Filter Design Problem Research Articles

[formula omitted] filtering for uncertain discrete-time singular switched positive systems with time delay and output quantization

This paper focuses on the design problem of an l1 filter for singular switched positive systems with time delay and uncertainty. In order to enhance resource efficiency and information transmission security, the quantization mechanism is introduced when designing the filter. Furthermore, sufficient conditions for causality, regularity, positivity, and exponential stability of the filtering error system are provided under the constraint of mode-dependent minimum dwell time (MDMDT). These conditions are obtained by selecting an appropriate co-positive Lyapunov function and are presented in the form of linear programming (LP). Subsequently, the disturbance attenuation performance is further analyzed, and a design methodology for the corresponding filter is outlined. Finally, a numerical example is presented to verify the validity of the theoretical results.

Fine-tuning digital FIR filters with gray wolf optimization for peak performance

The design of optimum filters constitutes a fundamental aspect within the realm of signal processing applications. The process entails the calculation of ideal coefficients for a filter in order to get a passband with a flat response and an unlimited level of attenuation in the stopband. The objective of this work is to solve the FIR filter design problem and to compare the optimal solutions obtained from evolutionary algorithms. The design of optimal FIR low pass (LP), high pass (HP), and band stop (BS) filters is achieved by the utilization of nature-inspired optimization approaches, namely gray wolf optimization ,cuckoo search, particle swarm optimization, and genetic algorithm. The filters are evaluated in terms of their stop band attenuation, pass band ripples, and departure from the anticipated response. In addition, this study compares the optimization strategies applied in the context of algorithm execution time which is achievement of global optimal outcomes for the design of digital finite impulse response (FIR) filters. The results indicate that when the Gray wolf algorithm is applied to the development of a finite impulse response (FIR) filter, it produces a higher level of performance than other approaches, as supported by enhanced design precision, decreased execution time, and achievement of an optimal solution.

Event-based filter design for singular positive Markov jump systems with parameter uncertainty and measurement delay

This paper is concerned with the filter design problem for a class of singular positive Markov jump systems with parameter uncertainty and measurement delay. Considering the limitation of communication bandwidth, the mode-dependent event-triggered (E-T) mechanism is introduced when designing the filter. In general, the phenomena of data collision and congestion can be reduced by employing this form of filter. On the basis of stochastic co-positive Lyapunov function technique, the regularity, causality, positivity, stochastic stability, and weighted l1-gain performance of the resulting filtering error system are discussed. In addition, the corresponding design method applied to filter parameters are also provided in detail. Finally, two numerical simulations are given to demonstrate the effectiveness and feasibility of the results proposed in this paper.

Design of fractional-order transitional filters of the Butterworth-Sync-Tuned, Butterworth-Chebyshev, and Chebyshev-Sync-Tuned types: optimization, simulation, and experimental verification

This paper presents the optimal and generalized design of three different fractional-order (FO) transitional filters for the first time in the literature. The transitional filters considered are of the FO Butterworth-sync-tuned, the FO Butterworth-Chebyshev, and the FO Chebyshev-sync-tuned types. A metaheuristic swarm intelligence optimizer, namely the Crow Search Algorithm (CSA), helps to achieve the optimal FO filter model that minimizes the magnitude error with the theoretical function. The accuracy of the proposed approximants is examined for 19 different combinations of orders of the constituent filters for each of the three types of FO transitional filters. Comparisons with the modified stability boundary locus-based second-, third-, and fourth-order filter approximants demonstrate the compactness and superior accuracy of the proposed models. The average performance regarding the approximation accuracy, computational time, and convergence of CSA for solving the proposed filter design problems is investigated. Circuit simulations conducted on the OrCAD PSPICE platform for the proposed filter using the current feedback operational amplifier as an active element highlight good matching between the proposed model and theoretical filter function. Experimental validation is also carried out to justify the practical feasibility of the proposed filter with printed circuit board fabricated FO capacitor emulators.

Non-fragile [formula omitted] filtering for delayed discrete-time Markov jump systems: An adaptive event-triggered strategy

This paper deals with the problem of non-fragile filter for delayed discrete-time Markov jump systems. The purpose is to design a mode-dependent filter such that the result filtering error system is stochastically stable and satisfies a prescribed H∞ performance lever γ. In order to improve the data transmission efficient, an adaptive event-triggered strategy is introduced. Then, with the help of the Lyapunov stability theory and matrix inequality, the sufficient conditions for the solution of the filter design problem proposed are established. Finally, two numerical examples are presented to verification the effectiveness of the proposed method.

Imperfect premise matching finite-time filter design for continuous-time Takagi–Sugeno fuzzy systems

An input–output finite-time filtering design problem for a class of delayed Takagi–Sugeno fuzzy systems with external disturbance input is discussed in this paper. Specifically, the filter design uses the imperfect premise matching scheme that relaxes the requirement that the filter and system membership functions be the same. This method can improve the flexibility of the filter design by incorporating membership function information into the input–output finite-time stability analysis. Using the system and filter states, an augmented filtering system is obtained. The required stability criteria are then derived using the Lyapunov–Krasovskii stability theorem and a few recent inequality approaches. Following that, the desired filter gain matrices are determined. The developed filtering design method is validated through some demonstrative examples.

Mixed H∞‐based finite‐time passive filtering for a class of uncertain nonlinear singular systems

AbstractThis article discusses the finite‐time mixed and passive filtering design problem for uncertain nonlinear singular systems. The parameter uncertainties are constrained by well‐defined upper bounds on their magnitudes. The objective is to design a full‐order filter to ensure that the augmented singular system to be finite‐time boundedness(FTB) with and passivity performance. Firstly, a sufficient condition for achieving singular finite‐time boundedness with mixed and passivity performance for uncertain nonlinear singular system is derived by introducing a free matrix. Secondly, a novel criterion is established for analyzing finite‐time and passivity problem of filtering error singular system based on augmented matrix technique. Thirdly, the filtering design conditions are presented and the relevant parameters of the desired filter are determined using linear matrix inequality decoupling principle. Finally, a practical circuit system and a numerical example are provided to demonstrate the feasibility of the proposed scheme.

Filter design and power allocation in multi-user universal filtered multi-carrier (MU-UFMC) systems

Universal Filtered Multi-Carrier (UFMC) system has been introduced as a candidate for the new generation. UFMC is a multi-carrier system, which can overcome challenges in wireless communications. In fact, the advantages of multi-carrier systems over single-carrier systems include higher bandwidth gain and higher robustness against frequency-selective fading. Generally, most multi-carrier systems suffer from notoriously sensitive to symbol-time offset (STO) and carrier-frequency offset (CFO). However, since UFMC systems utilize subband filters, sensitivity to CFO and STO can be reduced by designing efficient subband filters. In this paper, filter design problem is addressed in order to mitigate interference caused by effect of CFO in a multi-user UFMC (MU-UFMC) system under fair optimization framework. Since filter design problem is formulated as a non-convex optimization problem, we present two different approach in order to solve it. In the first approach, the formulated problem is relaxed so that one is converted to a standard second-order-cone programming (SOCP). In the second approach, we present a proposed algorithm with low complexity based on some lemma and relaxation. Then power allocation problem is solved to maximize the minimum achievable rate among all the users in a MU-UFMC system. The simulation results show the proposed schemes for filter design and power allocation outperform the benchmark schemes.

Asynchronous Resilent State Estimation of Switched Fuzzy Systems With Multiple State Impulsive Jumps.

This work researches the resilent mixed H∞ and energy-to-peak filter design problem of switched Takagi-Sugeno (T-S) fuzzy systems with asynchronous switching and multiple state impulsive jumps. The novelties include three points. First, a novel mixed H∞ and energy-to-peak performance index is proposed, which covers the H∞ performance index and energy-to-peak performance index as special cases. Second, in addition to designing the switching filters, the filter state jump rules are constructed at filter switching instants. Finally, both system states and filter states jump in a asynchronous manner. The switching law is devised through the mode-dependent average dwell time (MDADT) approach. A new type of Lyapunov-like functionals is constructed, which will increase when the subsystem is running with its mismatched filter and jump while the subsystem or the filter is switching. Then, new conditions are deduced to ensure the filtering error systems with multiple state impulsive jumps to be asymptotically stable with a mixed H∞ and energy-to-peak performance level. Filter design conditions expressing as linear matrix inequality (LMI) are obtained. Finally, the effectiveness of the derived results is illustrated by two examples.

A new generalized predictive current control algorithm with integration of fractional part function based modulation technique: Single phase self‐balanced type multilevel inverter topologies

SummaryIt is generally impossible to control the inverter output current (IOC) based on operator needs if only pulse width modulation (PWM) techniques are used. Conventionally, authors have reported the finite control set‐based predictive current control algorithm (FCS‐PCCA) to control the IOC with a fast dynamic response. However, this type of algorithm without a PWM stage generates a variable switching frequency (VSF) of operation, and it leads to filter design problems, inequitable thermal stress, and more current distortions that have been presented. To alleviate all these issues, a new generalized PCCA with the integration of a fractional part function‐based single carrier modulation technique (G‐PCCA‐FPF‐SCMT) has been proposed, and it provides constant switching frequency (CSF) of operation. In this technique, the normalized optimum inverter output voltage (N‐O‐IOV) has been fed with FPF‐SCMT. The particular modulation stage implementation is straightforward since even inverter level number increases, the number of references and triangular carrier signals is always only one. The complete control implementation process of the proposed technique is extremely low compared with all traditional CSF‐based PCCAs. To verify the proposed technique experimentally in both steady and transient state operations, one of the conventional five‐level switched capacitor‐based inverter topologies has been considered and elucidated vividly in both open‐loop and closed‐loop operations.

Security-guaranteed filter design for discrete-time Markovian jump delayed systems subject to deception attacks and sensor saturation

This work is devoted the problem of a security-guaranteed filter design for a class of discrete-time Markov jump systems that are vulnerable to stochastic deception attacks and have random sensor saturation. Deception attacks, in particular, are taken into account in the filter when the attacker attempts to modify the broadcast signal in communication networks by inserting some misleading information data into the assessment output. The Bernoulli distribution is satisfied by two sets of introduced stochastic variables. It shows the likelihood that the broadcaster’s data transmissions will be the focus of deception attacks and sensor saturation. The Lyapunov functional technique is established, and criteria are derived to ensure that the system is mean-square stable. Furthermore, explicit expression of the filter gains is obtained by solving a set of linear matrix inequalities. Lastly, two simulation examples including a synthetic genetic regulatory network are provided to further demonstrate the validity and efficiency of the suggested theoretical results.

Warmstarting strategies for convex optimization based multi-channel constrained active noise control filter design

In real-world applications of active noise control (ANC) systems, various constraints are supposed to be satisfied in the controller design process. The optimal control filter coefficients can be obtained by solving a constrained optimization problem, which usually requires a significant computational effort. Recently, a convex formulation in conic form was proposed for ANC filter design. The proposed formulation was shown to result in a computational time reduction by several orders of magnitude. It is of great interest to further improve its efficiency by using a priori information of the optimal filter coefficients. One potential way of achieving this goal is to introduce a warmstart technique so that the filter solution of a similar system or environment can be referred to for selecting the starting point of the optimization algorithm. However, the conic formulation should be solved by the interior-point method, which, in general, is challenging for applying warmstart techniques. In the current work, relaxation methods are proposed to the constraints of original ANC filter design formulation so that the warmstart techniques can be applied. Then, a warmstarting technique proposed in previous study is used to solve a series of perturbed problems, and the performance of the warmstarting technique is investigated. Results show that with the proposed modifications applied, the warmstarting strategy can significantly reduce the number of iterations needed for solving the conic formulation of the ANC filter design problem without much tuning efforts, and the method is effective and robust in various environmental setups.

Exploring the use of Genetic Algorithms Toolbox in Engineering Education: Did it Provide an Interesting Learning Experience for Students?

Teaching in engineering education using Genetic Algorithms (GAs) toolbox as a teaching tool in engineering education can be an effective approach, particularly in Signal Processing subjects, as it encourages students to learn how to find optimal values required in designing digital filters. This research investigates the use of GAs for teaching digital filter design, where the evaluation function of the problem is optimized using Gas. The GAs toolbox simulation is designed to yield a stable, lowest-order H[z] that meets the tolerance parameters and satisfies the design criteria. Teaching GAs involves representing the filter design problem in a way that can be accepted by genetic programming.

An adaptive constrained multi-channel active noise control filter design approach using convex cone optimization

In current practical active noise control (ANC) applications, solutions to three main technical challenges need to be sought: the requirement of a stable controller when acoustic feedback paths exist, a larger quiet zone, and adaptation to a time-varying environment. The imposed controller stability constraints can significantly increase the computational requirements and negatively impact the adaptation of ANC filters in real time. Multi-channel systems are usually needed if a larger quiet zone is required while the coupling between different channels can greatly lower the convergence rate of adaptive algorithms. In the current work, a multi-channel adaptive constrained ANC filter design method is proposed. The recently proposed convex cone formulation for ANC design is adopted to reduce the computational time of solving the constrained ANC filter design problem. The optimal filter coefficients are then redesigned continuously using convex optimization when the environment is time-varying. The experimental result shows that, compared with the traditional leaky FxLMS method, the proposed method has a faster convergence rate and a better steady-state noise control performance.

Distributed fusion filtering for cyber-physical systems under Round-Robin protocol: a mixed H 2/H ∞ framework

ABSTRACT In this paper, the distributed mixed fusion filter design problem is investigated for a class of cyber-physical systems subject to non-ideal measurements under Round-Robin protocol. To save the limited communication resources, the Round-Robin protocol is employed to schedule the data transmissions from the sensors to the remote filters. The measurement is imperfect by taking into account the noises, the random saturations, nonlinearity perturbations and packet dropouts. The objective of this study is to propose a desired fusion filtering method that ensures the prescribed performance constraints on both the local and fusion filtering error dynamics. With the aid of Lyapunov function and stochastic analysis technique, a sufficient condition is established to guarantee the mixed / performance index for the local filtering error systems, and then the filter parameter matrices are derived by resorting to the solutions to some matrix inequalities. Subsequently, on the basis of the obtained local state estimates, the proper fusion parameters are acquired by solving a convex optimisation problem. Finally, a numerical example is provided to demonstrate the effectiveness of the designed fusion filter.

Fuzzy-Affine-Model-Based Filtering Design for Continuous-Time Roesser-Type 2-D Nonlinear Systems.

This article tackles the problem of filtering design for continuous-time Roesser-type 2-D nonlinear systems via Takagi-Sugeno (T-S) fuzzy affine models. The aim is to design an admissible piecewise affine (PWA) filter such that the filtering error system is asymptotically stable with a prescribed disturbance attenuation level. First, 2-D Roesser nonlinear systems are approximated by a kind of 2-D fuzzy affine models with norm-bounded uncertainties. Then, the premise variable space of the 2-D fuzzy affine systems is partitioned into two classes of subspaces, that is: 1) crisp regions and 2) fuzzy regions. For each region, boundary continuity matrices and characterizing matrices are constructed by utilizing the space partition information and 2-D structure. After that, novel piecewise Lyapunov functions are constructed, based on which together with S-procedure, the asymptotic stability with performance is guaranteed for the filtering error system. By the projection lemma and some elegant convexification techniques, the PWA filtering design conditions are obtained. Finally, the less conservativeness and effectiveness of the proposed approach over a common Lyapunov function-based one are illustrated by simulation studies.

Design of non-Gaussian multispectral shortwave infrared filters assessed by surface spectral reflectances on the ECOSTRESS library.

This paper addresses the multispectral filter design problem for spectral ranges where a viewing subspace is not defined. The methodology of color filter design is extended to this case, which allows the optimization of custom filter transmittance that meets the physical constraints of available fabrication methods. Multispectral shortwave infrared filters are then designed for two scenarios: spectral reconstruction and false-color representation. The Monte Carlo method is used to verify the filter performance degradation due to deviations in fabrication. The results obtained indicate that the proposed method is useful for designing multispectral filters to be fabricated using generic processes without any additional constraints.

Reconstruction of a signal from multirate observations: A recursive approach

In this paper, we develop a recursive formulation for the reconstruction of a signal from multirate observations. We model the observations as the outputs of a decimated analysis bank and convert the reconstruction problem into a matrix synthesis filter design problem. We use the mean-square criterion to minimize the reconstruction error and obtain a synthesis bank solution for a given filter length and delay in reconstruction. We then derive a recursive method with arbitrary step size for computing the same beginning from any smaller length solution. We also derive a recursive formulation for the mean-square error (MSE) with similar flexibility. This method is computationally efficient when compared to the direct computation of a solution. Additionally, it aids in studying the properties of the solutions as a function of filter length. Finally, we present experimental results that demonstrate the advantages of the recursive method developed.

Asynchronous Fault Detection Filter Design for T–S Fuzzy Singular Systems via Dynamic Event-Triggered Scheme

This article considers the problem of asynchronous fault detection filter (FDF) design for Takagi–Sugeno (T–S) fuzzy singular systems via dynamic event-triggered scheme. A mode-dependent dynamic event-triggered scheme is adopted to alleviate the communication load. Besides, a hidden Markov model is introduced to describe the asynchronous phenomenon between the system and the FDF. First, some sufficient criteria are established to ensure that the residual system is stochastically admissible with a certain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> performance. Second, solvability criteria are presented to codesign the desired FDF gains and the event-triggered matrices. Finally, the correctness of the proposed method is shown by two examples.

A Model Randomization Approach to Statistical Parameter Privacy

In this article, we study a privacy filter design problem for a sequence of sensor measurements whose joint probability density function (p.d.f.) depends on a private parameter. To ensure parameter privacy, we propose a filter design framework which consists of two components: a randomizer and a nonlinear transformation. The randomizer takes the private parameter as input and randomly generates a pseudo parameter. The nonlinear mapping transforms the measurements such that the joint p.d.f. of the filter's output depends on the pseudo parameter rather than the private parameter. It also ensures that the joint p.d.f. of the filter's output belongs to the same family of distributions as that of the measurements. The design of the randomizer is formulated as an optimization problem subject to a privacy constraint, in terms of mutual information, and it is shown that the optimal randomizer is the solution of a convex optimization problem. Using information-theoretic inequalities, we show that the performance of any estimator of the private parameter, based on the output of the privacy filter, is limited by the privacy constraint. The structure of the nonlinear transformation is studied in the special cases of independent and identically distributed, Markovian, and Gauss-Markov measurements. Our results show that the privacy filter in the Gauss-Markov case can be implemented as two one-step ahead Kalman predictors and a set of minimum mean square error predictors. A numerical example on occupancy privacy in a building automation system illustrates the approach.