In order to measure the quality of the logs, one can with help of Fast Fourier Transform technique get the signals resonance peaks. With help of these peaks you can see whether the quality of a tree is good or bad. This report contains the work of a where a program has been developed to be able to process a vibration created by an automatic hammer hitting on a log of wood. From the processed signal the program should be able to show both the raw wavesignal and the processed measured data from the resonance peaks. Beyond the raw wavesignal and resonance peaks the program should also be able to control the automatic hammer. The goal with the project is to have a program that get the same measure results as an already functioning measuring equipment. The result was a success when with the help of the program you were both able to control the hammer, measure the results and save the data with an accurate results.

The importance of understanding non-metallic material behaviour at high strain rates is becoming ever more important as new materials are being developed and used in shock loading applications. Applying conventional methods for high strain rate testing to non-metallic materials proved ineffective due to impedance mismatch between the specimen and apparatus and so a new test method was developed. A polymeric Hopkinson bar was developed enabling non-metallic materials, such as polycarbonate and rubber, to be tested at strain rates from 500 s^-1 to 4000 s^-1. Conventional Hopkinson bar analysis is invalid due to the viscoelastic nature of the polymeric bar material. As waves propagate along the bar length, the inherent material behaviour causes the waves to undergo a degree of attenuation and dispersion. Through the use of spectral analysis, a comparison of the dispersive relationships for 6061 T-6 aluminium, extruded acrylic and low density polyethylene is presented. The application of spectral methods to viscoelastic wave analysis was validated by three separate methods. A comparison of predicted and measured waves along the bar length allowed the dispersive relationship to be substantiated. The use of an enhanced laser velocity system further verified the predicted wave magnitude. A comparison of results for polycarbonate and ballistic gelatin to published results showed good agreement.

Spectral geometry is the field of mathematics which concerns relationships between geometric structures of manifolds and the spectra of canonical differential operators. Inverse Spectral Geometry in particular concerns the geometric information that can be recovered from the knowledge of such spectra. A deep link between inverse spectral geometry and sampling theory has recently been proposed. Specifically, it has been shown that the very shape of a Riemannian manifold can be discretely sampled and then reconstructed up to a cutoff scale. In the context of Quantum Gravity, this means that, in the presence of a physically motivated ultraviolet cuttoff, spacetime could be regarded as simultaneously continuous and discrete, in the sense that information can. In this thesis, we look into the properties of the Laplace-Beltrami operator on a compact Riemannian manifold with no boundary. We discuss the behaviour of its spectrum regarding a perturbation of the Riemannian structure. Specifically, we concern ourselves with infinitesimal inverse spectral geometry, the inverse spectral problem of locally determining the shape of a Riemannian manifold. We discuss the recenSpectral geometry is the field of mathematics which concerns relationships between geometric structures of manifolds and the spectra of canonical differential operators. Inverse Spectral Geometry in particular concerns the geometric information that can be recovered from the knowledge of such spectra. A deep link between inverse spectral geometry and sampling theory has recently been proposed. Specifically, it has been shown that the very shape of a Riemannian manifold can be discretely sampled and then reconstructed up to a cutoff scale. In the context of Quantum Gravity, this means that, in the presence of a physically motivated ultraviolet cuttoff, spacetime could be regarded as simultaneously continuous and discrete, in the sense that information can. In this thesis, we look into the properties of the Laplace-Beltrami operator on a compact Riemannian manifold with no boundary. We discuss the behaviour of its spectrum regarding a perturbation of the Riemannian structure. Specifically, we concern ourselves with infinitesimal inverse spectral geometry, the inverse spectral problem of locally determining the shape of a Riemannian manifold. We discuss the recently presented idea that, in the presence of a cutoff, a perturbation of a Riemannian manifold could be uniquely determined by the knowledge of the spectra of natural differential operators. We apply this idea to the specific problem of determining perturbations of the two dimensional flat torus through the knowledge of the spectrum of the Laplace-Beltrami operator.tly presented idea that, in the presence of a cutoff, a perturbation of a Riemannian manifold could be uniquely determined by the knowledge of the spectra of natural differential operators. We apply this idea to the specific problem of determining perturbations of the two dimensional flat torus through the knowledge of the spectrum of the Laplace-Beltrami operator.

Mining operations can produce highly localized, low intensity earthquakes that are referred to as microseismic events. Monitoring of microseismic events is useful in predicting and comprehending hazards, and in evaluating the overall performance of a mine design. <p>A robust localization algorithm is used to estimate the source position of the microseismic event by selecting the hypothesized source location that maximizes an energy function generated from the sum of the time--aligned sensor signals. The accuracy of localization for the algorithm characterized by the variance depends in part upon the configuration of sensors. Two algorithms, MAXSRC and MINMAX, are presented that use the variance of localization error, in a particular direction, as a performance measure for a given sensor configuration.<p>The variance of localization error depends, in part, upon the energy spectral density of the microseismic event. The energy spectral density characterization of sensor signals received in two potash mines are presented and compared using two spectral estimation techniques: multitaper estimation and combined time and lag weighting. It is shown that the difference between the the two estimation techniques is negligible. However, the differences between the two mine characterizations, though not large, is significant. An example uses the characterized energy spectral densities to determine the variance of error for a single step localization algorithm.<p>The MAXSRC and MINMAX algorithms are explained. The MAXSRC sensor placement algorithm places a sensor as close as possible to the source position with the maximum variance. The MINMAX sensor placement algorithm minimizes the variance of the source position with the maximum variance after the sensor has been placed. The MAXSRC algorithm is simple and can be solved using an exhaustive search while the MINMAX algorithm uses a genetic algorithm to find a solution. These algorithms are then used in three examples, two of which are simple and synthetic. The other example is from Lanigan Potash Mine. The results show that both sensor placement algorithms produce similar results, with the MINMAX algorithm consistently doing better. The MAXSRC algorithm places a single sensor approximately 100 times faster than the MINMAX algorithm. The example shows that the MAXSRC algorithm has the potential to be an efficient and intuitively simple sensor placement algorithm for mine microseismic event monitoring. The MINMAX algorithm provides, at an increase in computational time, a more robust placement criterion which can be solved adequately using a genetic algorithm.

<p>Many numerical approaches exist to solving models of electrical activity in the heart. These models consist of a system of stiff nonlinear ordinary differential equations for the voltage and other variables governing channels, with the voltage coupled to a diffusion term. In this work, we propose a new algorithm that uses two common discretization methods, operator splitting and finite elements. Additionally, we incorporate a temporal integration process known as spectral deferred correction. Using these approaches,</p><p>we construct a numerical method that can achieve arbitrarily high order in both space and time in order to resolve important features of the models, while gaining accuracy and efficiency over lower order schemes.</p><p>Our algorithm employs an operator splitting technique, dividing the reaction-diffusion systems from the models into their constituent parts. </p><p>We integrate both the reaction and diffusion pieces via an implicit Euler method. We reduce the temporal and splitting errors by using a spectral deferred correction method, raising the temporal order and accuracy of the scheme with each correction iteration.</p><p> </p><p>Our algorithm also uses continuous piecewise polynomials of high order on rectangular elements as our finite element approximation. This approximation improves the spatial discretization error over the piecewise linear polynomials typically used, especially when the spatial mesh is refined. </p><p>As part of these thesis work, we also present numerical simulations using our algorithm of one of the cardiac models mentioned, the Two-Current Model. We demonstrate the efficiency, accuracy and convergence rates of our numerical scheme by using mesh refinement studies and comparison of accuracy versus computational time. We conclude with a discussion of how our algorithm can be applied to more realistic models of cardiac electrical activity.</p> / Dissertation

Digital predistortion is one of the most cost effective ways among all linearization techniques. However, most of the existing designs treat the power amplifier as a memoryless device. For wideband or high power applications, the power amplifier exhibits memory effects, for which memoryless predistorters can achieve only limited linearization performance. In this dissertation, we propose novel predistorters and their parameter extraction algorithms. We investigate a Hammerstein predistorter, a memory polynomial predistorter, and a new combined model based predistorter. The Hammerstein predistorter is designed specifically for power amplifiers that can be modeled as a Wiener system. The memory polynomial predistorter can correct both the nonlinear distortions and the linear frequency response that may exist in the power amplifier. Real-time implementation aspects of the memory polynomial predistorter are also investigated. The new combined model includes the memory polynomial model and the Murray Hill model, thus extending the predistorter's ability to compensate for strong memory effects in the power amplifier. The predistorter models considered in this dissertation include both even- and odd-order nonlinear terms. By including these even-order nonlinear terms, we have a richer basis set, which offers appreciable improvement. In reality, however, the performance of a predistortion system can also be affected by the analog imperfections in the transmitter, which are introduced by the analog components; mostly analog filters and quadrature modulators. There are two common configurations for the upconversion chain in the transmitter: two-stage upconversion and direct upconversion. For a two-stage upconversion transmitter, we design a band-limited equalizer to compensate for the frequency response of the surface acoustic wave (SAW) filter which is usually employed in the IF stage. For a direct upconversion transmitter, we develop a model to describe the frequency-dependent gain/phase imbalance and dc offset. We then develop two methods to construct compensators for the imbalance and dc offset. These compensation techniques help to correct for the analog imperfections, which in turn improve the overall predistortion performance.

The effect of finite Reynolds numbers on chaotic advection is investigated for two dimensional lid-driven cavity flows that exhibit topological chaos in the creeping flow regime. The emphasis in this endeavor is to study how the inertial effects present due to small, but non-zero, Reynolds number influence the efficacy of mixing. A spectral method code based on the Fourier-Chebyshev method for two-dimensional flows is developed to solve the Navier-Stokes and species transport equations. The high sensitivity to initial conditions and the exponentional growth of errors in chaotic flows necessitate an accurate solution of the flow variables, which is provided by the exponentially convergent spectral methods. Using the spectral coefficients of the basis functions as solved through the conservation equations, exponentially accurate values of velocity everywhere in the flow domain are obtained as required for the Lagrangian particle tracking. Techniques such as Poincare maps, the stirring index based on the box counting method, and the tracking of passive scalars in the flow are used to analyze the topological chaos and quantify the mixing efficiency.

The inverse spectral problem is the problem of understanding the potential function of the Sturm-Liouville operator from the set of eigenvalues plus some additional spectral data. The theory of transformation operators, first introduced by Marchenko, and then reinforced by Gelfand and Levitan, is a powerful method to deal with the different stages of the inverse spectral problem: uniqueness, reconstruction, stability and existence. In this thesis, we shall give a survey on the theory of transformation operators. In essence, the theory says that the transformation operator $X$ mapping the solution of a Sturm-Liouville operator $varphi$ to the solution of a Sturm-Liouville operator, can be written as $$Xvarphi=varphi(x)+int_{0}^{x}K(x,t)varphi(t)dt,$$ where the kernel $K$ satisfies the Goursat problem $$K_{xx}-K_{tt}-(q(x)-q_{0}(t))K=0$$ plus some initial boundary conditions. Furthermore, $K$ is related by a function $F$ defined by the spectral data ${(lambda_{n},alpha_{n})}$ where $alpha_{n}=(int_{0}^{pi}|varphi_{n}(t)|^{2})^{frac{1}{2}}$ through the famous Gelfand-Levitan equation $$K(x,y)+F(x,y)+int_{o}^{x}K(x,t)F(t,y)dt=0.$$ Furthermore, all the above relations are bilateral, that is $$qLeftrightarrow KLeftrightarrow FLeftarrow {(lambda_{n},alpha_{n})}.$$ hspace*{0.25in}We shall give a concise account of the above theory, which involves Riesz basis and order of entire functions. Then, we also report on some recent applications on the uniqueness result of the inverse spectral problem.

Cholesky Decomposition is usually used to deal with the correlation problem among a financial product's underlying assets. However, Cholesky Decomposition inherently suffers from the requirement that all eigenvalues must be positive. Therefore, Cholesky Decomposition can't work very well when the number of the underlying assets is high. The report takes a diffrent approach called spectral Decomposition in attempt to solve the problem. But it turns out that although Spectral Decomposition can meet the requirement of all-positive eigenvalue, the decomposision error will be larger as the number of underlying asset getting larger. Thus, although Spectral Decomposition does offer some help, it works better when the number of underlying assets is not very large.

Thesis (M.S.)--Mississippi State University. Department of Electrical and Computer Engineering. / Title from title screen. Includes bibliographical references.