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Dissertations / Theses on the topic 'Wavelet transform'

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Published: 4 June 2021

Last updated: 7 July 2024

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1

Anton, Wirén. "The Discrete Wavelet Transform." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-55063.

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In this thesis we will explore the theory behind wavelets. The main focus is on the discrete wavelet transform, although to reach this goal we will also introduce the discrete Fourier transform as it allow us to derive important properties related to wavelet theory, such as the multiresolution analysis. Based on the multiresolution it will be shown how the discrete wavelet transform can be formulated and show how it can be expressed in terms of a matrix. In later chapters we will see how the discrete wavelet transform can be generalized into two dimensions, and discover how it can be used in image processing.

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2

Navarro, Jaime. "The Continuous Wavelet Transform and the Wave Front Set." Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc277762/.

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In this paper I formulate an explicit wavelet transform that, applied to any distribution in S^1(R^2), yields a function on phase space whose high-frequency singularities coincide precisely with the wave front set of the distribution. This characterizes the wave front set of a distribution in terms of the singularities of its wavelet transform with respect to a suitably chosen basic wavelet.

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3

Huang, Wensheng. "Wavelet Transform Adaptive Signal Detection." NCSU, 1999. http://www.lib.ncsu.edu/theses/available/etd-19991104-151423.

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Wavelet Transform Adaptive Signal Detection is a signal detection method that uses the Wavelet Transform Adaptive Filter (WTAF). The WTAF is the application of adaptive filtering on the subband signals obtained by wavelet decomposition and reconstruction. The WTAF is an adaptive filtering technique that leads to good convergence and low computational complexity. It can effectively adapt to non-stationary signals, and thus could find practical use for transient signals. Different architectures for implementing the WTAF were proposed and studied in this dissertation. In terms of the type of the wavelet transform being used, we presented the DWT based WTAF and the wavelet tree based WTAF. In terms of the position of the adaptive filter in the signal paths of the system, we presented the Before-Reconstruction WTAF, in which the adaptive filter is placed before the reconstruction filter; and the After-Reconstruction WTAF, in which the adaptive filter is placed after the reconstruction filter. This could also be considered as implementing the adaptive filtering in different domains, with the Before-Reconstruction structure corresponding to adaptive filtering in the scale-domain, and the After-Reconstruction structure corresponding to adaptive filtering in the time-domain. In terms of the type of the error signal used in the WTAF, we presented the output error based WTAF and the subband error based WTAF. In the output error based WTAF, the output error signal is used as input to the LMS algorithm. In the subband error based WTAF, the error signal in each subband is used as input to the LMS algorithm. The algorithms for the WTAF were also generalized in this work. In order to speed up the calculation, we developed the block LMS based WTAF, which modifies the weights of the adaptive filter block-by-block instead of sample-by-sample. Experimental studies were performed to study the performance of different implementation schemes for the WTAF. Simulations were performed on different WTAF algorithms with a sinusoidal input and with a pulse input. The speed and stability properties of each structure were studied experimentally and theoretically. It was found that different WTAF structures had different tradeoffs in terms of stability, performance, computational complexity, and convergence speed. The WTAF algorithms were applied to an online measurement system for fabric compressional behavior and they showed encouraging results. A 3-stage DWT based WTAF and a block WTAF based on a 3-stage DWT was employed to process the noisy force-displacement signal acquired from the online measurement system. The signal-to-noise ratio was greatly increased by applying these WTAFs, which makes a lower sampling rate a possibility. The reduction of the required time for data sampling and processing greatly improves the system speed to meet faster testing requirements. The WTAF algorithm could also be used in other applications requiring fast processing, such as in the real-time applications in communications, measurement, and control.

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Ghafoori, Elyar. "Wavelet transform and neural network." Thesis, California State University, Long Beach, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=1527935.

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Automatic and accurate detection of Atrial Fibrillation (AF) from the noninvasive ECG signal is imperative in Electrocardiography. AF is mainly reflected in the ECG signal with the absence of P wave and/or irregular RR intervals. Signal processing tools can assess such detailed changes in the ECG, leading to an accurate diagnosis of AF. The proposed method relies on proper noise filtering, Stationary Wavelet Transform, and signal Power Spectrum Estimation. A feature extraction technique and a Neural Network classifier have been employed to determine the presence and absence of the AF episodes. Implementation of the proposed method with 5-fold cross validation on more than 230 hours of ECG data from MIT-BIH arterial fibrillation annotated database demonstrated an accuracy of 93% in classification of the AF and normal ECG signals.

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5

Xiao, Panrong. "Image compression by wavelet transform." [Johnson City, Tenn. : East Tennessee State University], 2001. http://etd-submit.etsu.edu/etd/theses/available/etd-0711101-121206/unrestricted/xiaop0720.pdf.

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6

Tieng, Quang Minh. "Wavelet transform based techniques for the recognition of objects in images." Thesis, Queensland University of Technology, 1996.

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Despite its short history, the wavelet transform has found application in a remarkable diversity of disciplines: Mathematics, Physics, Numerical Analysis,Signal Processing and others. In this thesis, we explore applications of this transform in image analysis and devise several algorithms for recognising objects in an image of a scene. Five different algorithms, consisting of representations and matching techniques, have been proposed for handling different kinds of objects in different situations.

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7

Grzeszczak, Aleksander. "VLSI architecture for Discrete Wavelet Transform." Thesis, University of Ottawa (Canada), 1995. http://hdl.handle.net/10393/9908.

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In this thesis, we present a new simple and efficient VLSI architecture (DWT-SA) for computing the Discrete Wavelet Transform. The proposed architecture is systolic in nature, modular and extendible to 1-D or 2-D DWT transform of any size. The DWT-SA has been designed, simulated and implemented in silicon. The following are the features of the DWT-SA architecture: (1) It has an efficient (close to 100%) hardware utilization. (2) It works with data streams of arbitrary size. (3) The design is cascadable, for computation of one, two or three dimensional DWT. (4) It requires a minimum interface circuitry on the chip for purposes of interconnecting to a standard communication bus. The DWT-SA design has been implemented using CMOS 1.2 um technology.

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8

Mudry, Andrew H. "Speaker identification using the wavelet transform." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq22123.pdf.

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9

Watkins, Lanier A. "Modulation characterization using the wavelet transform." DigitalCommons@Robert W. Woodruff Library, Atlanta University Center, 1997. http://digitalcommons.auctr.edu/dissertations/640.

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The focus of this research is to establish an Automatic Modulation Identifier (AMI) using the Continuous Wavelet Transform (CWT) and several different classifiers. A Modulation Identifier is of particular interest to the military, because it has the potential to quickly discriminate between different communication waveforms. The CWT is used to extract characterizing information from the signal, and an artificial Neural Network is trained to identify the modulation type. Various analyzing wavelets and various classifiers were used to assess comparative performance. The analyzing wavelets used were the Mexican Hat Wavelet, the Morlet Wavelet, and the Haar Wavelet. The variety of classifiers used were the Multi-Layer Perceptron, the K-Nearest Neighbor and the Fuzzy Artmap. The CWT served as a preprocessor, and the classifiers served as an identifier for Binary Phase Shift Keying (BPSK), Binary Frequency Shift Keying (BFSK), Binary Amplitude Shift Keying (BASK), Quadature Phase Shift Keying (QPSK), Eight Phase Shift Keying (8PSK), and Quadature Amplitude Modulation (QAM) signals. Separation of BASK, BFSK and BPSK was performed in part one of the research project, and separation of BPSK, QPSK, 8PSK, BFSK, and QAM comprised the second part of the project. Each experiment was performed for waveforms corrupted with Additive White Gaussian Noise ranging from 20 dB - 0 dB carrier to noise ratio (CNR). To test the robustness of the technique, part one of the research project was tested upon several carrier frequencies w/2, and w/3 which was different from the carrier frequency w that the classifiers were trained upon. In the separation of BASK, BFSK and BPSK, the AMI worked extremely well (100% correct classification) down to 5 dB CNR tested at carrier frequency w, and it worked well (80% correct classification) down to 5 dB CNR tested at carrier frequencies w/2, and w/3. In the separation of BPSK, QPSK, 8PSK, BFSK, and QAM, the AMI performed very well at 10 dB CNR (98.8% correct classification). Also a hardware design in the Hewlet Packard Visual Engineering Environment (HP-VEE) for implementation of the AMI algorithm was constructed and is included for future expansion of the project.

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10

Mudry, Andrew H. (Andrew Henry) Carleton University Dissertation Engineering Electronics. "Speaker identification using the wavelet transform." Ottawa, 1997.

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11

Schremmer, Claudia. "Multimedia applications of the wavelet transform." [S.l. : s.n.], 2002. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10605021.

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12

Yoon, Weon-Ki. "Power measurements via the wavelet transform /." free to MU campus, to others for purchase, 1998. http://wwwlib.umi.com/cr/mo/fullcit?p9924949.

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13

Jin, Shasha, and Ningcheng Gaoding. "Signal processing using the wavelet transform and the Karhunen-Loeve transform." Thesis, Högskolan Kristianstad, Sektionen för hälsa och samhälle, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:hkr:diva-9752.

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This degree project deals with Wavelet transform and Karhunen-Loeve transform. Through the mathematic description to understand and simulation to investigate the denoise ability of WT and the de-correlation ability of KLT. Mainly prove that the new algorithm which is the joint of these two algorithms is feasible.

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14

Yilmaz, Sener. "Generalized Area Tracking Using Complex Discrete Wavelet Transform: The Complex Wavelet Tracker." Phd thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/3/12608643/index.pdf.

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In this work, a new method is proposed that can be used for area tracking. This method is based on the Complex Discrete Wavelet Transform (CDWT) developed by Magarey and Kingsbury. The CDWT has its advantages over the traditional Discrete Wavelet Transform such as approximate shift invariance, improved directional selectivity, and robustness to noise and illumination changes. The proposed method is a generalization of the CDWT based motion estimation method developed by Magarey and Kingsbury. The Complex Wavelet Tracker extends the original method to estimate the true motion of regions according to a parametric motion model. In this way, rotation, scaling, and shear type of motions can be handled in addition to pure translation. Simulations have been performed on the proposed method including both quantitative and qualitative tests. Quantitative tests are performed on synthetically created test sequences and results have been compared to true data. The performance is compared with intensity-based methods. Qualitative tests are performed on real sequences and evaluations are presented empirically. The results are compared with intensity-based methods. It is observed that the proposed method is very accurate in handling affine deformations for long term sequences and is robust to different target signatures and illumination changes. The accuracy of the proposed method is compatible with intensity-based methods. In addition to this, it can handle a wider range of cases and is robust to illuminaton changes compared to intensity-based methods. The method can be implemented in real-time and could be a powerful replacement of current area trackers.

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Peyton, William M. "Multiresolution image recognition using the wavelet transform." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1996. http://handle.dtic.mil/100.2/ADA316566.

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Thesis (M.S. in Electrical Engineering and Electrical Engineer) Naval Postgraduate School, June 1996.
Thesis advisor(s): Murali Tummala. "June 1996." Includes bibliographical references. Also Available online.

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Vai, Mang I. "Detecting ECG late potentials using wavelet transform." Thesis, University of Macau, 2002. http://umaclib3.umac.mo/record=b1637077.

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Sari, Huseyin. "Motion Estimation Using Complex Discrete Wavelet Transform." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/1223205/index.pdf.

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The estimation of optical flow has become a vital research field in image sequence analysis especially in past two decades, which found applications in many fields such as stereo optics, video compression, robotics and computer vision. In this thesis, the complex wavelet based algorithm for the estimation of optical flow developed by Magarey and Kingsbury is implemented and investigated. The algorithm is based on a complex version of the discrete wavelet transform (CDWT), which analyzes an image through blocks of filtering with a set of Gabor-like kernels with different scales and orientations. The output is a hierarchy of scaled and subsampled orientation-tuned subimages. The motion estimation algorithm is based on the relationship between translations in image domain and phase shifts in CDWT domain, which is satisfied by the shiftability and interpolability property of CDWT. Optical flow is estimated by using this relationship at each scale, in a coarse-to-fine (hierarchical) manner, where information from finer scales is used to refine the estimates from coarser scales. The performance of the motion estimation algorithm is investigated with various image sequences as input and the effects of the options in the algorithm like curvature-correction, interpolation kernel between levels and some parameter values like confidence threshold iv maximum number of CDWT levels and minimum finest level of detail are also experimented and discussed. The test results show that the method is superior to other well-known algorithms in estimation accuracy, especially under high illuminance variations and additive noise.

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Ma, Yanjun. "Medical Image Fusion Based on Wavelet Transform." Thesis, Blekinge Tekniska Högskola, Sektionen för datavetenskap och kommunikation, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-4245.

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Medical image is a core step of medical diagnosis and has been diffusely applied in modern medical domain. The technology of modern medical image is more and more mature which could present images in different modes and features. Medical image fusion is the technology that could compound two mutual images into one according to certain rules to achieve clear visual effect. By observing medical fusion image, doctor could easily confirm the position of illness. According to the mutual features of CT medical image and MRI medical image, based on the technology of wavelet transform, the paper presents twp effective and applied medical image fusion methods. The first method is based on the features of certain area. The principle is to construct weighted factor and matching degree with certain related parameters to compound the area of high frequency which presents the detailed information. To the area of low frequency, principle of maximum absolute value is selected. Finally we get the fusion image by wavelet reconfiguration. By estimate of subjectivity and objectivity, the method is applied that could export excellent visual effect and good parameters. The other method is based on lifting wavelet. It decomposes the original image to area of low frequency and high frequency, and then transforms them with different fusion rules. To area of low frequency, weighted fusion is applied and to area of high frequency, rule of maximum standard deviation is chosen. Finally we get fusion image from wavelet reconstruction. By the estimate of subjectivity and objectivity, the method is an applied and excellent way that keeps the detailed information effectively and presents clear profile. At the same time, the executed time is shorter than others.

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Murray, Kevin B. "Wavelet transform analysis of turbulent wake flows." Thesis, Edinburgh Napier University, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.322272.

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Goh, Kwong Huang. "Wavelet transform based image and video coding." Thesis, University of Strathclyde, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.387720.

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LOUREIRO, FELIPE PRADO. "ACOUSTIC MODELING IN THE WAVELET TRANSFORM DOMAIN." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2004. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=4915@1.

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PETRÓLEO BRASILEIRO S. A.
O processamento de sinais sísmicos é peça chave na exploração petrolífera. O caminho entre aquisição de dados e interpretação sísmica é composto por uma trilha de processos interdependentes, entre eles os processos de modelagem e migração. A dissertação apresenta a composição de um algoritmo de modelagem acústica 2D no domínio da transformada wavelet a partir de ferramentas próprias e outras já existentes na literatura. São estabelecidas as aproximações necessárias à solução em meios heterogêneos e à independência entre os subdomínios de processamento. Esta independência possibilita a exploração de técnicas de processamento paralelo. Através de exemplos, seu desempenho é avaliado com comparações à solução via diferenças finitas. Estas soluções são ainda submetidas ao mesmo processo de migração baseado em um terceiro modo de solução.
Seismic signal processing is a key step to oil exploration. The path between data acquisition and seismic interpretation is composed by a sequence of interdependent processes, among which are modeling and migration processes. A 2D acoustic modeling algorithm in wavelet Transform domain, based on custom tools and tools already made known in literature is presented. Approximations necessary for the solution in inhomogeneous media and for complete independence between processing subspaces are established. Such independence allows exploration of parallel processing techniques. Throughout examples, performance is evaluated in comparison to finite-difference solution. These solutions are further processed by a migration technique based in yet another solution method.

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Waldspurger, Irène. "Wavelet transform modulus : phase retrieval and scattering." Thesis, Paris, Ecole normale supérieure, 2015. http://www.theses.fr/2015ENSU0036/document.

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Les tâches qui consistent à comprendre automatiquement le contenu d’un signal naturel, comme une image ou un son, sont en général difficiles. En effet, dans leur représentation naïve, les signaux sont des objets compliqués, appartenant à des espaces de grande dimension. Représentés différemment, ils peuvent en revanche être plus faciles à interpréter. Cette thèse s’intéresse à une représentation fréquemment utilisée dans ce genre de situations, notamment pour analyser des signaux audio : le module de la transformée en ondelettes. Pour mieux comprendre son comportement, nous considérons, d’un point de vue théorique et algorithmique, le problème inverse correspondant : la reconstruction d’un signal à partir du module de sa transformée en ondelettes. Ce problème appartient à une classe plus générale de problèmes inverses : les problèmes de reconstruction de phase. Dans un premier chapitre, nous décrivons un nouvel algorithme, PhaseCut, qui résout numériquement un problème de reconstruction de phase générique. Comme l’algorithme similaire PhaseLift, PhaseCut utilise une relaxation convexe, qui se trouve en l’occurence être de la même forme que les relaxations du problème abondamment étudié MaxCut. Nous comparons les performances de PhaseCut et PhaseLift, en termes de précision et de rapidité. Dans les deux chapitres suivants, nous étudions le cas particulier de la reconstruction de phase pour la transformée en ondelettes. Nous montrons que toute fonction sans fréquence négative est uniquement déterminée (à une phase globale près) par le module de sa transformée en ondelettes, mais que la reconstruction à partir du module n’est pas stable au bruit, pour une définition forte de la stabilité. On démontre en revanche une propriété de stabilité locale. Nous présentons également un nouvel algorithme de reconstruction de phase, non-convexe, qui est spécifique à la transformée en ondelettes, et étudions numériquement ses performances. Enfin, dans les deux derniers chapitres, nous étudions une représentation plus sophistiquée, construite à partir du module de transformée en ondelettes : la transformée de scattering. Notre but est de comprendre quelles propriétés d’un signal sont caractérisées par sa transformée de scattering. On commence par démontrer un théorème majorant l’énergie des coefficients de scattering d’un signal, à un ordre donné, en fonction de l’énergie du signal initial, convolé par un filtre passe-haut qui dépend de l’ordre. On étudie ensuite une généralisation de la transformée de scattering, qui s’applique à des processus stationnaires. On montre qu’en dimension finie, cette transformée généralisée préserve la norme. En dimension un, on montre également que les coefficients de scattering généralisés d’un processus caractérisent la queue de distribution du processus
Automatically understanding the content of a natural signal, like a sound or an image, is in general a difficult task. In their naive representation, signals are indeed complicated objects, belonging to high-dimensional spaces. With a different representation, they can however be easier to interpret. This thesis considers a representation commonly used in these cases, in particular for theanalysis of audio signals: the modulus of the wavelet transform. To better understand the behaviour of this operator, we study, from a theoretical as well as algorithmic point of view, the corresponding inverse problem: the reconstruction of a signal from the modulus of its wavelet transform. This problem belongs to a wider class of inverse problems: phase retrieval problems. In a first chapter, we describe a new algorithm, PhaseCut, which numerically solves a generic phase retrieval problem. Like the similar algorithm PhaseLift, PhaseCut relies on a convex relaxation of the phase retrieval problem, which happens to be of the same form as relaxations of the widely studied problem MaxCut. We compare the performances of PhaseCut and PhaseLift, in terms of precision and complexity. In the next two chapters, we study the specific case of phase retrieval for the wavelet transform. We show that any function with no negative frequencies is uniquely determined (up to a global phase) by the modulus of its wavelet transform, but that the reconstruction from the modulus is not stable to noise, for a strong notion of stability. However, we prove a local stability property. We also present a new non-convex phase retrieval algorithm, which is specific to the case of the wavelet transform, and we numerically study its performances. Finally, in the last two chapters, we study a more sophisticated representation, built from the modulus of the wavelet transform: the scattering transform. Our goal is to understand which properties of a signal are characterized by its scattering transform. We first prove that the energy of scattering coefficients of a signal, at a given order, is upper bounded by the energy of the signal itself, convolved with a high-pass filter that depends on the order. We then study a generalization of the scattering transform, for stationary processes. We show that, in finite dimension, this generalized transform preserves the norm. In dimension one, we also show that the generalized scattering coefficients of a process characterize the tail of its distribution

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Mao, Peilin. "Power transformer fault diagnosis based on wavelet transform and artificial neural network." Thesis, University of Bath, 2000. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.760740.

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Tsakiroglou, Evangelia. "Wavelet-based parametric spectrum estimation." Thesis, Imperial College London, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.342234.

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Sun, Pu. "Comparison of STFT and Wavelet Transform inTime-frequency Analysis." Thesis, Högskolan i Gävle, Avdelningen för elektronik, matematik och naturvetenskap, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-19072.

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The wavelet transform technique has been frequently used in time-frequency analysis as a relatively new concept. Compared to the traditional technique Short-time Fourier Transform (STFT), which is theoretically based on the Fourier transform, the wavelet transform has its advantage on better locality in time and frequency domain, but not significant as the solutions in spectrum. Wavelet transform has dynamic ‘window functions’ to represent time-frequency positions of raw signals, and can get better resolutions in time-frequency analysis. In this report, we shall first briefly introduce fuzzy sets and related concepts. And then we will evaluate their similarities and differences by not only the theoretic comparisons between STFT and wavelet transform, but also the process of the de-nosing to a noisy recorded signal.

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Wood, Mark. "Discriminant analysis using wavelet derived features." Thesis, University of Aberdeen, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.252149.

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This thesis examines the ability of the wavelet transform to form features which may be used successfully in a discriminant analysis. We apply our methods to two different data sets and consider the problem of selecting the 'best' features for discrimination. In the first data set, our interest is in automatically recognising the variety of a carrot from an image. After necessary image preprocessing we examine the usefulness of shape descriptors and texture features for discrimination. We show that it is better to use the different 'types' of features separately, and that the wavelet coefficients of the outline coordinates are more useful. In the second data set we consider the task of automatically identifying individual haddock from the sounds they produce. We use the smoothing property of wavelets to automatically isolate individual haddock sounds, and use the stationary wavelet transform to overcome the shift dependence of the standard wavelet transform. Again we calculate different 'types' of wavelet features and compare their usefulness in classification and show that including information on the source of the previous sound can substantially increase the correct classification rate. We also apply our techniques to recognise different species of fish which is also highly successful. In each analysis, we explore different allocation rules via regularised discriminant analysis and show that the highest classification rates obtained are only slightly better than linear discriminant analysis. We also consider the problem of selecting the best subset of features for discrimination. We propose two new measures for selecting good subsets and using a genetic algorithm we search for the 'best' subsets. We investigate the relationship between out measures and classification rates showing that our method is better than selection based on F-ratios and we also discover that our two measures are closely related.

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Logue, James K. "The discrete, orthogonal wavelet transform, a projective approach." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1995. http://handle.dtic.mil/100.2/ADA304330.

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Chan, Kenny Lee-Lung. "Finite wordlength effects in discrete time wavelet transform." Thesis, University of Ottawa (Canada), 1999. http://hdl.handle.net/10393/8698.

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This thesis investigates the finite wordlength effects in one-dimensional discrete-time wavelet transform (DTWT). A MATLAB DTWT model is written based on an efficient algorithm suggested by the Multiresolution Analysis (MRA). This model allows users to investigate the overall non-ideal effects of a MRA-based DTWT system by specifying round-off method for computation, the number of quantization bits employed in representing filter coefficient and internal computational results. Further, the possibility of discarding the high frequency portion of a signal in DTWT signal reconstruction phase (Selective Subband Reconstruction) is shown practical with the presence of finite wordlength effects. The feasibility of using either direct structure filter or lattice structure filter to realize a MRA-based DTWT system is also considered in this thesis. Simulation results show that the lattice structure filters have superior magnitude and phase responses in most scenarios under investigation to its direct structure-based counterparts. Moreover, lattice structure filter demands relatively less computation than direct structure filter in the same filter length and DTWT configuration. In conclusion, the lattice structure filter is a better alternative than the direct structure filter for MRA-based DTWT system implementation.

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Ariyani, Mathematics &amp Statistics Faculty of Science UNSW. "The generalized continuous wavelet transform on Hilbert modules." Publisher:University of New South Wales. Mathematics & Statistics, 2008. http://handle.unsw.edu.au/1959.4/42151.

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The construction of the generalized continuous wavelet transform (GCWT) on Hilbert spaces is a special case of the coherent state transform construction, where the coherent state system arises as an orbit of an admissible vector under a strongly continuous unitary representation of a locally compact group. In this thesis we extend this construction to the setting of Hilbert C*-modules. In particular, we define a coherent state transform and a GCWT on Hilbert modules. This construction gives a reconstruction formula and a resolution of the identity formula analogous to those found in the Hilbert space setting. Moreover, the existing theory of standard normalized tight frames in finite countably generated Hilbert modules can be viewed as a discrete case of this construction We also show that the image space of the coherent state transform on Hilbert module is a reproducing kernel Hilbert module. We discuss the kernel and the intertwining property of the group coherent state transform.

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Chan, Kenny. "Finite wordlength effects in discrete time wavelet transform." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/mq36674.pdf.

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31

Turner, Barry John. "Studies of atmospheric turbulence using the wavelet transform." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0018/NQ50273.pdf.

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Mujica, Fernando Alberto. "Spatio-temporal continuous wavelet transform for motion estimation." Diss., Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/15001.

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33

Lewis, A. S. "Image and video compression using the wavelet transform." Thesis, Imperial College London, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318148.

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34

Yi, Chih-Wei, and 易志偉. "Wavelet Transform, Wavelet Packet and Applications." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/24396936210917707441.

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35

Chiang, Arvin, and 姜義峰. "Current Transformer Saturation Detection Using Wavelet Transform." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/38630066492618497025.

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碩士
長榮大學
經營管理研究所
94
Digital protection relay for transmission lines utilizes voltage and current samples to discriminate faults in power system. Traditionally, current transformer (CT) is used to scale down the primary current to small secondary current for sampling. When a fault occurs on transmission lines, fault current contains an exponential decaying DC offset. It may cause the core of CT to saturate and result in distorted secondary current. Moreover, it results in a mal-operation in the protection relay. A CT saturation detection method is proposed in this thesis by analyzing the secondary current through Discrete Wavelet Transform (DWT). The level 1 detail coefficients in DWT are used to identify the start and end point when CT saturation occurs. The simulation results by MATLAB/SIMULINK revealed that the proposed method can detect the start and end point of CT saturation accurately.

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36

Yang, Min-Ta, and 楊明達. "The VLSI Design of Discrete Wavelet Transform and Inverse Discrete Wavelet Transform for JPEG2000." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/93707017269338386899.

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碩士
國立交通大學
電機與控制工程系
91
The discrete wavelet transform (DWT) technique has been widely used in signal processing and image processing. Since the DWT coefficients have the property of energy conservation in the low frequency part, it is suitable for data compression. In the recent industry standard, DWT has replaced DCT which is a main approach in image compression in JPEG2000 and MPEG4. Due to the drawback, the thesis focuses on the hardware architectures of 1-layer 1- dimensional DWT, multi-layer 1-dimensional DWT and Multi-layer 2-dimensional DWT which are the standard of JPEG2000. Based on the architecture, DWT and the inverse discrete wavelet transform (IDWT) can be integrated easily. Furthermore we can use the module design concept to implement DWT by different hardware architectures. Moreover, in the thesis, we use two different architectures to implement the multi-layer 1-dimensional DWT. Besides, accompanied with “2D-controller”the multi-layer 1-dimensional DWT can be adopted in multi-layer 2-dimension DWT hardware architecture. Consequently, the gate level simulation and P&R are done with Synopsys and Avant! tools. The chip has advantages in the ability of image processing, execution time and chip area.

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37

"Image Compression By Wavelet Transform." East Tennessee State University, 2001. http://etd-submit.etsu.edu/etd/theses/available/etd-0711101-121206/.

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38

"Parallelization of fast wavelet transform." Chinese University of Hong Kong, 1994. http://library.cuhk.edu.hk/record=b5895460.

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Shum Yu Hing.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1994.
Includes bibliographical references (leaves 140-143).
ABSTRACT --- p.1
Chapter 1. --- INTRODUCTION
Chapter 1.1. --- Fourier Analysis --- p.3
Chapter 1.2. --- Wavelet Analysis --- p.6
Chapter 1.3. --- Parallelization --- p.10
Chapter 1.3.1. --- Data Dependency Analysis
Chapter 2. --- LITERATURE SURVEY
Chapter 2.1. --- One Dimensional Fast Wavelet Transform (Discrete) --- p.13
Chapter 2.2. --- Shared Memory Architecture : Parallel Virtual Machine (PVM)
Chapter 2.3. --- Distributed Memory Architecture : Massively Parallel Machine (DECmpp) --- p.21
Chapter 3. --- THEORY
Chapter 3.1. --- Parallel Processing
Chapter 3.1.1. --- Amdahl ´ةs Law --- p.25
Chapter 3.1.2. --- Quality Factor --- p.31
Chapter 3.2. --- Parallel Architecture
Chapter 3.2.1. --- Pipelining --- p.32
Chapter 3.2.2. --- Vector Processors --- p.34
Chapter 3.2.3. --- Multiprocessor --- p.34
Chapter 3.2.4 --- Array Processors --- p.36
Chapter 3.2.5. --- Systolic Array Processing --- p.37
Chapter 3.2.6. --- Granularity --- p.40
Chapter 3.2.7. --- Load Balancing & Throughput --- p.42
Chapter 3.3. --- Parallel Programming --- p.43
Chapter 3.4. --- Parallel Numerical Algorithm
Chapter 3.4.1. --- Parallelism Within a Statement --- p.44
Chapter 3.4.2. --- Parallelism Between Statements --- p.47
Chapter 4. --- IMPLEMENTATION
Chapter 4.1. --- Sequential Version --- p.49
Chapter 4.2. --- Parallel Version
Chapter 4.2.1. --- Matrix Representation of Wavelet Transform
Chapter 4.2.1.1. --- Decomposition --- p.52
Chapter 4.2.1.2. --- Reconstruct ion --- p.55
Chapter 4.2.2. --- Parallel Virtual Machine (PVM)
Chapter 4.2.2.1. --- Parallel Algorithm
Chapter (a) --- HOST --- p.56
Chapter (b) --- NODE --- p.57
Chapter 4.2.2.2. --- Flowcharts --- p.59
Chapter 4.2.2.3. --- Timing Model Analysis --- p.65
Chapter 4.2.2.4 --- Quality Factor
Chapter (a) --- Decomposition --- p.71
Chapter (b) --- Reconstruction --- p.72
Chapter 4.2.3. --- Massively Parallel Machine - DECmpp --- p.73
Chapter 4.2.3.1. --- Parallel Algorithm for ACU & PEs
Chapter 4.2.3.2. --- Flowcharts --- p.75
Chapter 4.2.3.3. --- Timing Model Analysis
Chapter (a) --- Communication Strategy --- p.77
Chapter (b) --- Decomposition --- p.78
Chapter (c) --- Reconstruct ion --- p.87
Chapter 4.2.3.4. --- Quality Factor
Chapter (a) --- Decomposition --- p.89
Chapter (b) --- Reconstruction --- p.89
Chapter 4.2.3.5. --- Mapping --- p.92
Chapter 5. --- RESULT
Chapter 5.1. --- Parallel Virtual Machine (PVM)
Chapter 5.1.1. --- Sequential Version --- p.93
Chapter 5.1.2. --- Parallel Version --- p.103
Chapter 5.2. --- Massively Parallel Machine - DECmpp
Chapter 5.2.1. --- Sequential Vers ion --- p.104
Chapter 5.2.2. --- Parallel Version --- p.110
Chapter 5.3. --- Output File Generated from both machines --- p.118
Chapter 6. --- DISCUSSION
Chapter 6.1. --- Application on real time situation --- p.123
Chapter 6.2. --- Two dimensional or Multidimensional case --- p.123
Chapter 6.3. --- Block Algorithm Approach
Chapter 6.3.1. --- Blocked --- p.124
Chapter 6.3.2. --- Row Wrapped --- p.126
Chapter 6.4. --- Memory Requirement --- p.127
Chapter 6.5. --- Signal Size Prediction
Chapter 6.5.1. --- Method A --- p.131
Chapter 6.5.2. --- Method B --- p.133
Chapter 7. --- CONCLUSION --- p.134
Chapter 8. --- FUTURE MODIFICATION --- p.138
REFERENCE --- p.140
LISTING --- p.144
APPENDIX I - Technical Information of PVM --- p.145
Chapter II - --- Technical Information of DECmpp --- p.152
Chapter III - --- Some Tips/Guide --- p.165

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39

MING, CHANG KUANG, and 張光銘. "Texture Classification using Wavelet Transform." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/95894092784855595545.

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碩士
中華大學
電機工程學系碩士班
91
In the last decade , discrete wavelet transform (DWT) has proven to be a useful technique for a wide range of applications including signal analysis, signal compression , pattern recognition, biomedicine, and numerical analysis. In recent studies on image analysis an increasing effort has been carried out in the area of wavelet transform techniques for the discrimination and classification of textural images. This thesis presents an approach to the characterization of texture properties at multiple scales using the wavelet transform with wavelet basis and wavelet packet.

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40

Der, Lin Jen, and 林仁得. "Motion Estimation Using Wavelet Transform." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/57854011942187962832.

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41

Yu-ZhangYang and 楊玉章. "The Study of Pile Integrity Test Using Discrete Wavelet Transform and Complex Continuous Wavelet Transform." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/47t9e9.

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博士
國立成功大學
土木工程學系
106
The purpose of this research is to study in defect detecting for the concrete piles, offering the NDT methods to find out the defects whose size are less than 10%. The restriction of the signal analysis for traditional reflection method is that the small defects are not easy to be found. In this research, there are two ways to detect the defects of pile. The first method, the discrete wavelet transform (DWT) is applied in IR method. The results show that the defect is determined by introducing the DWT based procedure which would reduce the effects of the noise and clarify the signals in frequency domain, and thus it can improve the reliability of the evaluated small defect. Therefore, the resolution of the reflection signals on the defect and the constrained media would be increased when the DWT is introduced into the IR method. Second method is about using complex continuous wavelet transform (CCWT) to determine pile length and locations of defects on pile foundations by analyzing the time-frequency analysis in different frequency bands. The results show that complex continuous wavelet transform is not only able to provide high resolution results in different frequency bands, which are similar to those bands used by CCWT, but also simplifies the identification of the reflection of the defects. The location of the defects can then be easily determined by utilizing the analyzed phase diagram under the corresponding specific frequencies.

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42

Hong, Po-Sheng, and 洪博勝. "The Study of Wavelet Transform and Embedded Zerotree Wavelet Codec." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/79966812056968428112.

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碩士
長庚大學
電機工程研究所
90
With the progress of science and technology, the application range of digital images becomes more and more popular. However, the amount of data in a digital image is very large, so it is not practical to store and transmit a digital image in its original form. In general, a digital image needs to be compressed before it is stored or transmitted. One efficient method of image compression is to transform the digital image into signal bands with the wavelet transform, and then encode the signal bands with the EZW (Embedded Zero tree Wavelet) encoding scheme. In this thesis, we study the influences of using different wavelet transform schemes on the encoding efficiency of EZW. In our experiment, we measured the encoding efficiency of EZW with various wavelet transform schemes. We found that the SWP (Split Wavelet Pyramid), one variation of the traditional wavelet transform, can achieve better performance than the traditional wavelet transform.

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43

Wang, Jyh-Wei, and 王志雄. "The VLSI Design for Discrete Wavelet Transform and Inverse Discrete Wavelet Transform using Embedded Instruction Codes." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/06910225125080712632.

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Abstract:

碩士
國立交通大學
電機與控制工程系
89
The discrete wavelet transform (DWT) technique has been widely used in signal processing and image processing. Since the DWT coefficients have the property of energy conservation in the low frequency part, it is suitable for data compression. In the recent industry standard, DWT has replaced DCT which is a main approach in image compression in JPEG2000 and MPEG4. However, there are difficulties in implementation such as the heavy computation and complex operation procedures. Due to the drawback, the thesis purposes a design rule named “Embedded Instruction Code (EIC)”, as well as focus on the hardware architectures of 1-stage 1 dimension DWT, multi-stage 1 dimension DWT and Multi-stage 2 dimension DWT. Based on this rule, DWT and inverse discrete wavelet transform (IDWT) can be integrated easily. Furthermore we can use the module design concept to implement DWT by different hardware architectures. Using EIC, we can translate the computation of DWT and IDWT into the instruction codes of ALU. Moreover, the ALU architecture of 1-stage DWT is worked out by three different architectures. Besides, accompanied with “Recursive Pyramid Algorithm (RPA)” the EIC can be adopted in multi-stage 1 dimension DWT and multi-stage 2 dimension DWT. Consequently, the gate level simulation and P&R are done with Synopsys and Cadence tools. The chip has excellent advantages in the ability of image processing, execution time and chip area.

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44

Lee, Jeongmin. "Motion detection algorithm using wavelet transform." Thesis, 2003. http://hdl.handle.net/1957/31658.

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This thesis presents an algorithm that estimates motion in image sequence using wavelet transform. The motion detection is performed under unfavorable conditions of background movement, change of brightness, and noise. The algorithm is tolerant to brightness changes, noise, and small movement in the background. The false alarm rate of motion detection is reduced as compared to standard techniques. Using wavelet transform is numerically efficient and the storage requirements are significantly reduced. Also, a more accurate motion detection is achieved. Tests performed on real images show the effectiveness of this algorithm. Practical results of motion detection are presented.
Graduation date: 2003

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45

Tsung, Lin Jr, and 林志聰. "Wavelet transform of post-segmention ROI." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/55763756232542373465.

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碩士
大葉大學
資訊工程學系碩士班
93
Medical image need high image quality. But it is too large to using lossless image compression on total image.The large size make it impractical to transmit the image.The rigion of interest code supports the transmission of the medical image with a high compression rate and good quality, still this method has some defect.The ROI researches use the pre-segmentation approach to coding ROIs.The ROIs are decided and segmented befor encoding.If the decision of ROIs is error, fine feature of image will lose.This paper presents a post-segmentation ROI coding technique to avoid wrong decision.

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46

彭玉峰. "Wavelet Transform Applied on Speech Compression." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/51218865225905960850.

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47

Lin, Chan-Sheng, and 林展生. "Power Quality Analysis by Wavelet Transform." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/04880971287457796195.

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碩士
淡江大學
電機工程學系
91
The wavelet technique is proposed for the analysis of the characteristics of power quality problems. A brief theoretical background on the wavelet theory and suggestions of some applications in the area of power quality are presented. Gauss and Daubechies for wavelet transform are employed to analyze the fault transients for the development of a novel an analysis tool. The method has been tested on the analysis of various simulated disturbances of voltage waveform including harmonics, voltage flicker, momentary interruption voltage, voltage sag and voltage swell. Test results have demonstrated the practicality and advantages of the proposed method for the applications.

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48

"Image coding based on wavelet transform." 1998. http://library.cuhk.edu.hk/record=b6073117.

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Abstract:

Jianhua Chen.
Thesis (Ph.D.)--Chinese University of Hong kong, 1998.
Includes bibliographical references (p. 127-[134]).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Mode of access: World Wide Web.
Abstracts in English and Chinese.

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49

Huang, Sheng Zhong, and 黃聖鐘. "Radar target recognition by wavelet transform." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/39618003881742095560.

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50

Shen, Nu-Chuan, and 沈汝川. "Sectioned Convoluion for Discrete Wavelet Transform." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/79034618082699960740.

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碩士
國立臺灣大學
電信工程學研究所
96
Discrete wavelet transform (DWT) is a very popular mathematical tool. It has been widely applied in engineering, signal processing and image processing, etc. In this thesis, we will introduce the DWT and the application of it and then I will use a method called sectioned convolution that proposed in this thesis to reduce the complexity of the DWT. The sectioned convolution is a fast algorithm of convolution by splitting the input of signal into section by section with sectioned length L, so we do not have to do the convolution until all the signal is received. It not only finds out a way to solve the delay problem but also reduces the computation time and computation complexity very much. The sectioned convolution discrete wavelet transform (SCDWT) is an application of sectioned convolution. It replaces all the traditional convolution computation in the DWT into the sectioned convolution. The efficiency implementation sectioned convolution discrete wavelet transform (EISCDWT) is an efficient way to implement the DWT. Its concept just likes the efficient implementation discrete wavelet transform but we use the sectioned convolution to instead of the traditional convolution. By this replacement, we can reduce the computation complexity and computation time. Beside the advantages that we mention above, there is another advantage that we also reduce the system complexity. Because we split the signal into the same length L, the point of FFT is fixed, the complexity of system is reduced. Recently, there are many research works about the DWT. The DWT has been used for many applications. We believe that the algorithm that we proposed in this thesis can make the DWT more powerful and have a lot of potentiality in the future. In this thesis, I will introduce the research works about the DWT systematically, including the research works of my professor and I and do a detailed comparison to the previous works. In Chap. 1, I will introduce the basic ideas and history of the wavelet transform. In Chap. 2, I will introduce the definition and the computation complexity of the DWT, including the detailed derivation, property. In Chap. 3, I will introduce the applications of the DWT simply. In Chap. 4, I will introduce the EIDWT and compare it to the traditional DWT in computation complexity. In Chap. 5, I will introduce the sectioned convolution and compare it to the traditional convolution on computation time and computation complexity. Considering the fair competition, all the programmings in my thesis are written by myself. In Chap. 9, I will do a detailed analysis of SCDWT and EISCDWT and a comparison between the DWT, SCDWT and EISCDWT. In the end of this chapter, I will compare the JPEG2000 with EISCDWT and JPEG wit DCT. In Chaps. 7, 8, I will introduce other researches of method to improve the efficiency of DWT May this thesis be helpful for you.

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