The High Resolution Electrocardiogram (HRECG) is used to detect Ventricular Late Potentials (VLPs) in post-myocardial infarction patients. VLPs are low-amplitude, high-frequency signals that are usually found within the terminal part of the QRS complex. The aim of this research was to develop possible alternative methods and improve existing methods of detecting VLP activity. There are two main topics in this work: applications of the Continuous Wavelet Transform (CWT) and the Discrete Wavelet Transform (DWT) to the HRECG. For the CWT application, a Fractionation Factor (FF) method proposed by previous work was further investigated and improved by combining the CWT and DWT for distinction between patients with and those without VLPs. A Differential Fractionation Factor was proposed as an alternative approach to the FF with better results. Observation in the time-scale plot showed a difference in the energy distribution. A 2-dimensional Fractionation Factor was proposed to quantify this difference. A new concept of local intermittency was investigated to exhibit energy nonuniformity and then a Local Intermittency Factor was developed to quantify the degree of nonuniformity. The energy computed with the CWT was also used for patient distinction. Patients with VLPs may be also characterised by a slow rate of energy decay. The CWT can reveal a difference in ECG irregularity between the patients. A new approach of approximate entropy was implemented to quantify this irregularity. For the DWT application, the DWT can reveal irregularity of VLP activity and it was quantified by the approximate entropy to identify patients with VLPs. The wavelet entropy was utilised as an alternative method to the FF. The energy computed with the DWT was used for patient classification. The potentially promising results of both the CWT and DWT applications were obtained from the methods of computing the energy and approximate entropy

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.

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.

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.

The safety of pipelines distributed in the infrastructure of many industries has become very important since the industrial revolution. The guided ultrasonic wave technique can provide the possibility for rapid screening in long pipelines with corrosion. Especially the torsional mode T(0,1) of guided waves has been used in the cases of the pipe in the hidden region substantially. The ability of evaluating the inaccessible areas of the pipe makes the guided ultrasonic wave technique sit high on the roster of non-destructive testing tool for pipe inspection. However, the problem arises when attempting to detect the corrosions at the welded support bracket or under the bitumen coating on the pipe. The signal reflected from the corrosion will be covered by a large signal induced by the welded support or attenuated by the bitumen coating seriously. Therefore, the effects of welded support and bitumen coating on the T(0,1) mode are investigated by the experimental and the simulative methods. The continuous wavelet transform analysis is the signal processing method to extract the hidden signal of corrosion in this dissertation. There are five test pipes in the experiments. The response of the normal welded support is studied on the #1 test pipe. The #2 test pipe is used for attenuation investigation. The reflected signals of the features on the #3, #4, and #5 test pipes are measured and processed by continuous wavelet transform during defect detection process. In addition, the linear hexahedron elements are used to build the finite element models of the 6-inch steel pipe with support bracket and the pipe with bitumen coating. It is found that the effects of support bracket on the reflection comprise mode conversion, delayed appearance, trailing echoes, and frequency dependent behavior. When the T(0,1) mode impinges on to the support bracket, it will convert into the A0 mode inside the support due to the circumferential disturbance on the pipe surface. The reflection of the support bracket is identified as three parts formed by the direct echo, delayed echo and the trailing echo. The constructive interference of the A0 mode reflecting from the boundaries inside the support causes that the reflection spectrum shows two maxima peak at around 20-22 kHz (frequency regime of 0.0) and 32-34 kHz (frequency regime of 4.0) from both the experimental and simulated results. For the bitumen coating, the data collected from the welds and defects under the bitumen coating on the #2 test pipe show the attenuation effect on guided wave propagation and the difficulty of minor corrosion detection. In the finite element model of coated pipe, the results of predicted attenuation curves of T(0,1) mode indicate that the attenuation effect on guided wave propagation is aggravated with the increased value of the thickness, density or damping factor of the coated layer. Especially, in the case of 5-mm, the predicted attenuation curve shows a maximum point. Before this point, the attenuation increases with the operating frequency. For long range pipe inspection, it is the best way to avoid choosing the operating frequency around the corresponding frequency of the point. The measured data of corrosion affected by the welded support or the coated bitumen layer was processed by continuous wavelet transform to form a time-frequency analysis. The corrosion signals were identified in the contour map of the wavelet coefficient successfully. The understanding of the guided wave propagation on the pipe welded with support or pipe coated with bitumen is helpful to interpret the reflected signals. The use of continuous wavelet transform on signal processing techniques can improve the ability of defect detection on pipe with complex geometries.

This thesis proposes a bearing condition monitoring system using acceleration and acoustic emission (AE) signals. Bearings are perhaps the most omnipresent machine elements and their condition is often critical to the success of an operation or process. Consequently, there is a great need for a timely knowledge of the health status of bearings. Generally, bearing monitoring is the prediction of the component's health or status based on signal detection, processing and classification in order to identify the causes of the problem. As the monitoring system uses both acceleration and acoustic emission signals, it is considered a multi-sensor system. This has the advantage that not only do the two sensors provide increased reliability they also permit a larger range of rotating speeds to be monitored successfully. When more than one sensor is used, if one fails to work properly the other is still able to provide adequate monitoring. Vibration techniques are suitable for higher rotating speeds whilst acoustic emission techniques for low rotating speeds. Vibration techniques investigated in this research concern the use of the continuous wavelet transform (CWT), a joint time- and frequency domain method, This gives a more accurate representation of the vibration phenomenon than either time-domain analysis or frequency- domain analysis. The image processing technique, called binarising, is performed to produce binary image from the CWT transformed image in order to reduce computational time for classification. The back-propagation neural network (BPNN) is used for classification. The AE monitoring techniques investigated can be categorised, based on the features used, into: 1) the traditional AE parameters of energy, event duration and peak amplitude and 2) the statistical parameters estimated from the Weibull distribution of the inter-arrival times of AE events in what is called the STL method. Traditional AE parameters of peak amplitude, energy and event duration are extracted from individual AE events. These events are then ordered, selected and normalised before the selected events are displayed in a three-dimensional Cartesian feature space in terms of the three AE parameters as axes. The fuzzy C-mean clustering technique is used to establish the cluster centres as signatures for different machine conditions. A minimum distance classifier is then used to classify incoming AE events into the different machine conditions. The novel STL method is based on the detection of inter-arrival times of successive AE events. These inter-arrival times follow a Weibull distribution. The method provides two parameters: STL and L63 that are derived from the estimated Weibull parameters of the distribution's shape (y), characteristic life (0) and guaranteed life (to). It is found that STL and 43 are related hyperbolically. In addition, the STL value is found to be sensitive to bearing wear, the load applied to the bearing and the bearing rotating speed. Of the three influencing factors, bearing wear has the strongest influence on STL and L63. For the proposed bearing condition monitoring system to work, the effects of load and speed on STL need to be compensated. These issues are resolved satisfactorily in the project.

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.

Increased pressure on high voltage power distribution components has been created in recent years by a demand to lower costs and extend equipment lifetimes. This has led to a need for condition based maintenance, which requires a continuous knowledge of equipment health. Power transformers are a vital component in a power distribution network. However, there are currently no established techniques to accurately monitor and diagnose faults in real-time while the transformer is on-line. A major factor in the degradation of power transformer insulation is partial discharging. Left unattended, partial discharges (PDs) will eventually cause complete insulation failure. PDs generate a variety of signals, including electrical pulses that travel through the windings of the transformer to the terminals. A difficulty with detecting these pulses in an on-line environment is that they can be masked by external electrical interference. This thesis develops a method for identifying PD pulses and determining the number of PD sources while the transformer is on-line and subject to external interference. The partial discharge detection system (PDDS) acquires electrical signals with current and voltage transducers that are placed on the transformer bushings, making it unnecessary to disconnect or open the transformer. These signals are filtered to prevent aliasing and to attenuate the power frequency, and then digitised and analysed in Matlab, a numerical processing software package. Arbitrary narrowband interference is removed with an automated Fourier domain threshold filter. Internal PD pulses are separated from stochastic wideband pulse interference using directional coupling, which is a technique that simultaneously analyses the current and voltage signals from a bushing. To improve performance of this stage, the continuous wavelet transform is used to discriminate time and frequency information. This provides the additional advantage of preserving the waveshapes of the PD pulses for later analysis. PD pulses originating within the transformer have their waveshapes distorted when travelling though the windings. The differentiation of waveshape distortion of pulses from multiple physical sources is used as an input to a neural network to group pulses from the same source. This allows phase resolved PD analysis to be presented for each PD source, for instance, as phase/magnitude/count plots. The neural network requires no prior knowledge of the transformer or pulse waveshapes. The thesis begins with a review of current techniques and trends for power transformer monitoring and diagnosis. The description of transducers and filters is followed by an explanation of each of the signal processing steps. Two transformers were used to conduct testing of the PDDS. The first transformer was opened and modified so that internal PDs could be simulated by injecting artificial pulses. Two test scenarios were created and the performance of the PDDS was recorded. The PDDS identified and extracted a high rate of simulated PDs and correctly allocated the pulses into PD source groups. A second identically constructed transformer was energised and analysed for any natural PDs while external interference was present. It was found to have a significant natural PD source.

This thesis deals with analysis of dynamic forces and vibrations created during cutting with saw. The analysis is done on both simulation and experimental level. Acquired signals are evaluated with signal tools as STFT, CWT and DWT.

<p>The small intestine of the gastrointestinal tract displays a variety of motor patterns involved in the mixing, digestion, and propulsion of luminal content. Ultimately, it is the co-ordinated effort of smooth muscle contraction influenced by neural and myogenic stimulation that facilitate these motor patterns. While neural input from the enteric nervous system (ENS) and slow wave producing activity of the peacemaking interstitial cells of Cajal (ICC) in the myenteric plexus (ICC-MP) are key players in the manipulation of smooth muscle cells, the mechanisms behind the onset the segmentation motor pattern are currently unknown. I have demonstrated with intracellular recordings of electrical activity from circular smooth muscle cells, the same nutrient stimulants used to induce the segmentation motor pattern in whole organ preparations evokes the waxing waning phenomenon of the smooth muscle slow wave. Through the use of continuous wavelet transformation analysis on nutrient induced waxing waning, it was determined that the induction of a rhythmic low frequency component is responsible for the generation of waxing waning. Stimulated low frequency activity after methylene blue mediated elimination of ICC-MP slow wave activity suggested the low frequency component did not originate from the ICC-MP. The hypothesis emerged that the ICC of the deep muscular plexus (ICC-DMP), on the opposite side of the circular muscle thickness to the ICC-MP, were responsible for the low frequency oscillations. ICC-DMP networks in close physical proximity to nerve fibers were found to be under tonic inhibited by nitric oxide, and to respond to substance P stimulation. Both alleviation of the inhibition and stimulus by tachykinergic neurotransmission induced the low frequency component and waxing waning. The ENS and myogenic pacemakers play an important role in stimulating the segmentation motor pattern. ICC-DMP are the pacemakers responsible for generation of the low frequency component involved in waxing waning and segmentation.</p> / Master of Science (MSc)