In this thesis, a method to calculate scaling function coefficients for a new bi-orthogonal wavelet family derived directly from an impulse response waveform is presented. In literature, the Daubechies wavelets (DB wavelet) and the Morlet wavelet are the most commonly used wavelets for the dyadic wavelet transform (DWT) and the continuous wavelet transform (CWT), respectively. For a specific vibration signal processing application, a wavelet basis that is similar or is derived directly from the signal being studied proves to be superior to the commonly used wavelet basis. To assure a wavelet basis has a direct relationship to the signal being studied, a new formula is proposed to calculate coefficients which capture the characteristics of an impulse response waveform. The calculated coefficients are then used to develop a new bi-orthogonal wavelet family.

An experimental technique has been presented to probe the mechanical behavior of thin film materials. The method is capable of tensile testing thin films on substrate and free-standing thin film specimens. A mechanical gripper was designed to address the current challenges in gripping thin film specimens. In order to measure the strain field across the gage section, the moire interferometry technique was used and the respective optical setup was designed. A versatile microfabrication process has been developed to fabricate free-standing dog-bone specimens. Aluminum was used as the model material; however, any other metallization material can be integrated in the process. Thin film specimens have been characterized using SEM, AFM, and TEM. A process has been developed to fabrication diffraction gratings on the specimen by FIB milling. Different grating geometries were fabricated and the diffraction efficiency of the gratings was characterized. The structural damage induced by the Ga+ ions during the FIB milling of the specimens was partially characterized using STEM and EDS. In order to extract the strain field information from the moire interferogram data, a numerical postprocessing technique was developed based on continuous wavelet transforms (CWT). The method was applied on simulated uniform and nonuniform strain fields and the wavelet parameters were tuned to achieve the best spatial localization and strain accuracy.

A method for constructing a highly scalable bit stream for video coding is presented in detail and implemented in a demo application with a GUI in the Windows Vista operating system. The video codec uses the Discrete Wavelet Transform in both spatial and temporal directions together with a zerotree quantizer to achieve a highly scalable bit stream in the senses of quality, spatial resolution and frame rate. / I detta arbete presenteras en metod för att skapa en mycket skalbar videoström. Metoden implementeras sedan i sin helhet i programspråken C och C++ med ett grafiskt användargränssnitt på operativsystemet Windows Vista. I metoden används den diskreta wavelettransformen i såväl de spatiella dimensionerna som tidsdimensionen tillsammans med en nollträdskvantiserare för att åstakomma en skalbar videoström i avseendena bildkvalitet, skärmupplösning och antal bildrutor per sekund.

In typical statistical parametric mapping (SPM) of fMRI data, the functional data are pre-smoothed using a Gaussian kernel to reduce noise at the cost of losing spatial specificity. Wavelet approaches have been incorporated in such analysis by enabling an efficient representation of the underlying brain activity through spatial transformation of the original, un-smoothed data; a successful framework is the wavelet-based statistical parametric mapping (WSPM) which enables integrated wavelet processing and spatial statistical testing. However, in using the conventional wavelets, the functional data are considered to lie on a regular Euclidean space, which is far from reality, since the underlying signal lies within the complex, non rectangular domain of the cerebral cortex. Thus, using wavelets that function on more complex domains such as a graph holds promise. The aim of the current project has been to integrate a recently developed spectral graph wavelet transform as an advanced transformation for fMRI brain data into the WSPM framework. We introduce the design of suitable weighted and un-weighted graphs which are defined based on the convoluted structure of the cerebral cortex. An optimal design of spatially localized spectral graph wavelet frames suitable for the designed large scale graphs is introduced. We have evaluated the proposed graph approach for fMRI analysis on both simulated as well as real data. The results show a superior performance in detecting fine structured, spatially localized activation maps compared to the use of conventional wavelets, as well as normal SPM. The approach is implemented in an SPM compatible manner, and is included as an extension to the WSPM toolbox for SPM.

This thesis studies the application of the wavelet filter bank (WFB) in perceptual audio coding by providing brief overviews of perceptual coding, psychoacoustics, wavelet theory, and existing wavelet coding algorithms. Furthermore, it describes the poor frequency localization property of the WFB and explores one filter design method, in particular, for improving channel separation between the wavelet bands. A wavelet audio coder has also been developed by the author to test the new filters. Preliminary tests indicate that the new filters provide some improvement over other wavelet filters when coding audio signals that are stationary-like and contain only a few harmonic components, and similar results for other types of audio signals that contain many spectral and temporal components. It has been found that the WFB provides a flexible decomposition scheme through the choice of the tree structure and basis filter, but at the cost of poor localization properties. This flexibility can be a benefit in the context of audio coding but the poor localization properties represent a drawback. Determining ways to fully utilize this flexibility, while minimizing the effects of poor time-frequency localization, is an area that is still very much open for research.

An experimental technique has been presented to probe the mechanical behavior of thin film materials. The method is capable of tensile testing thin films on substrate and free-standing thin film specimens. A mechanical gripper was designed to address the current challenges in gripping thin film specimens. In order to measure the strain field across the gage section, the moire interferometry technique was used and the respective optical setup was designed. A versatile microfabrication process has been developed to fabricate free-standing dog-bone specimens. Aluminum was used as the model material; however, any other metallization material can be integrated in the process. Thin film specimens have been characterized using SEM, AFM, and TEM. A process has been developed to fabrication diffraction gratings on the specimen by FIB milling. Different grating geometries were fabricated and the diffraction efficiency of the gratings was characterized. The structural damage induced by the Ga+ ions during the FIB milling of the specimens was partially characterized using STEM and EDS. In order to extract the strain field information from the moire interferogram data, a numerical postprocessing technique was developed based on continuous wavelet transforms (CWT). The method was applied on simulated uniform and nonuniform strain fields and the wavelet parameters were tuned to achieve the best spatial localization and strain accuracy.

This thesis focused on developing a new wavelet for use with the continuous wavelet transform, a new detection method and two de-noising algorithms for rolling element bearing fault signals. The work is based on the continuous wavelet transform and implements a unique Fourier Series estimation algorithm that allows for least squares estimation of arbitrary frequency components of a signal. The final results of the research also included use of the developed detection algorithm for a novel method of estimating the center frequency and bandwidth for use with the industry standard detection algorithm, envelope demodulation, based on actual fault data. Finally, the algorithms and wavelets developed in this paper were tested against seven other wavelet based de-noising algorithms and shown to be superior for the de-noising and detection of inner and outer rolling element race faults.

This dissertation studies the performance of synchrophasor measurement obtained using substation Intelligent Electronic Devices (IEDs) and proposes new algorithms and test methodology to improve and verify their performance when used in power system applications. To improve the dynamic performance when exposed to sinusoidal waveform distortions, such as modulation, frequency drift, abrupt change in magnitude, etc, an adaptive approach for accurately estimating phasors while eliminating the effect of various transient disturbances on voltages and currents is proposed. The algorithm pre-analyzes the waveform spanning the window of observation to identify and localize the discontinuities which affect the accuracy of phasor computation. A quadratic polynomial signal model is used to improve the accuracy of phasor estimates during power oscillations. Extensive experimental results demonstrate the advantages. This algorithm can also be used as reference algorithm for testing the performance of the devices extracting synchronized phasor measurements. A novel approach for estimating the phasor parameters, namely frequency, magnitude and angle in real time based on a newly constructed recursive wavelet transform is developed. This algorithm is capable of estimating the phasor parameters in a quarter cycle of an input signal. It features fast response and achieves high accuracy over a wide range of frequency deviations. The signal sampling rate and data window size can be selected to meet desirable application requirements, such as fast response, high accuracy and low computational burden. In addition, an approach for eliminating a decaying DC component, which has significant impact on estimating phasors, is proposed using recursive wavelet transform. This dissertation develops test methodology and tools for evaluating the conformance to standard-define performance for synchrophasor measurements. An interleaving technique applied on output phasors can equivalently increase the reporting rate and can precisely depict the transient behavior of a synchrophasor unit under the step input. A reference phasor estimator is developed and implemented. Various types of Phasor Measurement Units (PMUs) and PMU-enabled IEDs (Intelligent Electronic Devices) and time synchronization options have been tested against the standards using the proposed algorithm. Test results demonstrate the effectiveness and advantages.

This dissertation studies the causes and mechanism of power system cascading outages and proposes the improved interactive scheme between system-wide and local levels of monitoring and control to quickly detect, classify and mitigate the cascading outages in power system. A novel method for evaluating the vulnerability of individual components as well as the whole power system, which is named as weighted vulnerability analysis, is developed. Betweenness centrality is used to measure the importance of each bus and transmission line in the modeled power system network, which is in turn used to determine the weights for the weighted vulnerability index. It features fast reaction time and achieves higher accuracy when dealing with the cascading outage detection, classification and mitigation over the traditional methods. The overload problem due to power flow redistribution after one line tripped is a critical factor contributing to the cascading outages. A parallel corridor searching method is proposed to quickly identify the most vulnerable components after tripping a transmission line. The power system topology model can be simplified into state graph after searching the domains for each generator, the commons for each bus, and links between the commons. The parallel corridor will be determined by searching the links and commons in system topology graph for the given state of power system operation. During stressed operating state, either stable or unstable power swing may have impacts on distance relay judgment and lead to relay misoperation, which will result in the power system lines being tripped and as a consequence power system operating state becoming even more stressful. At the local level, an enhanced fault detection tool during power system swing is developed to reduce the chance of relay misoperation. Comprehensive simulation studies have been implemented by using the IEEE 39-bus and 118-bus test systems. The results are promising because: The results from weighted vulnerability analysis could provide better system situational awareness and accurate information about the disturbance; The results form parallel corridor search method could identify the most vulnerable lines after power re-distribution, which will give operator time to take remedial actions; The results from new travelling wave and wavelet transform based fault detection could reduce the impact of relay misoperation.

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.