International Telemetering Conference Proceedings / October 21, 2002 / Town & Country Hotel and Conference Center, San Diego, California / Feher Keying (FK) signals are clock shaped baseband waveforms with the potential to attain very high spectral efficiencies. Two FK signals which have different level rectangular waveforms (named as FK-1) or sinusoidal waveforms (named as FK-2) for two binary symbols are considered in this paper. These signals have periodic components in the time domain. Therefore they have cyclostationary properties. This means that spectral correlation exists in the frequency domain. For each type of waveforms, spectral correlation has been investigated. FK signals can be expressed mathematically into two parts in the frequency domain – discrete part and continuous part. The discrete part has one or more discrete impulse(s) in their spectra and the continuous part has periodically the same shape of harmonics in their spectra. The correlations of their spectra have been obtained mathematically and by simulation. It is shown that FK signals have high correlation related to the symbol rate. Finally, some suggestions how these properties can be used to improve their performance by devising better demodulators are discussed. These properties can be used for interference rejection at the receiver, which results in low bit error rate performance.

International Telemetering Conference Proceedings / October 22-25, 2001 / Riviera Hotel and Convention Center, Las Vegas, Nevada / Performances of a subclass of a new spectral efficient modulation scheme, designated as Feher Keying [1], or FK, is evaluated. The Power Spectral Density (PSD) and Bit Error Rate (BER) characteristics of FK are presented. FK has ultra high spectral efficiency and satisfies the frequency mask for WLAN defined in FCC part 15, and it has a simple structure for high bit rate implementation.

As optical designs become more sophisticated and incorporate aspheric and free form surfaces, the need to specify limits on mid-spatial frequency manufacturing errors becomes more critical, particularly as we better understand the effects of these errors on image quality. While there already exist methods based on Fourier analysis to specify these errors in most commercial interferometry software, the method of calculation and the power spectral density (PSD) results remain obscure to many in the optical design and manufacturing field. We suggest that the structure functions (SF) contains the same information as in the Fourier based PSD but in a way that is much more transparent to analysis, interpretation and application as a specification. The units of measure are more familiar and the concept behind the analysis is simpler to understand. Further, the information contained in the structure function (or PSD) allows a complete specification of an optical surface from the finest measurable detail of roughness to the overall figure. We discuss the origin of the structure function in the field of astronomy to describe the effects of air turbulence on image quality, the simple mathematical definition of the structure function and its easy means of calculation and how its results should be scaled depending on the location of the optical surface in a system from pupil to image plane. Finally, we give an example of how to write a specification of an optical surface using the structure function.

Many real-world applications use random numbers generated by pseudo-random number and true random number generators (TRNG). Unlike pseudo-random number generators which rely on an input seed to generate random numbers, a TRNG relies on a non-deterministic source to generate aperiodic random numbers. In this research, we develop a novel and generic software-based TRNG using a random source extracted from compute architectures of today. We show that the non-deterministic events such as race conditions between compute threads follow a near Gamma distribution, independent of the architecture, multi-cores or co-processors. Our design improves the distribution towards a uniform distribution ensuring the stationarity of the sequence of random variables. We improve the random numbers statistical deficiencies by using a post-processing stage based on a heuristic evolutionary algorithm. Our post-processing algorithm is composed of two phases: (i) Histogram Specification and (ii) Stationarity Enforcement. We propose two techniques for histogram equalization, Exact Histogram Equalization (EHE) and Adaptive EHE (AEHE) that maps the random numbers distribution to a user-specified distribution. EHE is an offline algorithm with O(NlogN). AEHE is an online algorithm that improves performance using a sliding window and achieves O(N). Both algorithms ensure a normalized entropy of (0:95; 1:0]. The stationarity enforcement phase uses genetic algorithms to mitigate the statistical deficiencies from the output of histogram equalization by permuting the random numbers until wide-sense stationarity is achieved. By measuring the power spectral density standard deviation, we ensure that the quality of the numbers generated from the genetic algorithms are within the specified level of error defined by the user. We develop two algorithms, a naive algorithm with an expected exponential complexity of E[O(eN)], and an accelerated FFT-based algorithm with an expected quadratic complexity of E[O(N2)]. The accelerated FFT-based algorithm exploits the parallelism found in genetic algorithms on a homogeneous multi-core cluster. We evaluate the effects of its scalability and data size on a standardized battery of tests, TestU01, finding the tuning parameters to ensure wide-sense stationarity on long runs. / October 2016

Obtemos a expressão da densidade espectral de uma impureza no modelo de Anderson assimétrico. No regime de Kondo de baixas energias o modelo de Anderson descreve sistemas quânticos com impurezas magnéticas em meios não magnéticos. Para energias características do orbital de impureza simples ou duplamente ocupado iguais a εf e 2εf+U, respectivamente, o modelo é chamado simétrico para 2εf + U = 0 e assimétrico quando 2εf + U ≠ 0. Para o caso simétrico existe uma expressão devido a Frota que descreve ressonância de Kondo na densidade espectral. Todavia, no caso assimétrico a expressão de Frota deixa de ser válida e é necessária uma nova abordagem. Nesta dissertação, a partir de dados numéricos obtidos pelo consagrado método do Grupo de Renormalização Numérico criado por Wilson em 1974 e de tópicos da física de muitos corpos estudamos a assimetria do modelo de Anderson no regime de Kondo e propomos uma expressão mais geral que a de Frota para a densidade espectral da impureza. / We propose an analytical expression for the impurity spectral density in the Kondo regime of the spin-degenerate asymmetric Anderson model. The Anderson model describes quantum systems of magnetic impurities in nonmagnetic metals. For characteristic energies of single and double impurity occupations εf and 2εf+U, respectively, the model is particlehole symmetric for 2εf + U = 0 and asymmetrical 2εf + U ≠ 0. In the symmetric case, there is an expression due to Frota that describes the Kondo resonance in the spectral density. However, in the asymmetric case Frota´s expression is not valid, and a new approach is necessary. In this work, starting with numerical data provided by the Numerical Renormalization Group method developed by Wilson in 1974, we study the asymmetric Anderson model in the Kondo regime and propose an expression for the impurity spectral density that is more general than Frota´s.

O uso das quasi-particulas de Majorana que emergem nas bordas de um supercondutor topológico é uma plataforma promisora para computação quântica. Novas propostas usam quantum dots (QDs) para detectar sinais de Majorana. Este método tem duas vantagens: 1) Os QDs são os melhores dispositivos para estudar a co-existência de Kondo e Majorana, a qual têm sido reportada recentemente em experimentos. 2) O controle experimental preciso sobre os quantum dots que temos hoje em dia oferece a oportunidade única para manipular quasi-partículas de Majoranas dentro de sistemas com vários dots. Esta ideia abriu novos caminhos para o desenho de arquiteturas quânticas, nos aproximando do objetivo de implementar um computador quântico topológico. O caso mais simples em que se é possível manipular tais quasi-partículas é num quantum dot duplo (DQD). Este modelo oferece várias possibilidades para mover os Majoranas, incluindo múltiplas configurações geométricas dos dots como acoplamentos simétricos, lineares e em junções T. Neste trabalho vamos apresentar uma análise teórica das transiç?s dos sinais de Majorana dentro do DQD em sistemas interagentes e não interagentes. Vamos ver que é possível controlar a localização dos modos zero de Majorana mediante o incremento nas voltagens de gate dos QDs. Também vamos explorar como esses sinais interagem com o efeito Kondo que emerge em superposição com o modo zero de Majorana. Principalmente, vamos a usar dois métodos neste projecto: 1) Usamos as equações de movimento no formalismo de funções de Green para obter expressões exatas para a densidade de estados em sistemas não interagentes. Vamos apresentar o método the eliminação de Gauss-Jordan com grafos, o qual permite resolver rapidamente o sistema linear emergente nas equações de movimento. 2) Em sistemas Coulomb interagentes usamos NRG, no qual poderemos observar a interação entre o Majorana e o efeito Kondo. Vamos testar ambos os métodos nos modelos de um double quantum dot e um QD acoplado com uma cadeia de Majorana, com o qual vamos reproduzir os resultados presentes na literatura. Finalmente, incluímos a maior contribuição deste trabalho, o estudo de um DQD acoplado a uma cadeia de Majorana. / Majorana zero modes (MZMs) emerging at the edges of topological superconducting wires are a promising platform for fault-tolerant quantum computation. Novel proposals use quantum dots (QDs) coupled to the end of these wires to detect Majorana signatures. This detection method provides the following advantages: 1) This device allows to study the prospective coexistence of Kondo-Majorana signatures, which have been recently reported in experiments. 2) Today\'s precise experimental control over QDs offers the unique possibility of manipulating MZMs inside multi-dot systems. This innovative idea has enlightened the design of scalable quantum architectures, bringing us closer to the implementation of a topological quantum computer. The simplest case where Majorana manipulation is possible is in a double quantum dot (DQD). This system offers several possibilities for manipulation of MZMs, including different geometric configurations of the dots, from symmetric and linear couplings to T-dot junctions. In this project, we perform a theoretical study of the transitions of the Majorana signature in these geometries in non-interacting and interacting regimes. By tuning the dot\'s gate voltages, we will show that it is possible to control the localization of the MZM inside both dots. We will also explore the interplay of these signatures with the Kondo effect, which emerges in non-interacting dots in superposition with the MZM. We adopt two methods in this project: 1) The Green equations of motion (EOM) allow us to obtain exact expressions for the density of states in coulomb-non-interacting systems. We present the Graph -Gauss-Jordan elimination process as a simple-graphical method to solve the emergent linear systems in the EOM. 2) We use Wilson\'s numerical renormalization group (NRG) in interacting systems, to study the combined Kondo-Majorana physics. We will test these methods, first in a double quantum dot (DQD) (chapter 3) and then in a QD-Majorana model (chapter 4), where we confirm the results of previous papers [1-3]. Finally, we include the main contribution of this thesis, the study of a DQD coupled to a Majorana chain (chapter 5).

The present work introduces novel methodologies for damage detection and health monitoring of structural and mechanical systems. The new approach uses the angular velocity inside different mathematical forms, via a gyroscope, to detect, locate, and relatively quantify damage. This new approach has been shown to outperform the current state-of-the-art acceleration-based approach in detecting damage on structures. Additionally, the current approach has been shown to be less sensitive to environmental acoustic noises, which present major challenges to the acceleration-based approaches. Furthermore, the current approach has been demonstrated to work effectively on arch structures, which acceleration-based approaches have struggled to deal with. The efficacy of the new approach has been investigated through multiple forms of structural damage indices. The first methodology proposed a damage index that is based on the changes in the second spatial derivative (curvature) of the power spectral density (PSD) of the angular velocity during vibration. The proposed method is based on the output motion only and does not require information about the input forces/motions. The PSD of the angular velocity signal at different locations on structural beams was used to identify the frequencies where the beams show large magnitude of angular velocity. The curvature of the PSD of the angular velocity at these peak frequencies was then calculated. A damage index is presented that measures the differences between the PSD curvature of the angular velocity of a damaged structure and an artificial healthy baseline structure. The second methodology proposed a damage index that is used to detect and locate damage on straight and curved beams. The approach introduces the transmissibility and coherence functions of the output angular velocity between two points on a structure where damage may occur to calculate a damage index as a metric of the changes in the dynamic integrity of the structure. The damage index considers limited-frequency bands of the transmissibility function at frequencies where the coherence is high. The efficacy of the proposed angular-velocity damage-detection approach as compared to the traditional linear-acceleration damage-detection approach was tested on straight and curved beams with different chord heights. Numerical results showed the effectiveness of the angular-velocity approach in detecting damage of multiple levels. It was observed that the magnitude of the damage index increased with the magnitude of damage, indicating the sensitivity of the proposed method to damage intensity. The results on straight and curved beams showed that the proposed approach is superior to the linear-acceleration-based approach, especially when dealing with curved beams with increasing chord heights. The experimental results showed that the damage index of the angular-velocity approach outweighed that of the acceleration approach by multiple levels in terms of detecting damage. A third methodology for health-monitoring and updating of structure supports, which resemble bridges’ bearings, is introduced in this work. The proposed method models the resistance of the supports as rotational springs and uses the transmissibility and coherence functions of the output response of the angular velocity in the neighborhood of the bearings to detect changes in the support conditions. The proposed methodology generates a health-monitoring index that evaluates the level of deterioration in the support and a support-updating scheme to update the stiffness resistance of the supports. Numerical and experimental examples using beams with different support conditions are introduced to demonstrate the effectiveness of the proposed method. The results show that the proposed method detected changes in the state of the bearings and successfully updated the changes in the stiffness of the supports.

The primary goal of this paper is to demonstrate the application of a relatively esoteric and interdisciplinary technique, called spectral analysis, to dyadic social sciences data. Spectral analysis is an analytical and statistical technique, commonly used in engineering, that allows times series data to be analyzed for the presence of significant regular/periodic fluctuations/oscillations. These periodic fluctuations are reflected in the frequency domain as amplitude or energy peaks at certain frequencies. Furthermore, a Magnitude Squared Coherence analysis may be used to interrogate more than one time series concurrently in order to establish the degree of frequency domain correlation between the two series, as well to establish the phase (lead/lag) relationship between the coherent frequency components. In order to demonstrate the application of spectral analysis, the current study utilizes a secondary dyadic dataset comprising 30 daily reports of perceived sexual desire for 65 couples. The secondary goal of this paper is to establish a) whether there is significant periodic fluctuation in perceived levels of sexual desire for men and/or women, and at which specific frequencies, and b) how much correlation or `cross-spectral coherence' there is between partners' sexual desire within the dyads, and c) what the phase lead-lag relationship is between the partners at any of the identified frequency components. Sexual desire was found to have significant periodic components for both men and women, with a fluctuation of once per month being the most common frequency component across the groups of individuals under analysis. Mathematical models are presented in order to describe and illustrate these principal fluctuations. Partners in couples, on average, were found to fluctuate together at a number of identified frequencies, and the phase lead/lag relationships of these frequencies are presented.

Ultra Wideband (UWB) is an emerging technology for use in the indoor wireless personal area networks and ad hoc networks. The more common form of UWB which uses sub-nanosecond pulses without any form of carrier signal is considered in this research. UWB signals have a large bandwidth with allocated frequency spectrum from 3.1 GHz to 10.6 GHz and maximum power restricted to -41dBm/MHz. The IEEE 802.11a is a popular standard for high data rate wireless local area networks (WLANs). The operating frequency of the IEEE 802.11a WLAN is 5 GHz which is right inside the allocated UWB frequency spectrum. One of the main obstacles facing the implementation of UWB devices is the challenge of reducing interference caused by UWB to other systems and vice versa. The potential operating areas/frequencies of the IEEE 802.11a WLAN and UWB systems overlap and therefore the problem of UWB interference to the IEEE 802.11a WLANs and vice versa becomes significant. In this research we have focused on studying the effect of UWB interference on IEEE 802.11a WLANs. The different UWB parameters that affect the interference caused by UWB to IEEE 802.11a WLAN have been considered for determining their effect on the performance of the IEEE 802.11a WLAN. The effect of UWB multipath on the performance of the IEEE 802.11a WLAN has been observed. The UWB parameters have also been compared based on their effect on the performance of the IEEE 802.11a system in the presence of UWB multipath. Additionally, two different interference mitigation techniques that reduce UWB interference to the IEEE 802.11a WLANs have been studied.

A new statistical algorithm, the "modal distribution method", is proposed to statistically quantify the significance of changes in mean frequencies of individual modal vibrations of measured structural response data. In this new method, a power spectrum of measured structural response is interpreted as being a series of independent modal responses, each of which is isolated over a frequency range and treated as a statistical distribution. Pairs of corresponding individual modal distributions from different segments are compared statistically. The first version is the parametric MDM. This method is applicable to well- separated modes having Gaussian shape. For application to situations in which the signal is corrupted by noise, a new noise reduction methodology is developed and implemented. Finally, a non-parametric version of the MDM based on the Central Limit Theorem is proposed for application of MDM to general cases including closely spaced peaks and high noise. Results from all three MDMs are compared through application to simulated clean signals and the two extended MDMs are compared through application to simulated noisy signals. As expected, the original parametric MDM is found to have the best performance if underlying requirements are met: signals that are clean and have well-separated Gaussian mode shapes. In application of nonparametric methods to Gaussian modes with high noise corruption, the noise reduction MDM is found to have lower probability of false alarms than the nonparametric MDM, though the nonparametric is more efficient at detecting changes. In closely related work, the Hermite moment model is extended to highly skewed data. The aim is to enable transformation from non-Gaussian modes to Gaussian modes, which would provide the possibility of applying parametric MDM to well- separated non-Gaussian modes. A new methodology to combine statistical moments using a histogram is also developed for reliable continuous monitoring by means of MDM. The MDM is a general statistical method. Because of its general nature, it may find a broad variety of applications, but it seems particularly well suited to structural health monitoring applications because only very limited knowledge of the excitation is required, and significant changes in computed power spectra may indicate changes, such as structural damage.