is presented. This is the link that produces fractal coding in the wavelet domain, and presents a hybrid coding scheme called fractal-wavelet coders. We show that by using smooth wavelet basis in computing the wavelet transform, the tiling effect of fractal systems can be removed. The few wavelet-fractal coders that have been proposed in literature are discussed, showing advantages over the traditional fractal coders. This dissertation will present a new low-bit rate video compression system that is based on fractal coding in the wavelet domain. This coder makes use of the advantages of both the wavelet and fractal coders discussed in their review. The self-similarity property of fractal coders exploits the high spatial and temporal correlation between video frames. Thus the fractal coding step gives an approximate representation of the coded frame, while the wavelet technique adds detail to the frame. In this proposed scheme, each frame is decomposed using the pyramidal multi-resolution wavelet transform. Thereafter a motion detection operation is used in which the subtrees are partitioned into motion and non-motion subtrees. The nonmotion subtrees are easily coded by a binary decision, whereas the moving ones are coded using the combination of the wavelet SPIHT and fractal variable subtree size coding scheme. All intra-frame compression is performed using the SPIHT compression algorithm and inter-frame using the fractal-wavelet method described above. The proposed coder is then compared to current low bit-rate video coding standards such as the H.263+ and MPEG-4 coders through analysis and simulations. Results show that the proposed coder is competitive with the current standards, with a performance improvement been shown in video sequences that do not posses large global motion. Finally, a real-time implementation of the proposed algorithm is performed on a digital signal processor. This illustrates the suitability of the proposed coder being applied to numerous multimedia applications. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2004.

No description available.

The reconstruction of a function and its derivative from a set of measured samples is a fundamental operation in visualisation. Multiresolution techniques, such as wavelet signal processing, are instrumental in improving the performance and algorithm design for data analysis, filtering and processing. This dissertation explores the possibilities of combining traditional multiresolution analysis and processing features of wavelets with the design of appropriate filters for reconstruction of sampled data. On the one hand, a multiresolution system allows data feature detection, analysis and filtering. Wavelets have already been proven successful in these tasks. On the other hand, a choice of discrete filter which converges to a continuous basis function under iteration permits efficient and accurate function representation by providing a “bridge” from the discrete to the continuous. A function representation method capable of both multiresolution analysis and accurate reconstruction of the underlying measured function would make a valuable tool for scientific visualisation. The aim of this dissertation is not to try to outperform existing filters designed specifically for reconstruction of sampled functions. The goal is to design a wavelet filter family which, while retaining properties necessary to preform multiresolution analysis, possesses features to enable the wavelets to be used as efficient and accurate “building blocks” for function representation. The application to visualisation is used as a means of practical demonstration of the results. Wavelet and visualisation filter design is analysed in the first part of this dissertation and a list of wavelet filter design criteria for visualisation is collated. Candidate wavelet filters are constructed based on a parameter space search of the BC-spline family and direct solution of equations describing filter properties. Further, a biorthogonal wavelet filter family is constructed based on point and average interpolating subdivision and using the lifting scheme. The main feature of these filters is their ability to reconstruct arbitrary degree piecewise polynomial functions and their derivatives using measured samples as direct input into a wavelet transform. The lifting scheme provides an intuitive, interval-adapted, time-domain filter and transform construction method. A generalised factorisation for arbitrary primal and dual order point and average interpolating filters is a result of the lifting construction. The proposed visualisation filter family is analysed quantitatively and qualitatively in the final part of the dissertation. Results from wavelet theory are used in the analysis which allow comparisons among wavelet filter families and between wavelets and filters designed specifically for reconstruction for visualisation. Lastly, the performance of the constructed wavelet filters is demonstrated in the visualisation context. One-dimensional signals are used to illustrate reconstruction performance of the wavelet filter family from noiseless and noisy samples in comparison to other wavelet filters and dedicated visualisation filters. The proposed wavelet filters converge to basis functions capable of reproducing functions that can be represented locally by arbitrary order piecewise polynomials. They are interpolating, smooth and provide asymptotically optimal reconstruction in the case when samples are used directly as wavelet coefficients. The reconstruction performance of the proposed wavelet filter family approaches that of continuous spatial domain filters designed specifically for reconstruction for visualisation. This is achieved in addition to retaining multiresolution analysis and processing properties of wavelets.

Thesis (Ph. D.)--University of Hong Kong, 2007. / Also available online.

Thesis (Ph.D.)--McMaster University (Canada), 1995. / Source: Dissertation Abstracts International, Volume: 57-03, Section: B, page: 1839. Adviser: A. Peirce.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 206-216).

Thesis (Ph. D.)--Ohio University, June, 2000. / Title from PDF t.p.

Thesis (M.S.) -- Mississippi State University. Department of Electrical and Computer Engineering. / Title from title screen. Includes bibliographical references.