With the development of consumer electronics, the circuitry structure become more complex, For this reason, it might cause numerical errors to be cumulated in the simulation using the numerical electromagnetic algorithm, and result in simulated divergence or error. The two reasons of numerical error are passivity and causality, which priginate from the defect in the numerical calculation. In this thesis, for this problem, investigate the numerical compensation method for passivity, The occurrence of passive will make the frequency point of power is negative, this will makes the system divergence, Improve this problem, passivity verification and enforcement by eigenvalue in the Y-parameter, in the S-parameter by the singular value, causality conditions must be match with the imaginary part and the real part relationship, such as the Hilbert transform or the Kramer-Kronig relation, can be used to make causal verification and enforcement. Through some numerical methods, used simulation software such as: HFSS, ADS simulation of the microwave circuit model extraction, modified singular value, eigenvalue, and reached to reduce the numerical error, let it satisfy the convergence and avoid incorrect results, and minimize the impact of the initial data, does not change the characteristics of the original module, but also to solve the passive and the issue of causality.

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 78-79). Also available in electronic version. Access restricted to campus users.

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Problems in the demodulation of one, two, and three-dimensional signals are investigated. In one-dimensional linear systems the analytic signal and the Hilbert transform are central to the understanding of both modulation and demodulation. However, it is shown that an efficient nonlinear algorithm exists which is not explicable purely in terms of an approximation to the Hilbert transform. The algorithm is applied to the problem of finding the envelope peak of a white light interferogram. The accuracy of peak location is then shown to compare favourably with conventional, but less efficient, techniques. In two dimensions (2-D) the intensity of a wavefield yields to a phase demodulation technique equivalent to direct phase retrieval. The special symmetry of a Helmholtz wavefield allows a unique inversion of an autocorrelation. More generally, a 2-D (non-Helmholtz) fringe pattern can be demodulated by an isotropic 2-D extension of the Hilbert transform that uses a spiral phase signum function. The range of validity of the new transform is established using the asymptotic method of stationary phase. Simulations of the algorithm confirm that deviations from the ideal occur where the fringe pattern curvature is larger than the fringe frequency. A new self-calibrating algorithm for arbitrary sequences of phase-shifted interferograms is developed using the aforementioned spiral phase transform. The algorithm is shown to work even with discontinuous fringe patterns, which are known to seriously hamper other methods. Initial simulations of the algorithm indicate an accuracy of 5 milliradians is achievable. Previously undocumented connections between the demodulation techniques are uncovered and discussed.

Problems in the demodulation of one, two, and three-dimensional signals are investigated. In one-dimensional linear systems the analytic signal and the Hilbert transform are central to the understanding of both modulation and demodulation. However, it is shown that an efficient nonlinear algorithm exists which is not explicable purely in terms of an approximation to the Hilbert transform. The algorithm is applied to the problem of finding the envelope peak of a white light interferogram. The accuracy of peak location is then shown to compare favourably with conventional, but less efficient, techniques. In two dimensions (2-D) the intensity of a wavefield yields to a phase demodulation technique equivalent to direct phase retrieval. The special symmetry of a Helmholtz wavefield allows a unique inversion of an autocorrelation. More generally, a 2-D (non-Helmholtz) fringe pattern can be demodulated by an isotropic 2-D extension of the Hilbert transform that uses a spiral phase signum function. The range of validity of the new transform is established using the asymptotic method of stationary phase. Simulations of the algorithm confirm that deviations from the ideal occur where the fringe pattern curvature is larger than the fringe frequency. A new self-calibrating algorithm for arbitrary sequences of phase-shifted interferograms is developed using the aforementioned spiral phase transform. The algorithm is shown to work even with discontinuous fringe patterns, which are known to seriously hamper other methods. Initial simulations of the algorithm indicate an accuracy of 5 milliradians is achievable. Previously undocumented connections between the demodulation techniques are uncovered and discussed.

Electrocardiogram (ECG) time-domain signals contain important information about the heart. Several techniques have been proposed for creating a two-dimensional visualization of an ECG, called a Cardioid, that can be used to detect heart abnormalities with computer algorithms. The derivative method is the prevailing technique, which is popular for its low complexity, but it can introduce distortion into the Cardioid plot without additional signal processing. The Hilbert transform is an alternative method which has unity gain and phase shifts the ECG signal by 90 degrees to create the Cardioid plot. However, the Hilbert transform is seldom used and has historically been implemented with a computationally expensive process. In this thesis we show a low-complexity method for implementing the Hilbert transform as a finite impulse response (FIR) filter. We compare the fundamental differences between Cardioid plots generated with the derivative and Hilbert transform methods and demonstrate the feature-preserving nature of the Hilbert transform method. Finally, we analyze the RMS values of the transformed signals to show how the Hilbert transform method can create near 1:1 aspect ratio Cardioid plots with very little distortion for any patient data.

No description available.

Electromechanical systems dynamics analysis is approached through nonlinear differential equations and further creating a state space model for the system. There are three modules analyzed and validated, first module consists two magnet coupled with a mass spring damper system as a band-pass system, Low-pass equivalent system and Low-pass equivalent system through perturbation analysis. Initially Band Pass frameworks for the systems are formulated considering the relation between the mechanical forcing and current. Using Mathematical tools such as Hilbert transforms, Low-Pass equivalent of the systems are derived. The state equations of the systems are then used to design a working model in MATLAB and simulations investigated completely. The scope of the modules discussed for further development of tools various applications.

In this report we focus on the use of an economical way on how Scalar Network Analyzer (SNA) works instead of Vector Network Analyzer (VNA) to estimate the phase angle of signals in indoor channel. This is detailed in RMS delay theory and simulation section, experimental is designed in the according Experiment Design section, where we also state the required measurements known from the math part. In our work, data are recorded both from two different channel characteristics. Method of achieving amplitude is by using deconvolution theory. The condition of applying Hilbert transform are highlighted as impulse response h(t) in time domain should be causal.  The recorded data amplitude is computed by Hilbert Transform, and therefore validate the condition using Inverse Discrete Fourier Transform (IDFT) back to time domain to achieve h(t). Power delay profile P(t) is therefore presented afterwards. In paper calculations of rms delay τrms  of the channel which is the most important variable are also performed, the results calculated from different windowing truncation and the LOS and NLOS characteristics are compared in discussion and conclusion section, it also includes Opinions of window functions chosen for the phase estimation.

O monitoramento de vibração de máquinas rotativas é de grande interesse da indústria, uma vez que se tem a possibilidade de detectar, com certa antecedência, problemas relacionados à condição de funcionamento do equipamento, possibilitando reparos, ajustes ou consertos e, assim, minimizando custos no caso de falhas graves ou paradas inesperadas. Neste trabalho é feita a adequação de uma bancada de testes para estudo de técnicas de detecção de falhas em rolamentos de esferas por análise de vibração. O objetivo é o de localizar falhas em rolamentos utilizando o monitoramento dos sinais das vibrações (aceleração) no mancal que suporta o rolamento de teste e o posterior processamento com o auxílio de alguma técnica de detecção. Neste trabalho a técnica do envelope foi escolhida. A bancada, assim desenvolvida, permite a retirada e colocação dos rolamentos em estudo de maneira simples e rápida, permitindo a execução de diversos testes com rapidez. A investigação da detecção de falhas em rolamentos é feita comparando-se rolamentos em condições normais com rolamentos que têm um defeito induzido. Inicialmente é apresentada a descrição das origens e formas de propagação das falhas em elementos de rolamentos e também as formas como estas falhas são induzidas em locais específicos de cada rolamento. Uma breve revisão sobre métodos de detecção de falhas no domínio do tempo e da frequência é feita. Ênfase é dada ao método do envelope que faz uso da transformada de Hilbert (Hilbert Transform) conjuntamente com a transformada Rápida de Fourier (Fast Fourier Transform). Em seguida, descreve-se como foram geradas as falhas e separados os grupos de teste, também é descrito como os ensaios foram executados com os danos induzidos em local pré-determinado no rolamento. Os resultados obtidos possibilitaram identificar as origens das falhas induzidas tanto na pista externa quanto na interna dos rolamentos analisando os sinais de vibração do mancal onde está montado o rolamento em teste com o pós-processamento dos mesmos com a técnica investigada. Os testes simulam as condições extremas encontradas em sistemas rotativos de equipamentos industriais através da imposição de cargas verticais ao rolamento. Este estudo de detecção das falhas em rolamentos propiciou uma melhor compreensão e análise do processo de falha nestes componentes. / The vibration monitoring of rotating machines is of great interest to industries since it has the ability to detect, in advance, problems related to the operational condition of the equipment, enabling fixing, adjustments or repair, and thus, minimizing the cost in case of faults or unexpected downtime. In this work, the study of the adequacy of a test bench for detecting faults in ball bearings by vibration analysis techniques is developed. It aims at locating faults in ball bearings using vibration monitoring signals (acceleration) in the journal bearings that support this elements and further processing with the aid of some detection technique. In this work the envelope technique was chosen. The developed test bench thus allows the removal and placement of the bearings in a simple and fast way allowing running quickly several tests. The investigation of detecting faults in ball bearings is made by comparing the bearings under normal conditions with bearings which have an induced defect. First of all is presented a description of the origins and forms of propagation of faults in bearing elements and also the ways in which these failures are induced in specific locations of each bearing. A brief review of methods for detecting faults in the time and frequency domain is made. Emphasis is given to the Envelope Method which uses the Hilbert Transform with the Fast Fourier Transform. Then it is described how the tests were accomplished with the induced damage in predetermined sites in the bearing. The results obtained allowed to identify the origins of the induced bearing failures in both outer and inner races just by reading the vibration signals and post-processing them with the investigated technique. The tests take care to simulate conditions close to those found in actual rotatory systems of industrial equipment by imposing vertical loads to the bearing. This study in detecting flaws in balls bearings provided a better understanding of the analysis failure process in these components.