A coupled approximate deconvolution and dynamic mixed scale model for large-eddy simulation

Large-eddy simulations of incompressible Newtonian fluid flows with approximate deconvolution models based on the van Cittert method are reported. The Legendre spectral element method is used for the spatial discretization to solve the filtered Navier--Stokes equations. A novel variant of approximate deconvolution models blended with a mixed scale model using a dynamic evaluation of the subgrid-viscosity constant is proposed. This model is validated by comparing the large-eddy simulation with the direct numerical simulation of the flow in a lid-driven cubical cavity, performed at a Reynolds number of 12'000. Subgrid modeling in the case of a flow with coexisting laminar, transitional and turbulent zones such as the lid-driven cubical cavity flow represents a challenging problem. Moreover, the coupling with the spectral element method having very low numerical dissipation and dispersion builds a well suited framework to analyze the efficiency of a subgrid model. First- and second-order statistics obtained using this new model are showing very good agreement with the direct numerical simulation. Filtering operations rely on an invertible filter applied in a modal basis and preserving the C0-continuity across elements. No clipping on dynamic parameters was needed to preserve numerical stability

Discrete-Time Filter Synthesis using Product of Gegenbauer Polynomials

A new approximation to design continuoustime and discrete-time low-pass filters, presented in this paper, based on the product of Gegenbauer polynomials, provides the ability of more flexible adjustment of passband and stopband responses. The design is achieved taking into account a prescribed specification, leading to a better trade-off among the magnitude and group delay responses. Many well-known continuous-time and discrete-time transitional filter based on the classical polynomial approximations(Chebyshev, Legendre, Butterworth) are shown to be a special cases of proposed approximation method

On acceleration of Krylov-subspace-based Newton and Arnoldi iterations for incompressible CFD: replacing time steppers and generation of initial guess

We propose two techniques aimed at improving the convergence rate of steady state and eigenvalue solvers preconditioned by the inverse Stokes operator and realized via time-stepping. First, we suggest a generalization of the Stokes operator so that the resulting preconditioner operator depends on several parameters and whose action preserves zero divergence and boundary conditions. The parameters can be tuned for each problem to speed up the convergence of a Krylov-subspace-based linear algebra solver. This operator can be inverted by the Uzawa-like algorithm, and does not need a time-stepping. Second, we propose to generate an initial guess of steady flow, leading eigenvalue and eigenvector using orthogonal projection on a divergence-free basis satisfying all boundary conditions. The approach, including the two proposed techniques, is illustrated on the solution of the linear stability problem for laterally heated square and cubic cavities

Computer-Aided Design of Switched-Capacitor Filters

This thesis describes a series of computer methods for the design of switched-capacitor filters. Current software is greatly restricted in the types of transfer function that can be designed and in the range of filter structures by which they can be implemented. To solve the former problem, several new filter approximation algorithms are derived from Newton's method, yielding the Remez algortithm as a special case (confirming its convergency properties). Amplitude responses with arbitrary passband shaping and stopband notch positions are computed. Points of a specified degree of tangency to attenuation boundaries (touch points) can be placed in the response, whereby a family of transfer functions between Butterworth and elliptic can be derived, offering a continuous trade-off in group delay and passive sensitivity properties. The approximation algorithms have also been applied to arbitrary group delay correction by all-pass functions. Touch points form a direct link to an iterative passive ladder design method, which bypasses the need for Hurwitz factorisation. The combination of iterative and classical synthesis methods is suggested as the best compromise between accuracy and speed. It is shown that passive ladder prototypes of a minimum-node form can be efficiently simulated by SC networks without additional op-amps. A special technique is introduced for canonic realisation of SC ladder networks from transfer functions with finite transmission at high frequency, solving instability and synthesis difficulties. SC ladder structures are further simplified by synthesising the zeros at +/-2fs which are introduced into the transfer function by bilinear transformation. They cause cancellation of feedthrough branches and yield simplified LDI-type SC filter structures, although based solely on the bilinear transform. Matrix methods are used to design the SC filter simulations. They are shown to be a very convenient and flexible vehicle for computer processing of the linear equations involved in analogue filter design. A wide variety of filter structures can be expressed in a unified form. Scaling and analysis can readily be performed on the system matrices with great efficiency. Finally, the techniques are assembled in a filter compiler for SC filters called PANDDA. The application of the above techniques to practical design problems is then examined. Exact correction of sinc(x), LDI termination error, pre-filter and local loop telephone line weightings are illustrated. An optimisation algorithm is described, which uses the arbitrary passband weighting to predistort the transfer function for response distortions. Compensation of finite amplifier gain-bandwidth and switch resistance effects in SC filters is demonstrated. Two commercial filter specifications which pose major difficulties for traditional design methods are chosen as examples to illustrate PANDDA's full capabilities. Significant reductions in order and total area are achieved. Finally, test results of several SC filters designed using PANDDA for a dual-channel speech-processing ASIC are presented. The speed with which high-quality, standard SC filters can be produced is thus proven

Distinguishing Harmonic Behavior Of Longitudinal Resonant Combustion In A Variable Geometry Model Rocket Combustor

Throughout the study of high frequency combustion instability in a single element Continuously Variable Resonance Combustor (CVRC), the excitation of the fundamental longitudinal mode is closely followed by the excitation of higher harmonic modes. In an attempt to establish a heuristic relationship between the appearances of the fundamental mode and its harmonics, several unstable fixed geometry and variable geometry tests from the CVRC are analyzed through traditional Fourier-based methods and alternative signal processing methods such as wavelet analysis and Instantaneous Frequency (IF) Analysis from PC Signal Analysis. Early results led to the conclusion that traditional Fourier-based analysis provides believable and consistent results for the first three modes. However, Fourier analysis is sensitive to effects from non-sinusoidal waveforms. Further work using manufactured signals with both sinusoidal and steepfronted waveforms established that it is unclear which parts of the calculated harmonic signals are data artifacts and which are true signal. Supplementary assessment of IF Analysis and the traditional Fourier-based analysis explored the applicability of each method, the inherent data artifacts, and distinguishing behavior between the experimental data and those data artifacts. The results obtained from the IF Analysis provide good agreement with the traditional Fourier-based analysis, though one uses FIR filters and the other uses IIR filters. The validity of the results is sensitive to the settings chosen for these filters. It is shown that harmonic modal content exists in the CVRC, but it is also shown that the current results include indistinguishable Fourier artifacts. Both methods are sensitive to the sinusoidal assumption and cannot correctly interpret steep-fronted waveforms. This supplementary assessment has shown that IF Analysis is no worse than traditional Fourier-based analysis, but it fails to provide additional useful information. Qualitative modal behavior is distinguishable from the experimental data, including the sequential excitation of modes and the increasing growth rate with increasing mode number. However, quantitative results such as the growth rate or modal amplitude have been shown to be unreliable. The acoustic wave assumption is supported by the standing wave behavior observed in CVRC, specifically the decreasing amplitude of a mode near its equivalent pressure node location and the relative phase between modal signals on either side of its equivalent pressure node. However, the shock-like wave assumption has not been completely disproved. Additional work needs to be done with wavelet analysis using steep-fronted wavelet shapes to assess the potential steep-fronted waveform

Image Understanding and Robotics Research at Columbia University

The research investigations of the Vision/Robotics Laboratory at Columbia University reflect the diversity of interests of its four faculty members, two staff programmers and 15 Ph.D. students. Several of the projects involve either a visiting computer science post-doc, other faculty members in the department or the university, or researchers at AT&T Bell Laboratories or Philips laboratories. We list below a summary of our interest and results, together with the principal researchers associated with them. Since it is difficult to separate those aspects of robotic research that are purely visual from those that are vision-like (for example, tactile sensing) or vision-related (for example, integrated vision-robotic systems), we have listed all robotic research that is not purely manipulative

FIR Filter Design Using Distributed Maximal Flatness Method

In the paper a novel method for filter design based on the distributed maximal flatness method is presented. The proposed approach is based on the method used to design the most common FIR fractional delay filter – the maximally flat filter. The MF filter demonstrates excellent performance but only in a relatively narrow frequency range around zero frequency but its magnitude response is no greater than one. This ,,passiveness” is the reason why despite of its narrow band of accurate approximation, the maximally flat filter is widely used in applications in which the adjustable delay is required in feedback loop. In the proposed method the maximal flatness conditions forced in standard approach at zero frequency are spread over the desired band of interest. In the result FIR filters are designed with width of the approximation band adjusted according to needs of the designer. Moreover a weighting function can be applied to the error function allowing for designs differing in error characteristics. Apart from the design of fractional delay filters the method is presented on the example of differentiator, raised cosine and square root raised cosine FIR filters. Additionally, the proposed method can be readily adapted for variable fractional delay filter design regardless of the filter type.

Projeto de filtros digitais transicionais Cauer-Chebyshev inverso

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Engenharia Elétrica.O presente trabalho apresenta uma metodologia de projeto de filtros transicionais a partir de aproximações não-polinomiais. A implementação desses filtros é realizada com base em técnicas de síntese de filtros digitais IIR, com o objetivo de obter o melhor desempenho de respostas de magnitude, fase e tempo visando uma específica aplicação. A utilização de filtros transicionais não-polinomiais, mais especificamente filtros transicionais Cauer-Chebyshev Inverso, deve-se ao fato de a aproximação Cauer apresentar a menor ordem dentre todas as funções de filtros seletores e de a aproximação Chebyshev Inverso ser também não-polinomial e apresentar melhores características de fase e de tempo em relação à aproximação Cauer. Os exemplos de aplicação mostrados são avaliados através de seis técnicas de projeto de filtros digitais utilizando-se uma abordagem de projeto indireta. Na tentativa de obter o melhor desempenho de cada uma delas são consideradas algumas estratégias de projeto, tais como pré-distorção e principalmente transformação espectral, cujo estudo resultou em procedimentos que melhoram a aplicabilidade dessa última. Assim, é possível compará-las entre si, possibilitando a escolha da melhor estratégia de filtragem para cada problema. Para auxiliar no projeto de filtros digitais como também viabilizar algumas medidas de linearidade de fase consideradas, um software em ambiente Matlab foi desenvolvido

An RC active filter design handbook

The design of filters is described. Emphasis is placed on simplified procedures that can be used by the reader who has minimum knowledge about circuit design and little acquaintance with filter theory. The handbook has three main parts. The first part is a review of some information that is essential for work with filters. The second part includes design information for specific types of filter circuitry and describes simple procedures for obtaining the component values for a filter that will have a desired set of characteristics. Pertinent information relating to actual performance is given. The third part (appendix) is a review of certain topics in filter theory and is intended to provide some basic understanding of how filters are designed

New Class of Functions for the Synthesis of Chain Filters

Апроксимација и импементација ланчаних филтара је предмет анализе истраживања презентованих у дисертацији. Најважнији резултати истраживања су приказани у четири поглавља: Синтеза филтарских функција Jacobi-jeвим полиномима, Модификована Jacobijeева ланчана функција, Синтеза полиномских ланчаних филтара и Реализација. У Закључку су сумирани најважнији научни доприноси и правци будућих истраживања. Главни део представљене дисертације подељен је у пет поглавља. У другом поглављу, након увода, појам апроксимације амплитудске карактеристике полиномских филтара ортогоналним полиномима је проширен и на примену ортогоналних Jacobijeвих полинома. Једноставном модификацијом ортогоналних Jacobi-jевих полинома добијени су полиноми названи Модификовани-Jacobi-jеви полиноми, погодни за апроксимацију амплитудске карактеристике аналогних филтара пропусника ниских фреквенција. Треба напоменути да модификовани Jacobijeви полиноми нису ортогонални. Ако је степен филтара задат, оба параметра Jacobijевог полинома (α и β) су слободни параметри који се могу користити за континуирано подешавање амплитудске или фазне карактеристике филтра. То чини да су добијене фреквенцијске карактеристике флексибилније од апроксимација стандардним ортогоналним полиномима као што су апроксимације са Chebysheveвим или Legendrов полиномима. Треба напоменути да предложена апроксимација модификованим-Jacobijeвим полиномима, погодним избором параметара Jacobijeвих полинома, генерише многе напред поменуте апроксимације полиномских филтара, као на пример: Butterworth-ов, Chebyshevev, Chebysh-евев, Legendr-ов и њихове деривате које су предложили Ku и Drubin, итд. Описана техника синтезе анлогних филтара модификованим Jacobijeвим полиномима, учињена је још ефикаснијом додавњем коначних нула преноса у преносну функцију филтра. Као што је добро познато, коначне нуле преноса на реалним фреквенцијама, тј. на имагинарној оси, немају утицаја на фазну карактеристику филтра. Међутим оне се могу тако одредити да карактеристика слабљења има Chebyshевев карактер у непропусном опсегу. Наведени су подаци о положају полова ове класе филтара у s-равни за параметар Jacobijeв их полинома, који дају приближно монотону амплитудску карактеристику за степен филтра од три до десет. Извршено је детаљно порђење добијених резултата са познатим критично монотоним преносним функцијама, и показано је да предложена класа полинома нуди и боља решења од стандардних апроксимација. На крају ове главе извршено је и поређење нове класе филтара са коначним нулама преноса и инверзног Chebyshevev филтра. Показано је да синтеза филтара модификованим Jacobijeвим полиномима са коначним нулама преноса нуди боље перформансе од инверзних Chebyshevevih филтара. У трећем поглављу описана је нова класа преносних функција за синтезу ланчаних филтара. Ове ланчане функције, назване модификоване Jacobijeve ланчане финкције (mJCF),добијене су као производ модификованих Jacobijevих полинома нижег степена, назване seed функције. Оптимизација преносне функције се може завршити тако да све seed функције буду са истим параметрима. У том случају у Chebysheveve ланчане функције (CCF) и Legendrовe ланчане функије (LCF) су специјални случајеви модификованих Jacobijevиx ланчаних функција. Бољи резултати се могу добити ако се за задати степен филтра, поред оптимизаије броја seed функција, оптимизира се и свака seed функција која може да има различите параметре Jacobijevих полинома. У том случају је број могућих комбинација велики па је погодно најпре извршити оптимизацију са истим параметрима, а затим одабрати једну seed функцију којом ће се извршити накнадно подешавање неке од карактеристика у устаљеном или прелазном стању. Излагања у четвртом поглављу односе се на синтезу полиномских лачаних филтара. Посебна пажња је поклоњена ланчаним филтрим са две seed функије.Фактор доброте коњуговано комплексног пара полова, фактор нагиба и максимална вредност повратних губитака су коришћени за поређење преносних функција. Функције циља су повратни губици. На примерима преносних функција седмог, осмог, деветог и десетог реда анализирани су реазултати апроксимације. Показано је да се редукција повратног слабљења може остварити преносним функцијама вишег реда без велике промене Q-фактора пола и коефицијента нагиба. Ова техника је први пут примењена давне 1967 за редукцију Q-фактора критичног пара полова. Коначно, излагања у петој глави се односе на пасивну LC лесвичасту реализацију ланчаних филтара. Последњи корак у пројектовању филтара јесте формирање прототипа електричног кола које служи као основа за физичку реализацију (имплементацију) филтра. Наиме, реализаицја нископропусних прототипова филтара засновна је на елементима са концентрисаним параметрима двоприступне пасивне лесвичасте LC мреже. Филтар се побуђује реалним генератором који има унутрашњу отпорност, а на другом приступу затворен је отпорником. Управо ове конфигурације представљају везу између филтарске функције и физичке реализаије филтра. Посматрају се прототипски филтар пропусник ниских фреквенција и филтар пропусник опсега фреквенција и њихова имплементацја помоћу елемената са конентрисаним параметарима. Посебна пажња је посвећена реализацији ланчаног филтра пропусника ниских фреквенција заснованог на каскади секција водова