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.

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

Classically, we look at annual maximum precipitation series from the perspective of extreme value statistics, which provides a useful statistical distribution, but does not allow much flexibility in the context of climate change. Such distributions are usually assumed to be static, or else require some assumed information about possible trends within the data. For this study, we treat the maximum rainfall series as sums of underlying signals, upon which we perform a decomposition technique, Empirical Mode Decomposition. This not only allows the study of non-linear trends in the data, but could give us some idea of the periodic forces that have an effect on our series. To this end, data was taken from stations in the New England area, from different climatological regions, with the hopes of seeing temporal and spacial effects of climate change. Although results vary among the chosen stations the results show some weak signals and in many cases a trend-like residual function is determined.

在台灣證券市場中，有許多的技術分析方法或指標，市場參與者或財 務學者會利用歷史資料來做回溯測試，找出可運用的方法或指標，以此來 推測出台股加權指數未來的趨勢，也有學者利用類神經網路(Artificial Neural Network, ANN)考慮經濟景氣、技術分析指標等作為輸入變數來預測 台股加權指數，而本文則利用 EEMD(Ensemble Empirical Mode Decomposition)拆解出來的結果作為 ANN 的輸入變數，並將 ANN 預測出 的值轉換成 FK (Forward-calculated %K) 值，再搭配不同的交易方式，來 補捉台股加權指數的走勢，並比較各種交易方式的績效，找出一個能夠穩 定獲利的交易模型。

In this thesis we use pulse shaping system to generate pulse train. Using empirical mode decomposition(EMD) and short-time Fourier transform(STFT) to analyze the signal of terahertz radiation. we use pulse shaping system to modulate the amplitude and phase of light which provide for pulse train generation. Compare with other method, first, our method will improve the stability of time delay control. Second this method is easier to control the time delay and number of pulse in the pulse train. In the past, people find the occur time of high frequency by observed the time domain of terahertz radiation directly, but if the occur time near the time of the peak power of terahertz radiation, we can¡¦t find out the occur time of high frequency. Using STFT can find out the relationship between intensity and time, but if the modes in signal have different width of frequency STFT have to use different time window to get the best frequency resolution and time resolution. However the time window with different width will have different frequency resolution, and the relationship between intensity and time will change with different frequency resolution, therefore using different frequency resolution will get different result, so we need a new signal analysis method. To solve this problem we use EMD to decompose different mode in the signal of terahertz radiation into different intrinsic mode function(IMF), and analyze the signal of terahertz by STFT to find the occur time of high frequency of terahertz radiation. Because the modes are separated in to different IMF, we can use STFT with the same time window. We expect this method applied to narrow-band frequency-tunable THz wave generation will be better.