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.

Phase-extraction from fringe patterns is an inevitable procedure in the field of optical metrology and interferometry. However, speckle noise will introduce and influence the precision of wrapped phase map when a coherent light is used. In this thesis, we use the bidimensional empirical mode decomposition (BEMD) to perform the speckle-reduction. Moreover, different interpolation method in BEMD will be used to compare their performance in speckle-reduction. Finally, the database will be developed to make the BEMD a robotic tool to reduce noises. And the database also points out that the performance of BEMD is highly related to the fringe period, the fringe visibility, and the SNR of speckle noise.

Internal waves occur in the interface between two layers of fluids with density stratification. In order to better understand the characteristics of continuous internal waves, a series of experiments were conducted in a laboratory tank. The upper and lower layers are fresh water of 15 cm thick and salt water of 30 cm thick, respectively. The periods of internal waves are 2.5, 5.5 and 6.6 sec. A micro-ADV is used to measure velocity profiles. Wave profiles at the density interface and the free surface are monitored respectively by an ultrasonic and capacitance wave gauges. Our results indicate that particle velocities (u and w) above and below the density interface have opposite directions. The speed is peaked near the density interface and it becomes weaker further away from the interface. Empirical Mode Decomposition is used to remove noise from the observed particle velocities, and the period is consistent with those derived from the interface elevations. The observed particle velocities also compare favorably with the theoretical results. When internal waves propagate without the interference of a sloping bottom, the turbulence induced is rather insignificant. The turbulence is more significant only near the density interface. With the existence of a sloping bottom, the internal waves gradually shoal and deform, the crest becomes sharp and steep, finally the waves become unstable, break and overturn. In this study the effect of bottom slope and the steepness of internal waves on the reflectivity of incoming waves are investigated. The reflectivity is smaller with gentler slope, and it increases and reaches a constant value with steeper slopes. The observed energy dissipation rate£`is higher near the slope. Three methods were used to estimate the energy dissipation rate and shear stress; namely, the inertial dissipation, the TKE and auto-correlation method. The£` estimated from the auto-correlation method is larger than that from the other two methods, but their trend is similar. The energy dissipation rate is found to increase with a gentler sloping bottom.

Nan Wan is a half-closed embayment in the most southern part of Taiwan. While facing the Luzon Strait, it also connects to the Pacific Ocean in its southeast, and is adjacent the Taiwan Strait and the South China Sea . In view of general oceanic circulation, Nan Wan Bay happens to lie to the rim of South China Sea circumfluence and Kuroshio where a variety of water mass exchange has taken place, causing saline intrusion and mixed of water. Seasonal variation and tidal fluctuations also contribute to the exchange of water masses. The Third Nuclear Power Station of Taiwan Power Company is located in Nan Wan with its thermal discharge outlet adjacent to Maobitou to the west of the bay in order to minimize the effect of warm water discharge on the local marine ecology and coral . A long-term monitoring program on water temperature and other environmental factors has been set up implemented .this research report will first describe the archives regarding the hydrology in Nan Wan in support of monitoring the process in temperature variation . Previous research efforts are found somehow unable reveal precisely the physical mechanism leading to water temperature variations in the bay, due to limited facilities, short of information or poor analytical tools. This report adopts 14 records of water temperature at the thermal outlet of the Third Nuclear Power Station for signal analysis. As to non-linear and unstable data analysis, it is based on the Hilbert-Huang Transform. HHT includes Empirical Mode Decomposition, EMD which could decompose the raw data into numerous Intrinsic Mode Function, IMF. It is allowed to comprehend the main causes for the rising and dropping of water temperature based on the variation of spectroscopy by transferring through Hilbert and analyzing via IMF. Furthermore, the characteristic of each quantity could be developed according to the quantities acquired from the former method of HHT. The analytical report of water temperature covers 14 records dating from 1999 to 2003. In light of the analytical report, tide and wind account for the main cause of the temperature variation in waters while demanding information to ensure whether it is influenced by other factors like internal waves, water masses or landforms, etc. In addition, the report compares the difference in the same of data between FFT and HHT and moreover concludes the advantages and disadvantages as reference for researches.

The early detection of damage of in-service structural or mechanical systems is of vital importance. With early detection, the damage may be repaired before the integrity of the system is jeopardized, avoiding possible monetary losses, environmental impacts, injury and death. With this goal in mind, many structural health monitoring techniques have been developed which use a combination of sensors and algorithms to collect, process and interpret data to detect damage in a structure. This thesis presents work completed in support of the experimental validation of a novel structural health monitoring technique developed with the aim of providing improved qualitative results compared to those methods currently available.

Filtering is a key step in digital image processing and analysis. It is mainly used for amplification or attenuation of some frequencies depending on the nature of the application. Filtering can either be performed in the spatial domain or in a transformed domain. The selection of the filtering method, filtering domain, and the filter parameters are often driven by the properties of the underlying image. This thesis presents three different kinds of biomedical image filtering applications, where the filter parameters are automatically determined from the underlying images. Filtering can be used for image enhancement. We present a robust image dependent filtering method for intensity inhomogeneity correction of biomedical images. In the presented filtering method, the filter parameters are automatically determined from the grey-weighted distance transform of the magnitude spectrum. An evaluation shows that the filter provides an accurate estimate of intensity inhomogeneity. Filtering can also be used for analysis. The thesis presents a filtering method for heart localization and robust signal detection from video recordings of rat embryos. It presents a strategy to decouple motion artifacts produced by the non-rigid embryonic boundary from the heart. The method also filters out noise and the trend term with the help of empirical mode decomposition. Again, all the filter parameters are determined automatically based on the underlying signal. Transforming the geometry of one image to fit that of another one, so called image registration, can be seen as a filtering operation of the image geometry. To assess the progression of eye disorder, registration between temporal images is often required to determine the movement and development of the blood vessels in the eye. We present a robust method for retinal image registration. The method is based on particle swarm optimization, where the swarm searches for optimal registration parameters based on the direction of its cognitive and social components. An evaluation of the proposed method shows that the method is less susceptible to becoming trapped in local minima than previous methods. With these thesis contributions, we have augmented the filter toolbox for image analysis with methods that adjust to the data at hand.

This thesis investigates the presence of multiple (quasi-TEM) modes in inverted embedded microstrip lines. It has already been shown that parasitic modes do exist in inverted embedded microstrips due to field leakage inside the dielectric substrate, especially for high dielectric constants (like Silicon). This thesis expands upon that work and characterizes those modes for a variety of geometrical dimensions. Chapter 1 focuses on the theory behind the different transmission line modes, which may be present in inverted embedded microstrips. Based on the structure of the inverted embedded microstrip, the conventional microstrip mode, the quasi-conventional microstrip mode, and the stripline mode are expected. Chapter 2 discusses in detail the techniques used to decompose the total probed field into the various modes present in the inverted embedded microstrip lines. Firstly, a short explanation of the finite-difference time-domain method, that is used for the simulation and modeling of inverted microstrips up to 50 GHz is provided. Next, a flowchart of the process involved in decomposing the modes is laid out. Lastly, the challenges of this approach are also highlighted to give an appreciation of the difficulty in obtaining accurate results. Chapter 3 shows the results (dispersion diagrams, values/percentage of the individual mode energies ) obtained after running time-domain simulations for a variety of geometrical dimensions. Chapter 4 concludes the thesis by explaining the results in terms of the transmission line theory presented in Chapter 1. Next, possible future work is mentioned.

This thesis descibes a theoretical study of nonlinear self-focusing as applied to the metrology of the nonlinear optical parameters of a medium. It also studies the phe- nomenon of optical power limiting which utilizes self-focusing e ects. As an analytical tool, a mode decomposition method which uses an orthogonal and complete set of Gaussian-Laguerre modes as a basis set is used to treat these problems. Nonlinear media both in the thin and thick limits are investigated. For thin media, a closed form expression is derived which describes the optical eld of an initally Gaussian beam that is perturbed by a thin nonlinear material which exhibits nonlinear absorption as well as nonlinear refraction. This result is valid for any regime of nonlinearity in the thin medium approximation. Thick media are treated using a numerical extension of the Gaussian-Laguerre Mode Decomposition technique. Spatial scanning techniques such as the Z-scan that rely on self-focusing e ects and that are used to measure the nonlinear optical parameters of a material are studied in detail. Optical limiting in both thick and thin media is also investigated.