Design Of Linear Filters Research Articles

Fault Detection for T–S Fuzzy Systems With Unknown Membership Functions

This paper is concerned with the fault detection (FD) problem for Takagi-Sugeno (T-S) fuzzy systems with unknown membership functions. If the membership functions are unknown, the linear FD filter designs with fixed gains have been considered in the literature. To reduce the conservatism of the existing results, a switching mechanism that depends on the lower and upper bounds of the unknown membership functions is provided to construct an FD filter with varying gains. It is shown that the switching-type FD filter with varying gains can achieve a better FD performance than the linear FD filter with fixed gains. In addition, based on some time-domain inequalities, a novel weighting matrix design approach is introduced to transform the fault sensitivity specification into an H∞ constraint. Finally, two examples are given to show the advantages of the proposed FD method.

Optimal linear phase FIR filter design using particle swarm optimization with constriction factor and inertia weight approach with wavelet mutation

In this paper, Particle Swarm Optimization with Constriction Factor and Inertia Weight Approach is hybridized with Wavelet Mutation (PSOCFIWA-WM) strategy for the optimal design of linear phase FIR filters. Real coded genetic algorithm (RGA), particl

DAPSO and PSO-VAF in Linear Phase Digital Low Pass FIR Filter Design

Digital filters play a key role in the field of digital signal processing. This paper presents a linear phase digital low pass finite impulse response (FIR) filter design using particle swarm optimization and its two new variants, dynamic and adjustable particle swarm optimization (DAPSO) and particle swarm optimization with variable acceleration factor (PSO-VAF) and illustrates the superiority of the PSO-VAF method over PSO based methods. Two fitness functions are considered. The fitness1 is used to find the possible minimum ripples in pass band and stop band in case of PSO, DAPSO and PSO-VAF. Fitness2 is able to control the ripples in both bands separately. A comparison of simulation results demonstrates the performance of PSO and its methods in designing digital low pass FIR filters.

Single-Stage and Cascade Design of High Order Multiplierless Linear Phase FIR Filters Using Genetic Algorithm

In this work, a novel genetic algorithm (GA) is proposed for the design of multiplierless linear phase finite impulse response (FIR) filters. The filters under consideration are of high order and wide coefficient wordlength. Both the single-stage and cascade form are considered. In a practical filter design problem, when the filter specification is stringent, requiring high filter order and wide coefficient wordlength, GAs often fail to find feasible solutions, because the discrete search space thus constructed is huge and the majority of the solution candidates therein can not meet the specification. In the proposed GA, the discrete search space is partitioned into smaller ones. Each small space is constructed surrounding a base discrete coefficient set which is obtained by a proposed greedy algorithm. The partition of the search space increases the chances for the GA to find feasible solutions, but does not sacrifice the coverage of the search. The proposed GA applies to the design of single-stage filters. When a cascade form filter is designed, for each single-stage filter meeting the filter specification generated during the course of GA, an integer polynomial factorization is applied. Design examples show that the proposed GA significantly outperforms existing algorithms dealing with the similar problems in terms of design time, and the hardware cost is saved in most cases.

A new closed form method for design of variable bandwidth linear phase FIR filter using different polynomials

In this paper, a new method for the design of variable bandwidth linear-phase finite impulse response (FIR) filters using different polynomials such as shifted Chebyshev polynomials, Bernstein polynomials and shifted Legendre polynomials is proposed. For this purpose, the transfer function of a variable bandwidth filter, which is a linear combination of fixed-coefficient linear-phase filters and the above polynomials are separately exploited as tuning parameters to control bandwidth of the filter. In order to determine the filter coefficients, mean squared difference between the desired variable bandwidth filter and the practical filter is minimized by differentiating it with respect to its coefficients leading to a system of linear equations. The matrix elements can be expressed in form of Toeplitz-plus-Hankel matrix, which reduces the computational complexity. Several examples are included to demonstrate effectiveness of the proposed method in terms of passband error (ep), stopband error (es) and stopband attenuation (As).

Robust Design of Widely Linear Pre-Equalization Filters for Pre-Rake UWB Systems

Pre-rake ultra-wideband (UWB) systems are appealing for UWB communications applications which include devices with different processing capabilities so that signal processing complexity need to be shifted from the receiver of one or more devices to the transmitter of another. Recently, basic pre-rake schemes have been extended to include full pre-equalization, multiple-antenna, and multi-user interference processing. All these design approaches for pre-rake UWB systems have relied on the availability of accurate channel state information (CSI) at the transmitter. However, uncertainties in the acquisition of CSI can drastically affect the overall system performance. Therefore, in this paper, we present robust design methods for pre-equalization filters (PEFs) for pre-rake UWB systems that take CSI uncertainties into account. We treat the general case of a broadcast (i.e., multiuser) pre-rake UWB system, which includes single-user communication often considered in literature as a special case. For this general setting, we derive new PEF designs that improve system performance with imperfect CSI. Similar to the literature on robust filter designs for multiple-input multiple output (MIMO) systems, we consider two uncertainty models, namely stochastic and bounded uncertainty, which correspond to different performance optimization paradigms, and we adjust these according to channel estimation of UWB channels. As most of previous work on (pre-rake) UWB, we focus on binary transmission. We argue that widely linear filter design should be applied in this case and thus extend the robust filter design methodology accordingly. Our numerical results for typically UWB test channels demonstrate the efficacy of the proposed design procedures to achieve reliable communication in multiuser pre-rake UWB systems.

Regularized Zero-Forcing Interference Alignment for the Two-Cell MIMO Interfering Broadcast Channel

We present linear transmit-receive filter design strategies for the two-cell multiple-input multiple-output (MIMO) interfering broadcast channel (IBC) where inter-cell interference (ICI) exists in addition to inter-user interference (IUI) within the cell. We first formulate a generalized zero-forcing interference alignment (ZF-IA) method capable of handling multiple data streams for each user. We proceed to further adjust the transmit-receive filters based on the minimum weighted-mean-square-error (WMSE) principle using the weights obtained from the initial generalized ZF-IA design, in an effort to to enhance the sum-rate performance. In contrast to the existing weighted-sum-rate-maximizing scheme, our method does not require an iterative calculation of the weights. Because of this, the proposed scheme, while not designed specifically to maximize the sum-rate, is computationally efficient and delivers favorable tradeoffs between performance and information exchange overhead.

Digital FIR filter design using fitness based hybrid adaptive differential evolution with particle swarm optimization

This paper presents an efficient way of designing linear phase finite impulse response (FIR) low pass and high pass filters using a novel algorithm ADEPSO. ADEPSO is hybrid of fitness based adaptive differential evolution (ADE) and particle swarm optimization (PSO). DE is a simple and robust evolutionary algorithm but sometimes causes instability problem; PSO is also a simple, population based robust evolutionary algorithm but has the problem of sub-optimality. ADEPSO has overcome the above individual disadvantages faced by both the algorithms and is used for the design of linear phase low pass and high pass FIR filters. The simulation results show that the ADEPSO outperforms PSO, ADE, and DE in combination with PSO not only in magnitude response but also in the convergence speed and thus proves itself to be a promising candidate for designing the FIR filters.

Optimal Alarm Signal Processing: Filter Design and Performance Analysis

Accuracy and efficiency of alarm systems are of paramount importance in safe operations of industrial processes. Accuracy is measured by false and missed alarm rates (probabilities); while efficiency relates to the detection delay and complexity of the technique used. Moving average filters are often employed in industry for improved alarm accuracy. Can one do better than moving average filters? The following two problems are studied in this paper: First, given both normal and abnormal statistic distributions, how to design an optimal alarm filter (of fixed complexity) for best alarm accuracy, minimizing a weighted sum of false and missed alarm rates? Second, in what cases are moving average filters optimal? For the first problem, design of optimal linear FIR alarm filters is studied, and a numerical optimization based procedure is proposed. For the second problem, a sufficient condition is given under which the moving average filters are optimal.

Alternate MIMO AF Relaying Networks With Interference Alignment: Spectral Efficient Protocol and Linear Filter Design

In this paper, we study a two-hop relaying network consisting of one source, one destination, and three amplify-and-forward (AF) relays with multiple antennas. To compensate for the capacity prelog factor loss of 1/2 due to the half-duplex relaying, alternate transmission is performed among three relays, and the inter-relay interference due to the alternate relaying is aligned to make additional degrees of freedom. In addition, suboptimal linear filter designs at the nodes are proposed to maximize the achievable sum rate for different fading scenarios when the destination utilizes a minimum mean-square error filter.

Digital linear phase notch filter design based on IIR all-pass filter application

A new procedure for design of linear phase IIR notch filters is presented in this paper. Resulted filter is realized using parallel connection of two IIR all-pass filters with approximately linear phase. Adequate amplitude characteristic is obtained by approximation of all-pass filter phase. Amplitude characteristic satisfies all prescribed demands but it is not equiripple no matter both all-pass filters have equiripple phase. Algorithm exhibits fast convergence and easy initial values determination.

An improved particle swarm optimization method for multirate filter bank design

In this paper, a new particle swarm optimization (PSO) based method is proposed for the design of a two-channel linear phase quadrature mirror filter (QMF) bank in frequency domain. The origional particle swarm optimization technique is modified by introducing the concept of Scout Bee from Artificial Bee Colony (ABC) technique for designing a low pass prototype filter having ideal filter characteristics in the passband and stopband regions, and its magnitude response at quadrature frequency is 0.707. The design problem is formulated as a linear combination of passband error and residual stop band energy of the low pass filter, and the square error of the overall transfer function of the QMF bank at the quadrature frequency π/2, in the transition band. The design results included in the paper clearly show the improvement of the proposed PSO technique over earlier reported results.

Bacteria foraging optimisation algorithm for optimal FIR filter design

This paper presents a novel search algorithm, called bacteria foraging optimisation (BFO) for the design of linear phase positive symmetric FIR low pass, high pass, band pass and band stop filters, realising the respective ideal filter specifications. BFO is a population-based evolutionary optimisation concept used to solve nonlinear optimisation problem where each individual maintains the propagation of genes. BFO favours propagation of genes of those animals which have efficient foraging strategies and eliminate those animals that have weak foraging strategies i.e., method of finding, handling and taking in food. All animals with their own physiological and environmental constraints, try to maximise the consumption of energy per unit time interval. The performances of BFO-based FIR filter designs have proven to be superior as compared to those obtained by real coded genetic algorithm (RGA) and standard particle swarm optimisation (PSO) optimisation techniques. The simulation results justify that BFO is the best optimiser among the other optimisation techniques, not only in the convergence speed but also in the accuracy and the optimal performances of the designed filters.

Digital FIR Filter Design Using Hybrid Random Particle Swarm Optimization with Differential Evolution

Abstract This paper presents a novel approach of designing linear phase FIR low pass and high pass filter using Random PSO in hybrid with DE known as Random PSODE (RPSODE). In this paper, the Random PSO is used which utilises the weighted particle to guide the search direction for both explorative and exploitative searches. Differential evolution (DE) is one of the very fast and robust evolutionary algorithms which has shown superior performance for continuous global optimization; uses differential information to guide its search direction but sometime causes instability problem; whereas, PSO is a robust, population based stochastic search technique but has the problem of sub-optimality. This paper efficiently combines the Random PSO and DE so as to overcome the disadvantages faced by both the algorithms individually and is used for the design of linear phase low pass and high pass FIR filters. The simulation results show the superiority of RPSODE in global convergence properties and local search ability,...

Efficient and Accurate Optimal Linear Phase FIR Filter Design Using Opposition-Based Harmony Search Algorithm

In this paper, opposition-based harmony search has been applied for the optimal design of linear phase FIR filters. RGA, PSO, and DE have also been adopted for the sake of comparison. The original harmony search algorithm is chosen as the parent one, and opposition-based approach is applied. During the initialization, randomly generated population of solutions is chosen, opposite solutions are also considered, and the fitter one is selected as a priori guess. In harmony memory, each such solution passes through memory consideration rule, pitch adjustment rule, and then opposition-based reinitialization generation jumping, which gives the optimum result corresponding to the least error fitness in multidimensional search space of FIR filter design. Incorporation of different control parameters in the basic HS algorithm results in the balancing of exploration and exploitation of search space. Low pass, high pass, band pass, and band stop FIR filters are designed with the proposed OHS and other aforementioned algorithms individually for comparative optimization performance. A comparison of simulation results reveals the optimization efficacy of the OHS over the other optimization techniques for the solution of the multimodal, nondifferentiable, nonlinear, and constrained FIR filter design problems.

Improved Particle Swarm Optimization with wavelet mutation: Application to linear phase FIR filter design

In this paper, various swarm based algorithms like conventional Particle Swarm Optimization PSO, Improved Particle Swarm Optimization IPSO and another novel Improved Particle Swarm Optimization with Wavelet Mutation IPSOWM have been applied for the optimal design of linear phase FIR filters. Real coded genetic algorithm RGA has also been adopted for the sake of comparison. IPSO uses new definition for the velocity vector. Whereas in addition to the above-mentioned new definition added in IPSO, IPSOWM incorporates a new definition of swarm updating with the help of wavelet mutation based on wavelet theory. Wavelet mutation enhances the PSO to explore the solution space more effectively compared to the other optimization methods. IPSOWM is apparently free from getting trapped at local optima and premature convergence. Low pass LP, high pass HP, band pass BP and band stop BS FIR filters are designed with the proposed IPSOWM and other afore-mentioned algorithms individually for comparative optimization performance. A comparison of simulation results reveals the optimization efficacy of the IPSOWM over the other optimization techniques for the solution of the multimodal, non-differentiable, highly non-linear, and constrained FIR filter design problems.

Design of One-Dimensional Linear Phase Digital IIR Filters Using Orthogonal Polynomials

In the present paper, we discuss a method to design a linear phase 1-dimensional Infinite Impulse Response (IIR) filter using orthogonal polynomials. The filter is designed using a set of object functions. These object functions are realized using a set of orthogonal polynomials. The method includes placement of zeros and poles in such a way that the amplitude characteristics are not changed while we change the phase characteristics of the resulting IIR filter.

Seeker optimisation algorithm: application to the design of linear phase finite impulse response filter

This study presents a novel seeker optimisation algorithm (SOA) for the design of linear phase finite impulse response low pass, high pass, band pass and band stop digital filters. A new fitness function has been adopted in order to improve the stop band attenuation, stop band ripple and to have an accurate control on the transition width. A comparison of simulation results reveals the optimisation efficacy of SOA in terms of error fitness value, stop band attenuation and stop band ripple over the prevailing optimisation techniques reported in recent literatures.

Constructing an Efficient Self-Tuning Aircraft Engine Model for Control and Health Management Applications


 
 
 Self-tuning aircraft engine models can be applied for control and health management applications. The self-tuning feature of these models minimizes the mismatch between any given engine and the underlying engineering model describing an engine family. This paper provides details of the construction of a self-tuning engine model centered on a piecewise linear Kalman filter design. Starting from a nonlinear transient aerothermal model, a piecewise linear representation is first extracted. The linearization procedure creates a database of trim vectors and state-space matrices that are subsequently scheduled for interpolation based on engine operating point. A series of steady-state Kalman gains can next be constructed from a reduced-order form of the piecewise linear model. Reduction of the piecewise linear model to an observable dimension with respect to available sensed engine measurements can be achieved using either a subset or an optimal linear combination of “health” parameters, which describe engine performance. The resulting piecewise linear Kalman filter is then implemented for faster-than-real-time processing of sensed engine measurements, generating outputs appropriate for trending engine performance, estimating both measured and unmeasured parameters for control purposes, and performing on-board gas-path fault diagnostics. Computational efficiency is achieved by designing multidimensional interpolation algorithms that exploit the shared scheduling of multiple trim vectors and system matrices. An example application illustrates the accuracy of a self-tuning piecewise linear Kalman filter model when applied to a nonlinear turbofan engine simulation. Additional discussions focus on the issue of transient response accuracy and the advantages of a piecewise linear Kalman filter in the context of validation and verification. The techniques described provide a framework for constructing efficient self-tuning aircraft engine models from complex nonlinear simulations.
 
 

Design of IIR Notch Filter with Approximately Linear Phase

A method for design of linear phase notch IIR filters is presented in this paper. The filter is realized in the form of a parallel connection of two all-pass sub-filters. In order to achieve the resulting filter with an approximately linear phase in the pass-band, the applied all-pass sub-filters should be also with a linear phase. The desired amplitude characteristic of a resulting filter is obtained by all-pass sub-filter phase approximation. It can be achieved by applying either a pure delay or an IIR all-pass filter in one branch. If a pure delay is positioned in one branch, equiripple phase of all-pass sub-filter from the other branch is guaranteed for an equiripple amplitude characteristic of the resulting filter. Efficiency of the proposed algorithm is demonstrated on a few examples. The algorithm exhibits a fast convergence and an easy determination of initial values. In the case where IIR all-pass sub-filters are placed in both branches, the resulting amplitude characteristic satisfies all the prescribed demands, but the amplitude characteristic is not equiripple even when both all-pass sub-filters have equiripple phase.