Digital cameras use a single image sensor array with a color filter array (CFA) to measure a color image. Instead of measuring a red, green, and blue value at every pixel, these cameras have a filter built onto each pixel so that only one portion of the visible spectrum is measured. To generate a full-color image, the camera must estimate the missing two values at every pixel. This process is known as color filter array interpolation. The Bayer CFA pattern samples the green image on half of the pixels of the imaging sensor on a quincunx grid. The other half of the pixels measure the red and blue images equally on interleaved rectangular sampling grids. This thesis analyzes this problem with sampling theory. The red and blue images are sampled at half the rate of the green image and therefore have a higher probability of aliasing in the output image. This is apparent when simple interpolation algorithms like bilinear interpolation are used for CFA interpolation. Two reference algorithms, a projections onto convex sets (POCS) algorithm and an edge-directed algorithm by Adams and Hamilton (AH), are studied. Both algorithms address aliasing in the green image. Because of the high correlation among the red, green, and blue images, information from the red and blue images can be used to better interpolate the green image. The reference algorithms are studied to learn how this information is used. This leads to two new interpolation algorithms for the green image. The red and blue interpolation algorithm of AH is also studied to determine how the inter-image correlation is used when interpolating these images. This study shows that because the green image is sampled at a higher rate, it retains much of the high-frequency information in the original image. This information is used to estimate aliasing in the red and blue images. We present a general algorithm based on the AH algorithm to interpolate the red and blue images. This algorithm is able to provide results that are on average, better than both reference algorithms, POCS and AH.

In this thesis, we describe two approaches to automatically synthesize the emotional speech of a target speaker based on the hidden Markov model for his/her neutral speech. In the interpolation based method, the basic idea is the model interpolation between the neutral model of the target speaker and an emotional model selected from a candidate pool. Both the interpolation model selection and the interpolation weight computation are determined based on a model-distance measure. We propose a monophone-based Mahalanobis distance (MBMD). In the parallel model combination (PMC) based method, our basic idea is to model the mismatch between neutral model and emotional model. We train linear regression model to describe this mismatch. And then we combine the target speaker neutral model with the linear regression model. We evaluate our approach on the synthesized emotional speech of angriness, happiness, and sadness with several subjective tests. Experimental results show that the implemented system is able to synthesize speech with emotional expressiveness of the target speaker.

In 2010, Prof. Chang and Prof. Lee applied Lagrange interpolation formula to decode a class of binary cyclic codes, but they did not provide an effective way to calculate the Lagrange interpolation formula. In this thesis, we use the least common multiple of polynomials to compute it effectively. Let E be an extension field of degree m over F = F_p and £] be a primitive nth root of unity in E. For a nonzero element r in E, the minimal polynomial of r over F is denoted by m_r(x). Then, let Min (r, F) denote the least common multiple of m_r£]^i(x) for i = 0, 1,..., n-1 and be called the generalized minimal polynomial of over F. For any binary quadratic residue code mentioned in this thesis, the set of all its correctable error patterns can be partitioned into root sets of some generalized minimal polynomials over F. Based on this idea, we can develop an effective method to calculate the Lagrange interpolation formula.

We propose a dynamic programming (DP) approach for pricing American options over a finite time horizon. We model uncertainty in stock price that follows geometric Brownian motion (GBM) and let interest rate and volatility be fixed. A procedure based on dynamic programming combined with piecewise linear interpolation approximation is developed to price the value of options. And we introduce the free boundary problem into our model. Numerical experiments illustrate the relation between value of option and volatility.

¡@¡@In this thesis, we use a hidden Markov model which can use a small amount of corpus to synthesize speech with certain quality to implement speech synthesis system for Chinese. More, the emotional speech are synthesized by the flexibility of the parametric speech in this model. We conduct model interpolation and model adaptation to synthesize speech from neutral to particular emotion without target speaker¡¦s emotional speech. In model adaptation, we use monophone-based Mahalanobis distance to select emotional models which are close to target speaker from pool of speakers, and estimate the interpolation weight to synthesize emotional speech. In model adaptation, we collect abundant of data training average voice models for each individual emotion. These models are adapted to specific emotional models of target speaker by CMLLR method. In addition, we design the Latin-square evaluation to reduce the systematic offset in the subjective tests, making results more credible and fair. We synthesize emotional speech include happiness, anger, sadness, and use Latin square design to evaluate performance in three part similarity, naturalness, and emotional expression respectively. According to result, we make a comprehensive comparison and conclusions of two method in emotional speech synthesis.

The present study aims to explore dynamical behavior of the fluid-elastic instability of a circular cylinder in shear flow by numerical simulations. The theoretical model comprises two groups of transient conservation equations of mass and momentum and the governing equations are solved numerically with an iterative SIMPLEC(Semi-Implicit Method for Pressure-Linked Equations Consistent) algorithm to determine the flow property and to analysis structure stress simultaneously. Additionally, the TFI (Transfinite interpolation) computation procedure is applied to characterize the behavior of fluid-structure interaction. The predictions are in reasonable agreement with literature showing the validity of the present theoretical model. The numerical results indicate that there is a transverse force acting from high velocity side toward the low velocity side in shear flow. The magnitude of this transverse force increases with the shear parameter. The Strouhal number slightly increases as the shear parameter increases for all Reynolds number. As the pattern of the approach flow changes from the uniform to shear flow, the front stagnation point shifts to high velocity side, and the base pressure increase. The magnitude of the shift of front stagnation point is linear with the shear parameter. Furthermore, this study appraises the amplitude and orbit of fluid elastic vibration of a circular cylinder in shear flow, and shows the effects of the spring constant and damping factor on fluid elastic vibration of the cylinder. In addition, various effects including shear parameter and mass ratio on the critical velocity of the fluid elastic vibration also has been examined detail.

Abstract To improve the application of Point Interpolation Method (PIM) in Element Free Galerkin Method (EFG) is the aim of this study. The trait of EFG is using overlap of influence domain between different nodes to construct discretization nodes¡¦ connection. EFG just uses nodal data, but not element. For constructing shape function, EFG has two types of methods, Fitting and Interpolation. Fitting uses Moving Least Square Method (MLS). MLS-EFG has stable effect on numerical analysis; however, users who use it need to choose more numerical parameters and do more computation. Besides, users can not apply boundary conditions directly when using MLS-EFG. Interpolation method applies nodal coordinates to proceed computation, and it called PIM. Boundary conditions could be used directly and less computation is needs while using PIM. However, the coefficient of interpolation function of sample is singular. This study tries to construct Coordination Point Interpolation Method. It owns advantages of both methods that mentioned above, and extra numerical parameters are not needed. It applies the notion of influence domain of MLS-EFG, then search correlative efficient nodes which are contained in near field of sample. The correlative efficient nodes make up matrix that con cause inverse matrix. In addition, via numerical simulations, it shows that CPIM has excellent convergence and accurate solution, and is better that MLS-EFG.

In indoor environment, the multi-sensor system has been proved to be an efficient solution for target locating process in terms of lower estimation cost. However, the placement of designed multi-sensor has great impact on the location performance in an indoor environment. Based on the time difference of arrival (TDOA), closed-form least-square location methods, including the spherical-interpolation (SI) and the spherical-intersection (SX) methods, are used in the estimation of target locations. The two methods are apart from the usual process of iterative and nonlinear minimization. Consequently, under the influence of noise interference, the performance of the two methods also produce different results. In addition to the above issues, the limitation of these methods will also be examined. The geometric dilution of precision (GDOP) effects of TDOA location on location performance of both inside and outside of the multi-sensor environment in the 2-D scenario have been studied in the past. This thesis aims to further advance the performance of GDOP in 3-D scenarios, analyze the differences, and propose the suitable needs. Programmed 3-D scenario simulations are used in this research, designed according to multiple sensor arrays and the moving latitude of a target. The Setup interprets the degree of multi-sensor separation, and distances from targets to the sensor array. A suitable location algorithm and optimal multi-sensor deployments in an indoor environment were proposed according to the simulation results.

Derivative free optimization algorithms are implementations of trust region based derivative-free methods using multivariate polynomial interpolation. These are designed to minimize smooth functions whose derivatives are not available or costly to compute. The trust region based multilevel optimization algorithms for solving large scale unconstrained optimization problems resulting by discretization of partial differential equations (PDEs), make use of different discretization levels to reduce the computational cost. In this thesis, a derivative free multilevel optimization algorithm is derived and its convergence behavior is analyzed. The effectiveness of the algorithms is demonstrated on a shape optimization problem.

Modeling and forecasting of the unemployment rate of a country is very important to be able to take precautions on the governmental policies. The available unemployment rate data of Turkey provided by the Turkish Statistical Institute (TURKSTAT) are not in suitable format to have a time series model. The unemployment rate data between 1988 and 2009 create a problem of building a reliable time series model due to the insufficient number and irregular form of observations. The application of disaggregation methods to some parts of the unemployment rate data enables us to fit an appropriate time series model and to have forecasts as a result of the suggested model.