In the aspect of electric-ship grounding, the time-domain behavior of the ship hull is needed. The grounding scheme impacts the nature of voltage transients during switching events and faults, identifiability and locatability of ground faults, fault current levels, and power quality. Due to the large size of ships compared with the wavelengths of the desired signals, time-domain measurement or simulation is a time-consuming process. Therefore, it is preferred that the behavior be studied in the frequency-domain. In the frequency-domain one can break down the whole ship hull into small blocks and find the frequency behavior of each block (scattering parameters) in a short time and then connect these blocks and find the whole ship hull scattering parameters. Then these scattering pa- rameters should be transferred to the time-domain. The problem with this process is that the measured frequency-domain data (or the simulated data) is band-limited so, while calculating time-domain solutions, due to missing DC and low frequency content the time-domain response encounters causality, passivity and time-delay problems. Despite availability of several software and simulation packets that convert frequency-domain information to time-domain, all are known to suffer from the above mentioned problems. This dissertation provides a solution for computing the Time-Domain Impulse-Response for a system by using its measured or simulated scattering parameters. In this regard, a novel wavelet computational approach is introduced.

Optical lithography is an indispensible step in the process flow of Design for Manufacturability (DFM). Optical lithography simulation is a compute intensive task and simulation performance, or lack thereof can be a determining factor in time to market. Thus, the efficiency of lithography simulation is of paramount importance. Coherent decomposition is a popular simulation technique for aerial imaging simulation. In this thesis, we propose an approximate simulation technique based on the 2D wavelet transform and use a number of optimization methods to further improve polygon edge detection. Results show that the proposed method suffers from an average error of less than 6% when compared with the coherent decomposition method. The benefits of the proposed method are (i) > 20X increase in performance and more importantly (ii) it allows very large circuits to be simulated while some commercial tools are severely capacity limited and cannot even simulate a circuit as small as ISCAS-85 benchmark C17. Approximate simulation is quite attractive for layout optimization where it may be used in a loop and may even be acceptable for final layout verification.

A method of sensor location selection is introduced for distributed parameter systems. In this method, the sensitivities of spatial outputs to model parameters are computed by a model and transformed via continuous wavelet transforms into the time-scale domain to characterize the shape attributes of output sensitivities and accentuate their differences. Regions are then sought in the time-scale plane wherein the wavelet coefficient of an output-sensitivity surpasses all the others’ as indication of the output sensitivity’s uniqueness. This method yields a comprehensive account of identifiability each output provides for the model parameters as the basis of output selection. This output selection strategy is evaluated for a numerical case of pollutant dispersion by advection and discussion in a two-dimensional area.

This paper demonstrates the implementation of R-CNN in terms of electromyography-related signals to recognize hand gestures. The signal acquisition is implemented using electrodes situated on the forearm, and the biomedical signals are generated to perform the signals preprocessing using wavelet packet transform to perform the feature extraction. The R-CNN methodology is used to map the specific features that are acquired from the wavelet power spectrum to validate and train how the architecture is framed. Additionally, the real-time test is completed to reach the accuracy of 96.48% compared to the related methods. This kind of result proves that the proposed work has the highest amount of accuracy in recognizing the gestures.

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In this thesis, we establish the underlying research background necessary for tackling the problem of phase-shifting in the wavelet transform domain. Solving this problem is the key to reducing the redundancy and huge storage requirement in Image-Based Rendering (IBR) applications, which utilize wavelets. Image-based methods for rendering of dynamic glossy objects do not truly scale to all possible frequencies and high sampling rates without trading storage, glossiness, or computational time, while varying both lighting and viewpoint. This is due to the fact that current approaches are limited to precomputed radiance transfer (PRT), which is prohibitively expensive in terms of memory requirements when both lighting and viewpoint variation are required together with high sampling rates for high frequency lighting of glossy material. At the root of the above problem is the lack of a closed-form run-time solution to the nontrivial problem of rotating wavelets, which we solve in this thesis. We specifically target Haar wavelets, which provide the most efficient solution to solving the tripleproduct integral, which in turn is fundamental to solving the environment lighting problem. The problem is divided into three main steps, each of which provides several key theoretical contributions. First, we derive closed-form expressions for linear phase-shifting in the Haar domain for one-dimensional signals, which can be generalized to N-dimensional signals due to separability. Second, we derive closed-form expressions for linear phase-shifting for two-dimensional signals that are projected using the non-separable Haar transform. For both cases, we show that the coefficients of the shifted data can be computed solely by using the coefficients of the original data. We also derive closed-form expressions for non-integer shifts, which has not been reported before. As an application example of these results, we apply the new formulae to image shifting, rotation and interpolation, and demonstrate the superiority of the proposed solutions to existing methods. In the third step, we establish a solution for non-linear phase-shifting of two-dimensional non-separable Haar-transformed signals, which is directly applicable to the original problem of image-based rendering. Our solution is the first attempt to provide an analytic solution to the difficult problem of rotating wavelets in the transform domain.

Prolonged performance of repetitive movements can lead to muscle fatigue, negatively impacting human performance. As a result, researchers have explored methods to effectively assess and quantify this phenomenon, where surface electromyography (sEMG) is a popular method to reveal information regarding muscle contractions. The continuous wavelet transform (CWT) captures the instantaneous frequency components of signals, which make it suitable for sEMG analyses of dynamic muscle contractions. Moreover, sample entropy (SampEn) can be used to quantify the complexity of the sEMG signal, which provides novel insights for assessing muscle fatigue. However, the amount of research on sEMG complexity analyses to assess muscle fatigue during dynamic contractions is limited. Therefore, the goal of this work was to: 1) calculate and compare the major frequency components (MFC) from CWT and modified SampEn (MSE) of sEMG signals during a repetitive trunk flexion-extension (F-E) task; and 2) determine which sEMG metric is more closely related to ground truth fatigue indicators including the visual analogue scale (VAS), maximum pulling force, and kinematic variability of movements. Seven male and five female participants performed up to twelve sets of 50 repetitive trunk FE movements based on pre-defined stopping criteria. Their VAS and maximum pulling strength were measured immediately after each set. The MFC from CWT and the MSE values were calculated from both the left and the right lumbar erector spinae (LES) throughout the movements. Trunk dynamic kinematic variability of every set was quantified by the spine motion composite index (SMCI). Repeated measures correlation coefficients (r) were used to calculate the relationship between MFC and MSE, as well as between these outcome variables and VAS, maximum pulling force, and SMCI across all participants. Visual inspection revealed that on average that both the MFC and the MSE of sEMG signals decreased as the fatiguing protocol progressed, where a significant correlation was found between the two sEMG metrics (r = 0.270, p = 0.006). No significant correlations were found between the two sEMG measures and the maximum pulling strength (r_MFC = 0.101, p = 0.313; r_MSE = 0.193, p = 0.051). Nevertheless, both sEMG metrics showed significant correlations with fatigue VAS, with the MFC having stronger correlations across all the participants (r_MFC = −0.602, p < 0.001) than the MSE (r_MSE = −0.248, p = 0.011). Significant negative correlations were also observed between the SMCI and both sEMG MFC (r_MFC = −0.268, p = 0.010) and MSE (r_MSE = −0.335, p = 0.001). Both sEMG metrics mapped onto the perceived fatigue and movement pattern variations during the task, suggesting they could be used for assessing fatigue during dynamic movements. However, the MFC had a stronger correlation with participants' perceived fatigue whereas MSE was more strongly correlated with kinematic variability. Continued research is required to further examine these relationships, as well as determine the best method of assessing changes in force output with muscle fatigue.

Despite being the prefered approach for still-image compression for nearly a decade, wavelet-based coding for video has been slow to emerge, due primarily to the fact that the shift variance of the discrete wavelet transform hinders motion estimation and compensation crucial to modern video coders. Recently it has been recognized that a redundant, or overcomplete, wavelet transform is shift invariant and thus permits motion prediction in the wavelet domain. In this dissertation, other uses for the redundancy of overcomplete wavelet transforms in video coding are explored. First, it is demonstrated that the redundant-wavelet domain facilitates the placement of an irregular triangular mesh to video images, thereby exploiting transform redundancy to implement geometries for motion estimation and compensation more general than the traditional block structure widely employed. As the second contribution of this dissertation, a new form of multihypothesis prediction, redundant wavelet multihypothesis, is presented. This new approach to motion estimation and compensation produces motion predictions that are diverse in transform phase to increase prediction accuracy. Finally, it is demonstrated that the proposed redundant-wavelet strategies complement existing advanced video-coding techniques and produce significant performance improvements in a battery of experimental results.