Harmonic Domain Research Articles

Sparse Representation of Deformable 3D Organs with Spherical Harmonics and Structured Dictionary.

This paper proposed a novel algorithm to sparsely represent a deformable surface (SRDS) with low dimensionality based on spherical harmonic decomposition (SHD) and orthogonal subspace pursuit (OSP). The key idea in SRDS method is to identify the subspaces from a training data set in the transformed spherical harmonic domain and then cluster each deformation into the best-fit subspace for fast and accurate representation. This algorithm is also generalized into applications of organs with both interior and exterior surfaces. To test the feasibility, we first use the computer models to demonstrate that the proposed approach matches the accuracy of complex mathematical modeling techniques and then both ex vivo and in vivo experiments are conducted using 3D magnetic resonance imaging (MRI) scans for verification in practical settings. All results demonstrated that the proposed algorithm features sparse representation of deformable surfaces with low dimensionality and high accuracy. Specifically, the precision evaluated as maximum error distance between the reconstructed surface and the MRI ground truth is better than 3 mm in real MRI experiments.

Requirements for airborne gravity gradient terrain corrections

SummaryAccurate terrain corrections are important for all gravity surveying. In airborne surveys, a digital model of the terrain is constructed and terrain corrections are calculated at each airborne measurement point. Airborne gravity gradiometry is of high spatial resolution and is particularly sensitive to nearby topographic variations, placing particular requirements on the terrain corrections. A combination of mathematical analysis and simulation studies has led to quantification of the requirements: current on-shore, low-level gradiometer surveys require sub-metre accuracy in navigation and in digital terrain model heights; cell sizes (and therefore also topographic sampling) in the terrain model should be about one-third of the ground clearance. The choice of terrain correction density depends on the application and it is important that the interpreter of the corrected gravity data has the ability to test the impact of changes in this density.Accurate calculation of the gravity gradient field at the airborne sampling points may be achieved by a wide variety of either spatial or harmonic domain methods. Calculation in the harmonic domain is fast but assumes the data represent a periodic function on a planar surface. Padding methods for periodic extension and piecewise continuation away from a plane both add error and slow the calculation. Spatial domain methods are slower but can be sped up by the use of various approximations. In both cases, a clear understanding of accuracy requirements is essential for making an appropriate tradeoff between accuracy and speed.

Dynamic companion harmonic circuit models for analysis of power systems with embedded power electronics devices

In this paper a methodology that extends the dynamic harmonic domain (DHD) analysis of large networks is presented. The method combines DHD analysis and discrete companion circuit modeling resulting in a powerful analytic technique called dynamic companion harmonic circuit modeling. It provides for a complete dynamic harmonic analysis of the system while preserving the advantages of discrete companion circuit models. The methodology is illustrated by its application to a three-node power system, where reactive power compensation is achieved using a fixed-capacitor, thyristor-controlled reactor (FC-TCR) and its control system.

Maximum likelihood, parametric component separation and CMB B-mode detection in suborbital experiments

We investigate the performance of the parametric maximum likelihood component separation method in the context of the cosmic microwave background (CMB) B-mode signal detection and its characterization by small-scale CMB suborbital experiments. We consider high-resolution (FWHM = 8′) balloon-borne and ground-based observatories mapping low dust-contrast sky areas of 400 and 1000 square degrees, in three frequency channels, 150, 250, 410 GHz, and 90, 150, 220 GHz, with sensitivity of order 1 to 10 μK per beam-size pixel. These are chosen to be representative of some of the proposed, next-generation, bolometric experiments. We study the residual foreground contributions left in the recovered CMB maps in the pixel and harmonic domain and discuss their impact on a determination of the tensor-to-scalar ratio, r. In particular, we find that the residuals derived from the simulated data of the considered balloon-borne observatories are sufficiently low not to be relevant for the B-mode science. However, the ground-based observatories are in need of some external information to permit satisfactory cleaning. We find that if such information is indeed available in the latter case, both the ground-based and balloon-borne experiments can detect the values of r as low as ∼0.04 at 95 per cent confidence level. The contribution of the foreground residuals to these limits is found to be then subdominant and these are driven by the statistical uncertainty due to CMB, including E-to-B leakage, and noise. We emphasize that reaching such levels will require a sufficient control of the level of systematic effects present in the data.

NeedATool: A NEEDLET ANALYSIS TOOL FOR COSMOLOGICAL DATA PROCESSING

We introduce NeedATool (Needlet Analysis Tool), a software for data analysis based on needlets, a wavelet rendition which is powerful for the analysis of fields defined on a sphere. Needlets have been applied successfully to the treatment of astrophysical and cosmological observations, and in particular to the analysis of cosmic microwave background (CMB) data. Usually, such analyses are performed in real space as well as in its dual domain, the harmonic one. Both spaces have advantages and disadvantages: for example, in pixel space it is easier to deal with partial sky coverage and experimental noise; in harmonic domain, beam treatment and comparison with theoretical predictions are more effective. During the last decade, however, wavelets have emerged as a useful tool for CMB data analysis, since they allow to combine most of the advantages of the two spaces, one of the main reasons being their sharp localisation. In this paper, we outline the analytical properties of needlets and discuss the main features of the numerical code, which should be a valuable addition to the CMB analyst's toolbox.

Geomagnetic secular variation violating the frozen-flux condition at the core surface

We consider a method to extract the part of a given geomagnetic secular variation (SV) model that is not consistent with a frozen-flux condition. This condition is usually derived from the diffusionless radial induction equation at the core-mantle boundary (CMB), and is defined explicitly in the spatial domain: radial flux changes within closed null-flux curves at the core surface are not allowed at any instant. We study here this condition in the spherical harmonic (SH) domain, relying on the SH expansion of the diffusionless equation. SV models at a certain epoch are separated into advective and non-advective parts. The advective (resp. non-advective) part satisfies (resp. does not satisfy) the frozen-flux condition redefined in the SH domain. We show that this separation is not unique. In this work, we achieve a unique separation by assuming the orthogonality of the two parts in terms of the radial SV energy at the CMB. From the recent geomagnetic models, GRIMM and CM4, we find that the non-advective part shows up mainly in the small reverse patches of the radial magnetic field at the CMB. However, non-advective behaviors are also observed outside these patches. As far as no restriction is imposed on core flow configuration, time variations of the non-advective part are not correlated to those of the SV models. However, if the flow is restricted to be tangentially geostrophic, time variations of the SV models have to be partly non-advective. Furthermore, for this flow configuration, the secular decrease of the axial dipole has to be largely non-advective.

Integral equation methods with unique solution for all wavenumbers applied to acoustic radiation

The acoustic exterior Neumann problem is solved using an easy process based upon the boundary element method and able to eliminate effects of irregular frequencies in time harmonic domain. This technique is performed as follows: (i) two computations are done around the characteristic frequency, decreased and increased by a small imaginary part; (ii) average between pressures at these two frequencies ensures unique solution for all wavenumbers. This method is numerically tested for an infinite cylinder, an axisymmetric cylinder, a sphere and a three-dimensional cat’s eye structure. This work highlights ease and efficiency of the technique under consideration to remove the irregular frequencies effects.

Decoupled Newton Algorithms in the Harmonic Domain for the Harmonic Interaction of Line Commutated Converters With AC Systems

Under certain nonideal conditions, the harmonic interaction of line commutated converters with the ac network must be represented by suitable models with high level of detail. A complex and robust solution of this problem is achieved in previous works by means of an iterative procedure in the harmonic domain, where ac and dc harmonics and switching instants are updated simultaneously. This simultaneous method is a full Newton solution (FNS) and therefore it offers a very good convergence, but the integration of the converter model into the whole iterative process (WIP) is complicated due to the heterogeneous form of the Jacobian matrix. The main object of this paper is to present alternative procedures based on decoupled Newton solutions (DNS), where a sequential method of solving the iterative process is used. It leads to a much more modular approach for performing the WIP, since the integration of the converter in the WIP is significant simplified, even when the converter presents any dc side structure. Several critical cases and experiments have been tested in order to show the performance and the convergence properties of the DNS in comparison with FNS.

Correlated component analysis for diffuse component separation with error estimation on simulated Planck polarization data

We present a data analysis pipeline for CMB polarization experiments, running from multi-frequency maps to the power spectra. We focus mainly on component separation and, for the first time, we work out the covariance matrix accounting for errors associated to the separation itself. This allows us to propagate such errors and evaluate their contributions to the uncertainties on the final products.The pipeline is optimized for intermediate and small scales, but could be easily extended to lower multipoles. We exploit realistic simulations of the sky, tailored for the Planck mission. The component separation is achieved by exploiting the Correlated Component Analysis in the harmonic domain, that we demonstrate to be superior to the real-space application (Bonaldi et al. 2006). We present two techniques to estimate the uncertainties on the spectral parameters of the separated components. The component separation errors are then propagated by means of Monte Carlo simulations to obtain the corresponding contributions to uncertainties on the component maps and on the CMB power spectra. For the Planck polarization case they are found to be subdominant compared to noise.

The Effects of Mutual Coupling and Transformer Connection Type on Frequency Response of Unbalanced Three Phase Electrical Distribution System

In this paper, a novel harmonic modeling technique by utilizing the concept of multi-terminal components is presented and applied to frequency scan analysis in multiphase distribution system. The proposed modeling technique is based on gathering the same phase busses and elements as a separate group (phase grouping technique, PGT) and uses multi-terminal components to model three-phase distribution system. Using multi- terminal component and PGT, distribution system elements, particularly, lines and transformers can effectively be modeled even in harmonic domain. The proposed modeling technique is applied to a test system for frequency scan analysis in order to show the frequency response of the test system in single and three-phase conditions. Consequently, the effects of mutual coupling and transformer connection types on three-phase frequency scan responses are analyzed for symmetrical and asymmetrical line configurations.

Integral equation methods with unique solution for all wavenumbers applied to acoustic radiation

The acoustic exterior Neumann problem is solved using an easy process based upon the boundary element method and able to eliminate effects of irregular frequencies in time harmonic domain. This technique is performed as follows: (i) two computations are done around the characteristic frequency, decreased and increased by a small imaginary part; (ii) average between pressures at these two frequencies ensures unique solution for all wavenumbers. This method is numerically tested for an infinite cylinder, an axisymmetric cylinder, a sphere and a three-dimensional cat’s eye structure. This work highlights ease and efficiency of the technique under consideration to remove the irregular frequencies effects.

A Contribution Towards a General and Systematic Procedure for Modeling Line Commutated AC/DC Converters in the Harmonic Domain

Under certain nonideal conditions, harmonic domain models for ac/dc converters require a high level of detail and complexity in order to reproduce low-frequency interactions. In these cases, not only must the representations of the dc ripple but also the behavior of the dc current controller and the structure of the dc side be included. These aspects have been considered in previous works, where the converter operating point (COP) is only defined in terms of dc magnitudes. This paper present several refinements and improvements for modeling this kind of device. It is achieved by means of a systematic method where passive and active dc loads of any structure can be considered, controlled and uncontrolled converters can be modeled, and the COP can be defined in terms of ac or dc magnitudes. With this, great flexibility and accuracy for modeling line-commutated ac/dc converters are obtained.

Robust and less robust features in the tangential geostrophy core flows

SUMMARY A number of core surface flow models have been inferred from geomagnetic field models by applying the frozen-flux induction equation. It is well known, however, that the flow is not fully resolvable. Because of theoretical and observational setbacks, the model space of the flow involves a null-space. Elements of the effective null-space can be considered as flows generating geomagnetic secular variation (SV) not sufficiently large compared with the variance of SV models. In the flow inversion, spurious flows belonging to such an effective null-space, thereby practically free from the direct constraint from the SV, may possibly emerge in resulting flow models and disguise the true core flow image. In this paper, we investigate the typical manifestation of the effective null-space in the model flow space, to discuss which part of estimated flow models is subject to the ambiguity due to the false imaging. From existing flow models built with the tangential geostrophy (TG) assumption, we extract a part belonging to the effective null-space. The extraction is performed in the spherical harmonic domain, analyzing the observation equation matrix associating truncated spherical harmonic coefficients of SV and TG flow. This approach is applied to typical TG flow models, epoch by epoch, over the time-span 1842.5-1987.5. The extracted flows are prominent in the azimuthal direction particularly around the equatorial region and vary vigorously in time. They are largely responsible for the zonal toroidal component of the examined models at mid- and low latitudes, whereas not at the polar regions. It is shown, nevertheless, that this poorly robust flow part does not so seriously affect the prediction of the decadal length-of-day variations.

Improved inverse and probabilistic methods for geophysical applications of GRACE gravity data

SUMMARY Mapping time-varying gravity via satellite-to-satellite tracking systems holds great potential as a new way to monitor the Earth's global climate system. Measurement noises and systematic deficiencies in sampling, both in time and space, cause global geoid or surface mass solutions to have a structured spherical harmonic error spectrum, with strong degree and order dependences and cross-correlations. To extract average values of geoid or surface mass variations around global gridpoints on Earth's surface and over various geographic regions, both the shape of the averaging kernel and the resulting average uncertainties must be considered quantitatively and statistically. We investigate two methods of the Backus and Gilbert continuous geophysical inverse formalism for optimal averages around points on Earth's surface. The first averaging kernel optimally approximates the Dirac-δ function. With an equivalent measure of deviation from the Dirac-δ function, the optimal average has greater (up to 2.6 times) accuracy than does the most widely used isotropic Gaussian filter for GRACE analysis. The second method was crafted to decrease the kernel weight as the distance from the point of interest increases. A new method is presented to use a modified Gaussian averaging kernel that reduces average uncertainties with minimum loss of resolution. The modified method has some advantages over using the kernel that optimally approximates the Dirac-δ function. Both methods are computationally efficient and are applied to simulated and real GRACE data to compute improved averages around fine-resolution global gridpoints and used with non-diagonal covariance matrices to intelligently reduce effects of correlated errors. The optimal probabilistic method of least squares with a priori information is discussed in the spherical harmonic domain. The property of optimality will be preserved when the estimates are mapped to the geographic domain for spatial averages. A regionally-bounded Gaussian a priori function is derived in the spherical harmonic domain to better represent different change regimes separated by major geographic boundaries. We also introduce an algorithm to derive the optimal regional average incorporating a constraint such that the average weight over the region is unity. Applications of such more realistic a priori information (and/or constraint) can produce improved average estimates using satellite gravity data.

Harmonic domains and synchronization in typically and atypically developing Hebrew-speaking children

This paper presents a comparative study of typical and atypical consonant harmony (onset–onset place harmony), with emphasis on (i) the size of the harmonic domain, (ii) the position of the harmonic domain within the prosodic word, and (iii) the maximal size of the prosodic word that exhibits consonant harmony. The data, drawn from typically and atypically developing Hebrew-speaking children, reveal the following characteristics: (i) The harmonic domain is usually limited to two consonants in typical harmony, but may span to up to four consonants in atypical harmony. (ii) The harmonic domain usually aligns with the left edge of the prosodic word in typical harmony, but may also align with the right edge of the prosodic word in atypical harmony. (iii) Typical consonant harmony is usually limited to maximally trisyllabic productions, while atypical harmony is also found in quadrisyllabic productions. In addition, the sporadic variation characterizing early typical speech appears in advanced stages in atypical speech. With reference to the hierarchical structure of the word, these distinctions are analyzed here in terms of (a-)synchronization between the development of the prosodic word layer (number of syllables) and the segmental layer. The formal analysis is couched within the framework of Optimal Domains Theory (Cole, J., Kisseberth, C., 1994. An optimal domain theory of harmony. Studies in the Linguistic Sciences 24, 1–13, ROA-22; Cole, J., Kisseberth, C., 1995a. Paradoxical strength conditions in harmony systems, ROA-48; Cole, J., Kisseberth, C., 1995b. Nasal harmony in optimal domain theory, ROA-49; Cole, J., Kisseberth, C., 1996. Restricting multi-level constraint evaluation: opaque rule interaction in Yawelmani vowel harmony, ROA-98; Cassimjee, F., Kisseberth, C., 1997. Optimal domain theory and Bantu tonology: a case study from Isixhosa and Shingazidja, ROA-176; Cassimjee, F., Kisseberth, C., 1998. Tonal variation across Emakhuwa dialects, ROA-289; Cassimjee, F., Kisseberth C., 1999. A conspiracy argument for optimality theory: Emakhuwa dialectoloy, ROA-331), a branch of optimality theory (Prince, A., Smolensky, P., 1993. Optimality theory: Constraint Interaction in Generative Grammar. Ms. Rutgers University and University of Colorado, Boulder).

Dynamic Harmonic Domain Modeling of Transients in Three-Phase Transmission Lines

This paper presents a traveling wave based transmission line model which includes harmonics in transient state. The line model is interfaced with a nonlinear load and both are simulated through the dynamic harmonic domain technique. This technique permits the user to follow step-by-step the harmonics of the propagating waveforms during transient conditions. An illustrative example involving a transmission line network with nonlinear loads is presented and the proposed model is compared with its time domain counterpart.

Extremal harmonic active control of power for rotating machines

Most of the time, the speed of rotating machines oscillates in synchronization with the rotor position. Those speed fluctuations, generated by disturbance torques, can be actively controlled with a second torque source coupled to the shaft of the machine. To achieve this active control, the problem is reformulated in the harmonic domain with regard to the main order of the fluctuations. The control objective is to extremalize an energetic criterion like kinetic energy (cancelling the speed ripple), reactive power (to add a virtual flywheel) or active power (to charge a battery). To reach those objectives, two extremal controllers are proposed with implicit or explicit criterion management. The controllers are tested on an academic test bed. The results show that the controllers converge at the extremum of each criterion.

Surround sound echo cancellation in the spherical harmonic domain

The problem of creating a multiuser hands‐free immersive telecommunications environment poses many challenges for acoustic signal processing. The most pressing is the creation of a fast multichannel acoustic echo canceller (MCAEC) to eliminate acoustic feedback created in the speaker‐microphone loop. Traditional multichannel adaptive algorithms for echo cancellation are not fast enough to work in systems with highly correlated multichannel signals like those found in the traditional telecommunications setup. This work presents analysis of a proposed acoustic echo cancellation system that operates in the spherical harmonic domain. Transforming the microphone and speaker signals into the spherical harmonic domain reduces both the number of channels and the correlation between channels for faster convergence of the adaptive MCAEC filters. This method also has the added benefit of being independent of the microphone and speaker array configuration, resulting in a hybrid mono/stereo/multichannel acoustic echo canceller. This work is funded by NSF Grant IIS‐0534221.

Nonlinear modelling and analysis of active magnetic bearing systems in the harmonic domain: a case study

The methodology for the nonlinear modelling and analysis of active magnetic bearing (AMB) systems in the harmonic domain (HD) is presented. This approach is based on the HD linearisation of the AMB system around nonlinear stationary solutions at different rotating speeds. The main advantage obtained is the representation of the periodic LTV models that describe the steady-state dynamics for each speed, by means of LTI models in the HD. In order to show its possibilities, the proposed approach is applied to an AMB laboratory testbed based on the MBC500 Rotor Dynamics from Launchpoint Technologies. This analysis explains the nonlinear nature of the response that appears at high speeds, due to the large oscillations introduced by the shaft unbalance, and detects a low-frequency gain loss when increasing the rotating speed. This phenomenon causes the instability of the system, leading to destructive crashes. In addition, the analysis allows to take into account the effect of the delay introduced by the calculation time in the system behaviour when the controller is implemented by using digital devices.

Operation of synchronous generator under the influence of time and space harmonics

In stability studies, it is necessary to compute the initial steady-state values of synchronous machine variables as a function of non-sinusoidal terminal quantities. In this paper, the impact of current time and inductance space harmonics on the steady state operation and load angle of synchronous generator is investigated. A nonlinear model of salient-pole synchronous generator based on the abc-frame of reference in harmonic domain is used to investigate the impact of harmonics on the stator flux. It is shown that the fundamental component of stator flux contains additional terms due to the interaction between time and space harmonics. Park transformation is applied to this modified fundamental stator flux to compute the load angle. Simulation results provide new information about the steady-state operating point of synchronous generator under harmonically polluted operating conditions. It is also shown that damper windings and current harmonics phase angles have considerable effects on the operation of synchronous generator.