Showing papers on "Filter design published in 2011"
TL;DR: This paper demonstrates a frequency-domain-model-based approach to determine the optimum filter parameters that provide the necessary performance under all operating conditions given the necessary design constraints.
Abstract: This paper describes the design procedure and performance of an LCL grid filter for a medium-voltage neutral-point clamped converter to be adopted for a multimegawatt (multi-MW) wind turbine. The unique filter design challenges in this application are driven by a combination of the medium-voltage converter, a limited allowable switching frequency, component physical size and weight concerns, and the stringent limits for allowable injected current harmonics. Traditional design procedures of grid filters for lower power and higher switching frequency converters are not valid for a multi-MW filter connecting a medium-voltage converter switching at low frequency to the electric grid. This paper demonstrates a frequency-domain-model-based approach to determine the optimum filter parameters that provide the necessary performance under all operating conditions given the necessary design constraints. To achieve this goal, new concepts, such as virtual-harmonic content and virtual filter losses are introduced. Moreover, a new passive-damping technique that provides the necessary damping with low losses and very little degradation of the high-frequency attenuation is proposed.
383 citations
TL;DR: This paper is devoted to the presentation of a new linear and nonlinear filter modeling based on a gravitational search algorithm (GSA) where unknown filter parameters are considered as a vector to be optimized.
340 citations
TL;DR: The problem of asynchronous filtering for the underlying systems in linear cases is formulated and the conditions of the existence of admissible asynchronous filters are obtained.
Abstract: Switched dynamical systems can be found in many practical electronic circuits, such as various kinds of power converters, chaos generators, etc. This paper is concerned with the filter design problem for a class of switched system with average dwell time switching. Mode-dependent full-order filters are designed taking a more practical phenomenon, the asynchronous switching into account, where “asynchronous” means that the switching of the filters to be designed has a lag to the switching of the system modes. New results on the stability and l2-gain analyses for the systems are first given where the Lyapunov-like functions during the running time of subsystems are allowed to increase. In light of the proposed Lyapunov-like functions, the desired mode-dependent filters can be designed in that the unmatched filters are allowed to perform in the interval of the asynchronous switching before the matched ones are applied. In H∞ sense, the problem of asynchronous filtering for the underlying systems in linear cases is formulated and the conditions of the existence of admissible asynchronous filters are obtained. Two examples are provided to show the potential of the developed results.
286 citations
TL;DR: This technical note introduces a new class of discrete-time networked nonlinear systems with mixed random delays and packet dropouts, and the H∞ filtering problem for such systems is investigated, and sufficient conditions for the existence of an admissible filter are established.
Abstract: In this technical note, a new class of discrete-time networked nonlinear systems with mixed random delays and packet dropouts is introduced, and the H∞ filtering problem for such systems is investigated The mixed stochasitc time-delays consist of both discrete and infinite distributed delays and the packet dropout phenomenon occurs in a random way Furthermore, new techniques are presented to deal with the infinite distributed delay in the discrete-time domain Sufficient conditions for the existence of an admissible filter are established, which ensure the asymptotical stability as well as a prescribed H∞ performance Finally, examples are given to demonstrate the effectiveness of the proposed filter design scheme in this technical note
257 citations
TL;DR: The main purpose of this paper is to design a robust filter, over a given finite-horizon, such that the H∞ disturbance attenuation level is guaranteed for the time-varying Markovian jump systems in the presence of both the randomly occurring nonlinearities and the sensor saturation.
Abstract: This paper addresses the robust H∞ filtering problem for a class of discrete time-varying Markovian jump systems with randomly occurring nonlinearities and sensor saturation. Two kinds of transition probability matrices for the Markovian process are considered, namely, the one with polytopic uncertainties and the one with partially unknown entries. The nonlinear disturbances are assumed to occur randomly according to stochastic variables satisfying the Bernoulli distributions. The main purpose of this paper is to design a robust filter, over a given finite-horizon, such that the H∞ disturbance attenuation level is guaranteed for the time-varying Markovian jump systems in the presence of both the randomly occurring nonlinearities and the sensor saturation. Sufficient conditions are established for the existence of the desired filter satisfying the H∞ performance constraint in terms of a set of recursive linear matrix inequalities. Simulation results demonstrate the effectiveness of the developed filter design scheme.
240 citations
TL;DR: The co-design approach for the integration of filter and antenna is introduced and the proposed structure provides good design accuracy and filter skirt selectivity as compared to the filter simple cascade with antenna and a bandpass filter of the same order.
Abstract: Synthesis and design of a new printed filtering antenna is presented in this communication. For the requirements of efficient integration and simple fabrication, the co-design approach for the integration of filter and antenna is introduced. The printed inverted-L antenna and the parallel coupled microstrip line sections are used for example to illustrate the synthesis of a bandpass filtering antenna. The equivalent circuit model for the inverted-L antenna, which is mainly a series RLC circuit, is first established. The values of the corresponding circuit components are then extracted by comparing with the full-wave simulation results. The inverted-L antenna here performs not only a radiator but also the last resonator of the bandpass filter. A design procedure is given, which clearly indicates the steps from the filter specifications to the implementation. As an example, a 2.45 GHz third-order Chebyshev bandpass filter with 0.1 dB equal-ripple response is tackled. Without suffering more circuit area, the proposed structure provides good design accuracy and filter skirt selectivity as compared to the filter simple cascade with antenna and a bandpass filter of the same order. The measured results, including the return loss, total radiated power, and radiation gain versus frequency, agree well with the designed ones.
200 citations
15 May 2011
TL;DR: The derivation of the optimal filter is based on the use of minimum principle of Pontryagin coupled with the Lagrange multiplier method and the results of generalized inverse of matrices for type-II sensors.
Abstract: This paper is concerned with the problem of filter design for target tracking over sensor networks. Different from most existing works on sensor networks, we consider the heterogeneous sensor networks with two types of sensors different on processing abilities (denoted as type-I and type-II sensors, respectively). However, questions of how to deal with the heterogeneity of sensors and how to design a filter for target tracking over such kind of networks remain largely unexplored. We propose in this paper a novel distributed consensus filter to solve the target tracking problem. Two criteria, namely, unbiasedness and optimality, are imposed for the filter design. The so-called sequential design scheme is then presented to tackle the heterogeneity of sensors. The minimum principle of Pontryagin is adopted for type-I sensors to optimize the estimation errors. As for type-II sensors, the Lagrange multiplier method coupled with the generalized inverse of matrices is then used for filter optimization. Furthermore, it is proven that convergence property is guaranteed for the proposed consensus filter in the presence of process and measurement noise. Simulation results have validated the performance of the proposed filter. It is also demonstrated that the heterogeneous sensor networks with the proposed filter outperform the homogenous counterparts in light of reduction in the network cost, with slight degradation of estimation performance.
158 citations
TL;DR: A nonlinear system, which given the input and output of the system is regarded as linear time-varying, is proposed and a Kalman filter is applied to successfully estimate the system state.
153 citations
TL;DR: A sequential averaging filter is developed that adaptively varies the number of complexes included in the averaging based on the characteristics of the ECG signal, which demonstrates that, without using a priori knowledge on signal characteristics, the Filter with adaptive noise estimation performs similar to the filter with optimized fixed noise covariance.
Abstract: The ongoing trend of ECG monitoring techniques to become more ambulatory and less obtrusive generally comes at the expense of decreased signal quality. To enhance this quality, consecutive ECG complexes can be averaged triggered on the heartbeat, exploiting the quasi-periodicity of the ECG. However, this averaging constitutes a tradeoff between improvement of the SNR and loss of clinically relevant physiological signal dynamics. Using a Bayesian framework, in this paper, a sequential averaging filter is developed that, in essence, adaptively varies the number of complexes included in the averaging based on the characteristics of the ECG signal. The filter has the form of an adaptive Kalman filter. The adaptive estimation of the process and measurement noise covariances is performed by maximizing the Bayesian evidence function of the sequential ECG estimation and by exploiting the spatial correlation between several simultaneously recorded ECG signals, respectively. The noise covariance estimates thus obtained render the filter capable of ascribing more weight to newly arriving data when these data contain morphological variability, and of reducing this weight in cases of no morphological variability. The filter is evaluated by applying it to a variety of ECG signals. To gauge the relevance of the adaptive noise-covariance estimation, the performance of the filter is compared to that of a Kalman filter with fixed, (a posteriori) optimized noise covariance. This comparison demonstrates that, without using a priori knowledge on signal characteristics, the filter with adaptive noise estimation performs similar to the filter with optimized fixed noise covariance, favoring the adaptive filter in cases where no a priori information is available or where signal characteristics are expected to fluctuate.
146 citations
TL;DR: A new necessary and sufficient condition for a class of discrete-time Markovian jump singular systems to be stochastically Markovians jump admissible is proposed in the form of strict linear matrix inequalities.
Abstract: This paper addresses the problem of fault detection filter design for discrete-time Markovian jump singular systems with intermittent measurements. The measurement transmission from the plant to the fault detection filter is assumed to be imperfect and a stochastic variable is utilized to model the phenomenon of data missing. Our attention is focused on the design of a fault detection filter such that the residual system is stochastically Markovian jump admissible and satisfies some expected performances. A new necessary and sufficient condition for a class of discrete-time Markovian jump singular systems to be stochastically Markovian jump admissible is proposed in the form of strict linear matrix inequalities. Sufficient conditions are established for the existence of the fault detection filter. Finally, a numerical example is provided to demonstrate the usefulness and applicability of the developed theoretical results.
143 citations
TL;DR: This article researches the problem of finite frequency (FF) H∞ filtering for linear discrete-time state-delayed systems and proposes a new FF bounded real lemma (BRL) based on the generalized Kalman-Yakubovich-Popov lemma.
Abstract: This article researches the problem of finite frequency (FF) H∞ filtering for linear discrete-time state-delayed systems. The disturbance is assumed to reside in low/middle/high frequency ranges. To reduce the conservatism of the results, delay-partitioning idea is used to derive a new FF bounded real lemma (BRL). By applying the generalized Kalman-Yakubovich-Popov lemma, two equivalent approaches to the proof of the proposed FF BRL are given, respectively, starting from transfer function and Lyapunov-Krasovskii functional. A new FF H∞ filter design method is proposed in terms of solving a set of linear matrix inequalities. Finally, a numerical example clearly demonstrates the merits and effectiveness of the proposed method.
TL;DR: In this article, a design methodology and equations are described for lumped-element filter prototypes having lowpass, high-pass, bandpass, or bandstop characteristics with theoretically perfect input-and output-match at all frequencies.
Abstract: A design methodology and equations are described for lumped-element filter prototypes having low-pass, high-pass, bandpass, or bandstop characteristics with theoretically perfect input- and output-match at all frequencies. Such filters are a useful building block in a wide variety of systems in which the highly reactive out-of-band termination presented by a conventional filter is undesirable. The filter topology is first derived from basic principles. The relative merits of several implementations and tunings are then compared via simulation. Finally, measured data on low-pass and bandpass filter examples are presented, which illustrate the practical advantages, as well as showing excellent agreement between measurement and theory.
TL;DR: It is proven in this paper that the unscented Kalman filter using the suggested optimal parameter is a subset of the sparse Gauss― Hermite quadrature filter, which is more flexible to use and more efficient than the conventional Gauss ―Hermite quadRature filter.
Abstract: A novel sparse Gauss―Hermite quadrature filter is proposed using a sparse-grid method for multidimensional numerical integration in the Bayesian estimation framework. The conventional Gauss―Hermite quadrature filter is computationally expensive for multidimensional problems, because the number of Gauss―Hermite quadrature points increases exponentially with the dimension. The number of sparse-grid points of the computationally efficient sparse Gauss―Hermite quadrature filter, however, increases only polynomially with the dimension. In addition, it is proven in this paper that the unscented Kalman filter using the suggested optimal parameter is a subset of the sparse Gauss―Hermite quadrature filter. The sparse Gauss-Hermite quadrature filter is therefore more flexible to use than the unscented Kalman filter in terms of the number of points and accuracy level, and it is more efficient than the conventional Gauss―Hermite quadrature filter. The application to the spacecraft attitude estimation problem demonstrates better performance of the sparse Gauss―Hermite quadrature filter in comparison with the extended Kalman filter, the cubature Kalman filter, and the unscented Kalman filter.
TL;DR: This work proposes the use of a compact integer-order transfer function approximation of the fractional-order Laplacian operator s^@a to realize fractionsal-step filters of orders n+@a.
TL;DR: SVF was demonstrated to outperform the BSS and FIR filtering methods in terms of contrast-to-noise ratio (CNR) and motion tracking performance and to provide superior clutter rejection when filtering was achieved using complex pulse-echo received data and non-binary filter coefficients.
Abstract: A general filtering method, called the singular value filter (SVF), is presented as a framework for principal component analysis (PCA) based filter design in medical ultrasound imaging. The SVF approach operates by projecting the original data onto a new set of bases determined from PCA using singular value decomposition (SVD). The shape of the SVF weighting function, which relates the singular value spectrum of the input data to the filtering coefficients assigned to each basis function, is designed in accordance with a signal model and statistical assumptions regarding the underlying source signals. In this paper, we applied SVF for the specific application of clutter artifact rejection in diagnostic ultrasound imaging. SVF was compared to a conventional PCA-based filtering technique, which we refer to as the blind source separation (BSS) method, as well as a simple frequency-based finite impulse response (FIR) filter used as a baseline for comparison. The performance of each filter was quantified in simulated lesion images as well as experimental cardiac ultrasound data. SVF was demonstrated in both simulation and experimental results, over a wide range of imaging conditions, to outperform the BSS and FIR filtering methods in terms of contrast-to-noise ratio (CNR) and motion tracking performance. In experimental mouse heart data, SVF provided excellent artifact suppression with an average CNR improvement of 1.8 dB (P <; 0.05) with over 40% reduction (P <; 0.05) in displacement tracking error. It was further demonstrated from simulation and experimental results that SVF provided superior clutter rejection, as reflected in larger CNR values, when filtering was achieved using complex pulse-echo received data and non-binary filter coefficients.
TL;DR: A novel and simple bandwidth and wavelength-tunable optical bandpass filter based on silicon microrings in a Mach-Zehnder interferometer (MZI) structure is proposed and demonstrated.
Abstract: A novel and simple bandwidth and wavelength-tunable optical bandpass filter based on silicon microrings in a Mach-Zehnder interferometer (MZI) structure is proposed and demonstrated. In this filter design, the drop transmissions of two microring resonators are combined to provide the desired tunability. A detailed analysis and the design of the device are presented. The shape factor and extinction ratio of the filter are optimized by thermally controlling the phase difference between the two arms of the MZI. Simultaneous bandwidth and wavelength tunability with in-band ripple control is demonstrated by thermally tuning the resonance offset between the two microring resonators.
TL;DR: This paper presents new convex optimization procedures for full order robust H 2 and H ∞ filter design for continuous and discrete-time uncertain linear systems, outperforming the existing methods.
TL;DR: A delay-dependent condition is established to guarantee the filtering error systems to be stochastically admissible and achieve a prescribed l"2-l"~ performance index and full-order and reduced-order filters with mode-independent characterization are designed in a unified framework.
TL;DR: This paper investigates the problem of H∞ filtering for a class of nonlinear discrete-time systems with measurement quantization and packet dropouts with a piecewise-Lyapunov function and proposes an approach to the design of H ∞-piecewise filter such that the filtering-error system is stochastically stable with a guaranteed H⩽ performance.
Abstract: This paper investigates the problem of H∞ filtering for a class of nonlinear discrete-time systems with measurement quantization and packet dropouts. Each output is transmitted via an independent communication channel, and the phenomenon of packet dropouts in transmission is governed by an individual random binary distribution, while the quantization errors are treated as sector-bound uncertainties. Based on a piecewise-Lyapunov function, an approach to the design of H∞-piecewise filter is pro posed such that the filtering-error system is stochastically stable with a guaranteed H∞ performance. Some slack matrices are introduced to facilitate the filter design procedure by eliminating the coupling between the Lyapunov matrices and the system matrices. The filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs), which are numerically tractable with commercially available software. Finally, two illustrative examples are provided to show the effectiveness of the proposed method.
TL;DR: The proposed cultural firework algorithm is a multi-dimensional search algorithm for optimisation of real numbers, which uses mechanisms of cultural evolution to update the locations of cultural sparks to achieve optimal value of filter design parameters in the parameter space with parallel search.
Abstract: The substance of the digital filter design is a multi-parameter optimisation problem. This paper presents a joint objective function to design finite impulse response (FIR) digital filters and infinite impulse response (IIR) digital filters, and a cultural firework (CF) algorithm is proposed to implement filter designs. The design of the filter is transformed into the constrained optimisation problem, and the cultural firework algorithm is used to search optimal value of filter design parameters in the parameter space with parallel search. The proposed cultural firework algorithm is a multi-dimensional search algorithm for optimisation of real numbers, which uses mechanisms of cultural evolution to update the locations of cultural sparks. Computer simulations have showed that FIR and IIR digital filters based on the CF algorithm are superior to previous filters based on particle swarm optimisation (PSO), quantum-behaved particle swarm optimisation (QPSO) and adaptive quantum-behaved particle swarm optimisation (AQPSO) in the convergence speed and optimisation results. The effectiveness and superiority of the CF are also demonstrated by computer simulations.
TL;DR: This article is concerned with the problem of H ∞ filter design for nonlinear Markovian jump neutral systems through the Takagi–Sugeno fuzzy model approach and presents a delay-dependent bounded real lemma (BRL) in terms of linear matrix inequalities.
Abstract: This article is concerned with the problem of H∞ filter design for nonlinear Markovian jump neutral systems through the Takagi-Sugeno fuzzy model approach. By using a novel Markovian switched Lyapunov functional, a delay-dependent bounded real lemma (BRL) is presented in terms of linear matrix inequalities. Based on the derived BRL, both normal H∞ filters and non-fragile H∞ filters are designed, which guarantee that the corresponding filtering error systems are stochastically stable with a specified H∞ performance level. A numerical example is given to demonstrate the effectiveness of the proposed approach.
TL;DR: This paper focuses on the problem of designing H∞ filters for nonlinear systems with time-varying delay via Takagi-Sugeno (T-S) fuzzy models and proposes some new results by estimating the upper bounds of the derivatives of Lyapunov functionals without ignoring some useful terms, which improve the existing ones.
Abstract: This paper focuses on the problem of designing H∞ filters for nonlinear systems with time-varying delay via Takagi-Sugeno (T-S) fuzzy models. Some new results on H∞ filter design are proposed by estimating the upper bounds of the derivatives of Lyapunov functionals without ignoring some useful terms, which improve the existing ones. In addition, a sufficient condition for the existence of such an H∞ filter is established in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, two examples are given to demonstrate the effectiveness of the proposed method.
01 Feb 2011
TL;DR: A low-complexity Kalman filter implementation in which the filter gain is approximated by its steady-state form, computed offline before real-time decoding commences, which reduces the computational load for decoding the firing rates of 25±3 single units by a factor of 7.9.
Abstract: The Kalman filter is commonly used in neural interface systems to decode neural activity and estimate the desired movement kinematics. We analyze a low-complexity Kalman filter implementation in which the filter gain is approximated by its steady-state form, computed offline before real-time decoding commences. We evaluate its performance using human motor cortical spike train data obtained from an intracortical recording array as part of an ongoing pilot clinical trial. We demonstrate that the standard Kalman filter gain converges to within 95% of the steady-state filter gain in 1.5 ± 0.5 s (mean ±s.d.). The difference in the intended movement velocity decoded by the two filters vanishes within 5 s, with a correlation coefficient of 0.99 between the two decoded velocities over the session length. We also find that the steady-state Kalman filter reduces the computational load (algorithm execution time) for decoding the firing rates of 25±3 single units by a factor of 7.0±0.9. We expect that the gain in computational efficiency will be much higher in systems with larger neural ensembles. The steady-state filter can thus provide substantial runtime efficiency at little cost in terms of estimation accuracy. This far more efficient neural decoding approach will facilitate the practical implementation of future large-dimensional, multisignal neural interface systems.
TL;DR: In this article, the performance of the RAW filter in semi-implicit integrations of the elastic pendulum equations is examined. And the results suggest that replacing the RA filter with RAW filter could reduce time-stepping errors in semisupervised integrations.
Abstract: Errors caused by discrete time stepping may be an important component of total model error in contemporary atmospheric and oceanic simulations. To reduce time-stepping errors in leapfrog integrations, the Robert–Asselin–Williams (RAW) filter was proposed by the author as a simple improvement to the widely used Robert–Asselin (RA) filter. The present paper examines the behavior of the RAW filter in semi-implicit integrations. First, in a linear theoretical analysis, the stability and accuracy are interrogated by deriving analytic expressions for the amplitude errors and phase errors. Then, power-series expansions are used to interpret the leading-order errors for small time steps and hence to identify optimal values of the filter parameters. Finally, the RAW filter is tested in a realistic nonlinear setting, by applying it to semi-implicit integrations of the elastic pendulum equations. The results suggest that replacing the RA filter with the RAW filter could reduce time-stepping errors in semi-im...
Patent•
01 Sep 2011TL;DR: In this article, a method and an apparatus for reproducing a sound signal is presented, which includes generating an output sound signal to be transmitted to speakers by transmitting a first input sound signal through a filter.
Abstract: A method and an apparatus for reproducing a sound signal are provided. The method includes generating an output sound signal to be transmitted to speakers by transmitting a first input sound signal through a filter; acquiring magnitude information of the output sound signal; determining frequency response parameters related to frequency responses of the filter based on the magnitude information; and adaptively adjusting coefficients of the filter based on the determined frequency response parameters.
TL;DR: This paper proposes a LC filter design method for PWM inverters considering both the voltage dynamics and the inverter stack size and an experimental P WM inverter system based on the proposed outputLC filter design guideline is built and tested.
Abstract: The cutoff frequency of the output LC filters of PWM inverters limits the control bandwidth of the converter system while it attenuates voltage ripples that are caused by inverter switching activities. For a selected cutoff frequency of an output LC filter, an infinite number of L-C combinations is possible. This paper analyses the characteristics of output LC filters for PWM inverters terms of the L-C combinations. Practical circuit conditions such as no-loads, full resistive-loads, and inductive-load conditions are considered in the analysis. This paper proposes a LC filter design method for PWM inverters considering both the voltage dynamics and the inverter stack size. An experimental PWM inverter system based on the proposed output LC filter design guideline is built and tested.
TL;DR: Modifications are proposed to an iterative, time-domain PEVD method, known as the sequential best rotation (SBR2) algorithm, which enables its effective application to the problem of FIR orthonormal filter bank design for efficient subband coding.
Abstract: The problem of paraunitary (PU) filter bank design for subband coding has received considerable attention in recent years, not least because of the energy preserving property of this class of filter banks. In this paper, we consider the design of signal-adapted, finite impulse response (FIR), PU filter banks using polynomial matrix EVD (PEVD) techniques. Modifications are proposed to an iterative, time-domain PEVD method, known as the sequential best rotation (SBR2) algorithm, which enables its effective application to the problem of FIR orthonormal filter bank design for efficient subband coding. By choosing an optimization scheme that maximizes the coding gain at each stage of the algorithm, it is shown that the resulting filter bank behaves more and more like the infinite-order principle component filter bank (PCFB). The proposed method is compared to state-of-the-art techniques, namely the iterative greedy algorithm (IGA), the approximate EVD (AEVD), standard SBR2 and a fast algorithm for FIR compaction filter design, called the window method (WM). We demonstrate that for the calculation of the subband coder, the WM approach offers a low-cost alternative at lower coding gains, while at moderate to high complexity, the proposed approach outperforms the benchmarkers. In terms of run-time complexity, AEVD performs well at low orders, while the proposed algorithm offers a better coding gain than the benchmarkers at moderate to high filter order for a number of simulation scenarios.
TL;DR: In this paper, the structural parameters of the SIR are obtained analytically according to the two passband center frequencies and bandwidths of the filter, and the achievable specifications of the dual-band filter can be rapidly determined.
Abstract: This paper proposes an analytical method to design a dual-band Alter using the short-circuit terminated half-wavelength stepped-impedance resonator (SIR). The SIR has an advantage to easily control the first and second resonances by adjusting its structural parameters. In the proposed method, the structural parameters of the SIR are obtained analytically according to the two passband center frequencies and bandwidths of the filter. As a result, the achievable specifications of the dual-band filter can be rapidly determined. The coupling between adjacent SIRs is realized by a short-circuited stub, which is characterized as a K-inverter network. The dual-frequency transformer incorporated with the tapped-line input/output structure is used for the external coupling. Applying the analytical equations in the design process, a dual-band filter can be easily and quickly realized. More importantly, compared to the published dual-band filters, the proposed method is easier to design, especially for a relatively high-order dual-band filter. Two fourth-order and one sixth-order dual-band filters are designed and fabricated to demonstrate the proposed method.
TL;DR: A filter design formalism is presented for the synthesis of coupled-resonator optical waveguide (CROW) filters and a method is described for the conversion of the coupling coefficients to the parameters based on ring resonators and grating defect resonators.
Abstract: We present a filter design formalism for the synthesis of coupled-resonator optical waveguide (CROW) filters. This formalism leads to expressions and a methodology for deriving the coupling coefficients of CROWs for the desired filter responses and is based on coupled-mode theory as well as the recursive properties of the coupling matrix. The coupling coefficients are universal and can be applied to various types of resonators. We describe a method for the conversion of the coupling coefficients to the parameters based on ring resonators and grating defect resonators. The designs of Butterworth and Bessel CROW filters are demonstrated as examples.
TL;DR: In this paper, the bias of the ensemble Kalman filter was analyzed from a statistical perspective and a debiasing method called the nonlinear ensemble adjustment filter was proposed to transform the forecast ensemble in a statistically principled manner so that the updated ensemble has the desired mean and variance.
Abstract: The ensemble Kalman filter is now an important component of ensemble forecasting. While using the linear relationship between the observation and state variables makes it applicable for large systems, relying on linearity introduces nonnegligible bias since the true distribution will never be Gaussian. This paper analyzes the bias of the ensemble Kalman filter from a statistical perspective and proposes a debiasing method called the nonlinear ensemble adjustment filter. This new filter transforms the forecast ensemble in a statistically principled manner so that the updated ensemble has the desired mean and variance. It is also easily localizable and, hence, potentially useful for large systems. Its performance is demonstrated and compared with other Kalman filter and particle filter variants through various experiments on the Lorenz-63 and Lorenz-96 systems. The results show that the new filter is stable and accurate for challenging situations such as nonlinear, high-dimensional systems with spar...