In this thesis, a method proposed by Han et al. [40] for detecting and locating damage in a structural member was adapted. The method was based on the energies that were calculated from the CWT coefficients of vibrational response of a cantilever beam. A transverse cut at varying depths was introduced. The presence and location of crack was investigated by processing experimentally acquired acceleration signals. Results of modal analysis and wavelet analysis of the beam with different cut depths were compared. In addition, effect of using different mother wavelets in CWT analysis for damage detection capability was investigated. Acceleration data were analyzed through CWT at different scales and CWT coefficients were calculated. Those CWT coefficients obtained from different scales were evaluated from the standpoint of damage detection. Effectiveness of energy indices associated with CWT coefficients in damage detection was demonstrated as independent of the type of mother wavelet.

A lot of research have been carried in the field of optical character recognition. Selection of a feature extraction scheme is probably the most important factor in achieving high recognition performance. Fourier and wavelet transforms are among the popular feature extraction techniques allowing rotation invariant recognition. The performance of a particular feature extraction technique depends on the used dataset and the classifier. Dierent feature types may need dierent types of classifiers. In this thesis Fourier and wavelet based features are compared in terms of classification accuracy. The influence of noise with dierent intensities is also analyzed. Character recognition system is implemented with Matlab. Isolated gray scale character image first transformed into one dimensional function. Then, set of features are extracted. The feature set are fed to a classifier. Two types of classifier were used, Nearest Neighbor and Linear Discriminant Function. The performance of each feature extraction and classification methods were tested on various rotated and scaled character images.

The main goal of this research is to estimate the model parameters and to detect multiple change points in the long memory parameter of Gaussian ARFIMA(p, d, q) processes. Our approach is Bayesian and inference is done on wavelet domain. Long memory processes have been widely used in many scientific fields such as economics, finance and computer science. Wavelets have a strong connection with these processes. The ability of wavelets to simultaneously localize a process in time and scale domain results in representing many dense variance-covariance matrices of the process in a sparse form. A wavelet-based Bayesian estimation procedure for the parameters of Gaussian ARFIMA(p, d, q) process is proposed. This entails calculating the exact variance-covariance matrix of given ARFIMA(p, d, q) process and transforming them into wavelet domains using two dimensional discrete wavelet transform (DWT2). Metropolis algorithm is used for sampling the model parameters from the posterior distributions. Simulations with different values of the parameters and of the sample size are performed. A real data application to the U.S. GNP data is also reported. Detection and estimation of multiple change points in the long memory parameter is also investigated. The reversible jump MCMC is used for posterior inference. Performances are evaluated on simulated data and on the Nile River dataset.

Ultrasonic guided waves having the ability to inspect long distance pipeline is one of the non-destructive testing methods. The reflected echoes as well as mode conversion phenomena indicate the presence of defect or other features on the pipe. To study the feasibility of guided wave quantification of sludge inside pipes, this thesis applies the transient simulation by finite element method to analyze the scattering of the guided T(0,1) mode by non-axisymmetry layer inside a pipe. Both the Two-dimensional Fourier transform and Wavelet transform were used to process the signals to understand the scattering behavior. The numerical analyses revealed the following phenomena. First, partial energy of the T(0,1) mode will leaky into the asymmetric layer when T(0,1) mode propagates along the pipe and impinge onto the asymmetric layer inside a pipe named a composite pipe. The T(0,1) mode will convert to the propagating modes of the composite pipe model. Secondly, the composite pipe will reflect the T(0,1) and modes of higher circumferential order. The percentage of asymmetric layer inside a pipe is one of the parameter controlling the reflection spectrum response. To sum up, in this study, the reflection spectrum response could used to predict the quantified accumulation of sludge by wavelet transform through time-frequency analysis.

Using ultrasonic guided waves can achieve long range inspection along the pipeline rapidly. The presence of defect or other features on the pipe were identified by analyzing the reflected echoes as well as mode conversion phenomena. However, it is difficult for guided wave to find a minor corrosion, such as pitting. Therefore, a study of the reflection of torsional T(0,1) mode from pits on the pipe has been carried out and an advanced signal processing method wavelet transform is adopted to process the reflected echoes in this study. In order to understand that characteristic of the reflected echoes of pits, the propagation of guided wave T(0,1) through pits was simulated by the finite element method. The frequency response of the signal reflected from the pits with different sizes was discussed both by finite element method and experimental method. Then, we discuss two types of pitting including regular- distributed pitting and the random-distributed pitting. We not only discuss the relation between the axial length of regular pitting and wave length of the T(0,1) mode, but also the reflected singal of four random pittings. The experiments were performed on 3 inch carbon steel pipe for measuring the reflected signals from different pittings with different frequencies. The results of the simulation, indicate that the wave was easily scattered by pitting because the shape of geometry. It is the reason of reducing the amplitude of reflected signals. To receive a dominate signal reflected from pitting, the excitation with higher frequency was choosen within the frequency range of interest. The experimental results indicate that the signals would be too weak to be detected by guided waves when the estimated cross sectional loss of the pitting is less than 2 percent. However, the results after wavelet transform showed the feasibility of improving the abilities of detecting minor pitting. In the case of regular pitting, the maximu value of the reflected signal appeared when the axial length of the pitting equals to the 66 % of the wavelength. It is because the constructive interference. The mode conversion phenomena is another behavior of the reflected signal cased by the non-axissymetric geometry of the pitting. As for the random pitting, The reflected echo shows different behavior with the regular pitting. The amplitude of the signal is bigger with lower frequency we use. The different level of random pitting on the pipe were also identified successfully by wavelet transform. Understanding the phenomena of interaction between the guided wave and the pitting is helpful to the guided wave inspection.

Time-frequency analysis techniques are proposed as a necessary tool for the analysis of acoustics generated by helicopter transient maneuvering flight. Such techniques are necessary as the acoustic signals related to transient maneuvers are inherently unsteady. The wavelet transform is proposed as an appropriate tool, and it is compared to the more standard short-time Fourier transform technique through an investigation using several appropriately sized interrogation windows. It is shown that the wavelet transform provides a consistent spectral representation, regardless of employed window size. The short-time Fourier transform, however, provides spectral amplitudes that are highly dependent on the size of the interrogation window, and so is not an appropriate tool for this situation. An extraction method is also proposed to investigate blade-vortex interaction noise emitted during helicopter transient maneuvering flight. The extraction method allows for the investigation of blade-vortex interactions independent of other sound sources. The method is based on filtering the spectral data calculated through the wavelet transform technique. The filter identifies blade-vortex interactions through their high amplitude, high frequency impulsive content. The filtered wavelet coefficients are then inverse transformed to create a pressure signature solely related to blade-vortex interactions. This extraction technique, along with a prescribed wake model, is applied to experimental data extracted from three separate flight maneuvers performed by a Bell 430 helicopter. The maneuvers investigated include a steady level flight, fast- and medium-speed advancing side roll maneuvers. A sensitivity analysis is performed in order to determine the optimal tuning parameters employed by the filtering technique. For the cases studied, the optimized tuning parameters were shown to be frequencies above 7 main rotor harmonics, and amplitudes stronger than 25% (−6 dB) of the energy in the main rotor harmonic. Further, it is shown that blade-vortex interactions can be accurately extracted so long as the blade-vortex interaction peak energy signal is greater or equal to the energy in the main rotor harmonic. An in-depth investigation of the changes in the blade-vortex interaction signal during transient advancing side roll maneuvers is then conducted. It is shown that the sound pressure level related to blade-vortex interactions, shifts from the advancing side, to the retreating side of the vehicle during roll entry. This shift is predicted adequately by the prescribed wake model. However, the prescribed wake model is shown to be inadequate for the prediction of blade-vortex interaction miss distance, as it does not respond to the roll rate of the vehicle. It is further shown that the sound pressure levels are positively linked to the roll rate of the vehicle. Similar sound pressure level directivities and amplitudes can be seen when vehicle roll rates are comparable. The extraction method is shown to perform admirably throughout each maneuver. One limitation with the technique is identified, and a proposal to mitigate its effects is made. The limitation occurs when the main rotor harmonic energy drops below an arbitrary threshold. When this happens, a decreased spectral amplitude is required for filtering; which leads to the extraction of high frequency noise unrelated to blade-vortex interactions. It is shown, however, that this occurs only when there are no blade-vortex interactions present. Further, the resulting sound pressure level is identifiable as it is significantly less than the peak blade-vortex interaction sound pressure level. Thus the effects of this limitation are shown to be negligible. / text

Manual sleep scoring, executed by visual inspection of the EEG, is a very time consuming activity, with an inherent subjective decisional component. Automatic sleep scoring could ease the job of the technicians, because faster and more accurate. Frequency information characterizing the main brain rhythms, and consequently the sleep stages, needs to be extracted from the EEG data. The approach used in this study involves a wavelet filter bank for the EEG frequency features extraction. The wavelet packet analysis tool in MATLAB has been employed and the frequency information subsequently used for the automatic sleep scoring by means of an artificial neural network. Finally, the automatic sleep scoring has been employed for epoching the fMRI data, thus allowing for studying brain resting state networks during sleep. Three resting state networks have been inspected; the Default Mode Network, The Attentional Network and the Salience Network. The networks functional connectivity variations have been inspected in both healthy and narcoleptic subjects. Narcolepsy is a neurobiological disorder characterized by an excessive daytime sleepiness, whose aetiology may be linked to a loss of neurons in the hypothalamic region.

Στο πείραμα των μικροσυστοιχιών, η απόκτηση εικόνας συνοδεύεται πάντα από θόρυβο, ο οποίος είναι έμφυτος σε τέτοιου είδους διεργασίες. Είναι λοιπόν επιτακτική ανάγκη να χρησιμοποιηθούν τεχνικές προς καταστολή αυτού. Στην παρούσα εργασία αναλύονται μέθοδοι και παρουσιάζονται τα αποτελέσματά τους σε 5 επιλεγμένα παραδείγματα. Ιδιαίτερη έμφαση δίνεται στο wavelet denoising και συγκεκριμένα στους αλγορίθμους soft thresholding, hard thresholding και stationary wavelet transform. / The subject of this diploma thesis is the manufacturing of a driver assistance system. Robust and reliable vehicle detection from images acquired by a moving vehicle (i.e., on road vehicle detection) is an important problem with applications to driver assistance systems and autonomous, self-guided vehicles. The focus of this diploma is on the issues of feature extraction and classification for rear-view vehicle detection. Specifically, by treating the problem of vehicle detection as a two-class classification problem, we have investigated several different feature extraction methods such as wavelets and Gabor filters. To evaluate the extracted features, we have experimented with two popular classifiers, neural networks and support vector machines (SVMs).

The major task of imaging systems used in non-destructive testing is detection of defects (flaws, holes) echoes and evaluation or their dimensions and position. Images generated by direct imaging are poor quality due to diffraction, coherent echoes, limited capabilities of system, white noise. So acoustic images and optic images are very different. Solving these problems, numerical methods are used for signal processing and analysis. An application for ultrasonic signal processing of wavelet transformations was investigated in the work. The investigation was signals distortion type and level when wavelets transformation may give effective results. The investigation was performed using modeling and signal processing of the experimental signals.

Šiame darbe pateikiama trumpa efektyvaus vaizdų kodavimo metodų ir požiūrių apžvalga. Susipažįstama su diskrečiosiomis (Haaro, Daubechies) bangelių transformacijomis bei įvertinamos jų specifinės savybės: diskretaus bangelių spektro koeficiento sąsaja su vaizdo fragmentu, nulinių medžių egzistavimas spektre. Darbo tikslas – įvertinus diskrečiųjų bangelių transformacijos savybes, algoritmizuoti, realizuoti ir ištirti vieną perspektyviausių progresyviojo skaitmeninių vaizdų kodavimo algoritmų EZW (Embedded-Zerotree-Wavelet). / This paper discusses specific properties of the discrete orthogonal wavelet transform, namely: relationships between the wavelet coefficients and image fragments, existence of zerotrees in the discrete wavelet spectrum of an image, etc. In parallels, the progressive image encoding idea and an efficient image encoding/decoding algorithm EZW (Embedded-Zerotree-Wavelet), based on the discrete wavelet (Haar, Daubechies) transform, are presented. Some preliminary experimental analysis results are discussed.