Empirical mode decomposition was proposed recently as a time frequency analysis tool for nonlinear and nonstationary signals. Despite from its many advantages, problems such as “uniqueness” problem have been discovered which limit the application. Although this problem has been addressed to some extent by various extensions of the original algorithm, the solution is far from satisfactory in some scenarios. In this work we propose two variants of the original algorithm, with emphasis on providing unified representations. R-EMD makes use of a set of reference signals to guide the decomposition therefore guarantees unified representation for multiple 1D signals. 2D- BEMD takes advantage of a projection procedure and is capable of providing unified representation between a pair of 2D signals. Application of the proposed algorithms on different problems in biometric and image processing demonstrates promising results and indicates the effectiveness of the proposed framework.

Empirical mode decomposition was proposed recently as a time frequency analysis tool for nonlinear and nonstationary signals. Despite from its many advantages, problems such as “uniqueness” problem have been discovered which limit the application. Although this problem has been addressed to some extent by various extensions of the original algorithm, the solution is far from satisfactory in some scenarios. In this work we propose two variants of the original algorithm, with emphasis on providing unified representations. R-EMD makes use of a set of reference signals to guide the decomposition therefore guarantees unified representation for multiple 1D signals. 2D- BEMD takes advantage of a projection procedure and is capable of providing unified representation between a pair of 2D signals. Application of the proposed algorithms on different problems in biometric and image processing demonstrates promising results and indicates the effectiveness of the proposed framework.

Hilbert-Huang Transform (HHT) is a data analysis tool, first developed in 1998, which can be used to extract the periodic components embedded within oscillatory data. This thesis is dedicated to the understanding, application, and development of this tool. First, the background theory of HHT will be described and compared with other spectral analysis tools. Then, a number of applications will be presented, which demonstrate the capability for HHT to dissect and analyze the periodic components of different oscillatory data. Finally, a new algorithm is presented which expands HHT ability to analyze discontinuous data. The sum result is the creation of a number of useful tools developed from the application of HHT, as well as an improvement of the HHT tool itself.

In this thesis, a novel technique based on the empirical mode decomposition (EMD) methodology is proposed and examined for the noise-robustness of automatic speech recognition systems. The EMD analysis is a generalization of the Fourier analysis for processing nonlinear and non-stationary time functions, in our case, the speech feature sequences. We use the intrinsic mode functions (IMF), which include the sinusoidal functions as special cases, obtained from the EMD analysis in the post-processing of the log energy feature. We evaluate the proposed method on Aurora 2.0 and Aurora 3.0 databases. On Aurora 2.0, we obtain a 44.9% overall relative improvement over the baseline for the mismatched (clean-training) tasks. The results show an overall improvement of 49.5% over the baseline for Aurora 3.0 on the high-mismatch tasks. It shows that our proposed method leads to significant improvement.

Bandwidth enhancement of low-profile omnidirectional, electrically-small antennas has evolved from the design and construction of AM transmitter towers eighty years ago to current market demand for battery-powered personal communication devices. Electrically-small antenna theory developed with well-known approximations for characterizing radiation properties of antenna structures that are fractions of the radiansphere. Current state-of-the-art wideband small antennas near kaH1 have achieved multiple-octave impedance bandwidths when utilizing volume-efficient designs. Significant advances in both the power and miniaturization of microelectronics have created a second possible approach to enhance bandwidth. Frequency agility, via switch tuning of reconfigurable structures, offers the possibility of the direct integration of high-speed electronics to the antenna structure. The potential result would provide a means to translate a narrow instantaneous bandwidth across a wider operating bandwidth. One objective of the research was to create a direct comparison of the passive- multi-resonant and active-reconfigurable approaches to enhance bandwidth. Typically, volume-efficient, wideband antennas are unattractive candidates for low-profile applications and conversely, active electronics integrated directly antenna elements continue to introduce problematic loss mechanisms at the proof-of-concept level The dissertation presents an analysis method for wide bandwidth self-resonant antennas that exist in the 0.5dkad1.0 range. The combined approach utilizes the quality factor extracted directly from impedance response data in addition to near-and-far field modal analyses. Examples from several classes of antennas investigated are presented with practical boundary conditions. The resultant radiation properties of these antenna-finite ground plane systems are characterized by an appreciable percentage of radiated power outside the lowest-order mode. Volume-efficient structures and non-omnidirectional radiation characteristics are generally not viable for portable devices. Several examples of passive structures, representing different antenna classes are investigated. A PIN diode, switch-tuned low-profile antenna prototype was also developed for the comparison which demonstrated excessive loss in the physical prototype. Lastly, a passive, low-profile multi-resonant antenna element with monopole radiation is introduced. The structure is an extension of the planar inverted-F antenna with the addition of a capacitance-coupled parasitic to enhance reliable operation in unknown environments. / Ph. D.

The foreign exchange market is one of the largest and most active financial markets with enormous daily trading volumes. Exchange rates are influenced by the interactions of a large number of agents, each operating with different intentions and on different time scales. This gives rise to nonlinear and non-stationary behaviour which complicates modelling. This research proposes a neural network based model trained on data filtered with a novel Empirical Mode Decomposition (EMD) filtering method for the forecasting of exchange rates. One minor and two major exchange rates are evaluated in this study. Firstly the ideal prediction horizons for trading are calculated for each of the exchange rates. The data is filtered according to this ideal prediction horizon using the EMD-filter. This EMD-filter dynamically filters the data based on the apparent number of intrinsic modes in the signal that can contribute towards prediction over the selected horizon. The filter is employed to filter out high frequency noise and components that would not contribute to the prediction of the exchange rate at the chosen timescale. This results in a clearer signal that still includes nonlinear behaviour. An artificial neural network predictor is trained on the filtered data using different sampling rates that are compatible with the cut-off frequency. The neural network is able to capture the nonlinear relationships between historic and future filtered data with greater certainty compared to a neural network trained on unfiltered data. Results show that the neural network trained on EMD-filtered data is significantly more accurate at prediction of exchange rates compared to the benchmark models of a neural network trained on unfiltered data and a random walk model for all the exchange rates. The EMD-filtered neural network’s predicted returns for the higher sample rates show higher correlations with the actual returns, and significant profits can be made when applying a trading strategy based on the predictions. Lower sample rates that just marginally satisfy the Nyquist criterion perform comparably with the neural network trained on unfiltered data; this may indicate that some aliasing occurs for these sampling rates as the EMD low-pass filter has a gradual cut-off, leaving some high frequency noise within the signal. The proposed model of the neural network trained on EMD-filtered data was able to uncover systematic relationships between the filtered inputs and actual outputs. The model is able to deliver profitable average monthly returns for most of the tested sampling rates and forecast horizons of the different exchange rates. This provides evidence that systematic predictable behaviour is present within exchange rates, and that this systematic behaviour can be modelled if it is properly separated from high frequency noise. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2015

The foreign exchange market is one of the largest and most active financial markets with enormous daily trading volumes. Exchange rates are influenced by the interactions of a large number of agents, each operating with different intentions and on different time scales. This gives rise to nonlinear and non-stationary behaviour which complicates modelling. This research proposes a neural network based model trained on data filtered with a novel Empirical Mode Decomposition (EMD) filtering method for the forecasting of exchange rates. One minor and two major exchange rates are evaluated in this study. Firstly the ideal prediction horizons for trading are calculated for each of the exchange rates. The data is filtered according to this ideal prediction horizon using the EMD-filter. This EMD-filter dynamically filters the data based on the apparent number of intrinsic modes in the signal that can contribute towards prediction over the selected horizon. The filter is employed to filter out high frequency noise and components that would not contribute to the prediction of the exchange rate at the chosen timescale. This results in a clearer signal that still includes nonlinear behaviour. An artificial neural network predictor is trained on the filtered data using different sampling rates that are compatible with the cut-off frequency. The neural network is able to capture the nonlinear relationships between historic and future filtered data with greater certainty compared to a neural network trained on unfiltered data. Results show that the neural network trained on EMD-filtered data is significantly more accurate at prediction of exchange rates compared to the benchmark models of a neural network trained on unfiltered data and a random walk model for all the exchange rates. The EMD-filtered neural network’s predicted returns for the higher sample rates show higher correlations with the actual returns, and significant profits can be made when applying a trading strategy based on the predictions. Lower sample rates that just marginally satisfy the Nyquist criterion perform comparably with the neural network trained on unfiltered data; this may indicate that some aliasing occurs for these sampling rates as the EMD low-pass filter has a gradual cut-off, leaving some high frequency noise within the signal. The proposed model of the neural network trained on EMD-filtered data was able to uncover systematic relationships between the filtered inputs and actual outputs. The model is able to deliver profitable average monthly returns for most of the tested sampling rates and forecast horizons of the different exchange rates. This provides evidence that systematic predictable behaviour is present within exchange rates, and that this systematic behaviour can be modelled if it is properly separated from high frequency noise. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2015

abstract: Epilepsy is a group of disorders that cause seizures in approximately 2.2 million people in the United States. Over 30% of these patients have epilepsies that do not respond to treatment with anti-epileptic drugs. For this population, focal resection surgery could offer long-term seizure freedom. Surgery candidates undergo a myriad of tests and monitoring to determine where and when seizures occur. The “gold standard” method for focus identification involves the placement of electrocorticography (ECoG) grids in the sub-dural space, followed by continual monitoring and visual inspection of the patient’s cortical activity. This process, however, is highly subjective and uses dated technology. Multiple studies were performed to investigate how the evaluation process could benefit from an algorithmic adjust using current ECoG technology, and how the use of new microECoG technology could further improve the process. Computational algorithms can quickly and objectively find signal characteristics that may not be detectable with visual inspection, but many assume the data are stationary and/or linear, which biological data are not. An empirical mode decomposition (EMD) based algorithm was developed to detect potential seizures and tested on data collected from eight patients undergoing monitoring for focal resection surgery. EMD does not require linearity or stationarity and is data driven. The results suggest that a biological data driven algorithm could serve as a useful tool to objectively identify changes in cortical activity associated with seizures. Next, the use of microECoG technology was investigated. Though both ECoG and microECoG grids are composed of electrodes resting on the surface of the cortex, changing the diameter of the electrodes creates non-trivial changes in the physics of the electrode-tissue interface that need to be accounted for. Experimenting with different recording configurations showed that proper grounding, referencing, and amplification are critical to obtain high quality neural signals from microECoG grids. Finally, the relationship between data collected from the cortical surface with micro and macro electrodes was studied. Simultaneous recordings of the two electrode types showed differences in power spectra that suggest the inclusion of activity, possibly from deep structures, by macroelectrodes that is not accessible by microelectrodes. / Dissertation/Thesis / Doctoral Dissertation Bioengineering 2015

Koopman theory is widely used for data-driven modeling of nonlinear dynamical systems. One of the well-known algorithms that stem from this approach is the Extended Dynamic Mode Decomposition (EDMD), a data-driven algorithm for uncontrolled systems. In this thesis, we will start by discussing the EDMD algorithm. We will discuss how this algorithm encompasses Dynamic Mode Decomposition (DMD), a widely used data-driven algorithm. Then we will extend our discussion to input-output systems and identify ways to extend the Koopman Operator Theory to input-output systems. We will also discuss how various algorithms can be identified as instances of this framework. Special care is given to Wavelet-based Dynamic Mode Decomposition (WDMD). WDMD is a variant of DMD that uses only the input and output data. WDMD does that by generating auxiliary states acquired from the Wavelet transform. We will show how the action of the Koopman operator can be simplified by using the Wavelet transform and how the WDMD algorithm can be motivated by this representation. We will also introduce a slight modification to WDMD that makes it more robust to noise. / Master of Science / To analyze a real-world phenomenon we first build a mathematical model to capture its behavior. Traditionally, to build a mathematical model, we isolate its principles and encode it into a function. However, when the phenomenon is not well-known, isolating these principles is not possible. Hence, rather than understanding its principles, we sample data from that phenomenon and build our mathematical model directly from this data by using approximation techniques. In this thesis, we will start by focusing on cases where we can fully observe the phenomena, when no external stimuli are present. We will discuss how some algorithms originating from these approximation techniques can be identified as instances of the Extended Dynamic Mode Decomposition (EDMD) algorithm. For that, we will review an alternative approach to mathematical modeling, called the Koopman approach, and explain how the Extended DMD algorithm stems from this approach. Then we will focus on the case where there is external stimuli and we can only partially observe the phenomena. We will discuss generalizations of the Koopman approach for this case, and how various algorithms that model such systems can be identified as instances of the EDMD algorithm adapted for this case. Special attention is given to the Wavelet-based Dynamic Mode Decomposition (WDMD) algorithm. WDMD builds a mathematical model from the data by borrowing ideas from Wavelet theory, which is used in signal processing. In this way, WDMD does not require the sampling of the fully observed system. This gives WDMD the flexibility to be used for cases where we can only partially observe the phenomena. While showing that WDMD is an instance of EDMD, we will also show how Wavelet theory can simplify the Koopman approach and thus how it can pave the way for an easier analysis.

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