Design Of Infinite Impulse Response Digital Filters Research Articles

Enhancing power quality in vehicle-to-grid (V2G) operations of FCEVs through the integration of real-time digital IIR filters in power calculations

Fuel cell electric vehicles (FCEVs) are estimated as the future's mobile distributed generators with vehicle-to-grid (V2G) functions. Besides, V2G topologies are required to be designed with an appropriate analog filter by accurately measuring the reference current and voltage values of inverters and converters. Thus, the highest accuracy is required in control structures for charging and grid connection of FCEVs to improve the power quality (PQ). In this study, PQ improvement of V2G operation of FCEVs is proposed by considering the developed real-time digital infinite impulse response (IIR) filters in generating reference signals in the power calculation stage. A band-pass digital IIR filter design is realized with the inverter using LabVIEW infrastructure, and reference signals are smoothed by using IIR filters. The performances of developed different IIR filters' results are examined in the study. Developed filters are designed using the order estimation method. Elliptic, Chebyshev, and Butterworth filters are applied to the voltage and current signals, and the best results are obtained in reference power signals with the Butterworth filter. The Butterworth filter maintains stability in current RMS, induces a 0.09 % decrease in voltage RMS, and shows a slight 0.30 % increase in active power. The proposed approach removes distortions in reference power signals by using a designed filter for a reliable V2G operation of FCEVs.

Kalman filter/smoother-based design and implementation of digital IIR filters

Recently, a unified framework was proposed for forward-backward filtering and penalized least-squares optimization. It was shown that forward-backward filtering can be presented as instances of penalized least-squares optimization. In other words, the output of a zero-phase digital infinite-impulse response (IIR) filter can be computed by solving a constrained optimization problem, in which the weight controlling the constraint is directly related to cutoff frequencies with closed-form equations. It was also shown that a zero-phase digital IIR filter can be formed as an optimal smoothing Wiener filter for a random process obtained from an autoregressive (AR) or AR-moving average (ARMA) model driven by input (innovation) noise in presence of an observation noise.In this paper, the problem of zero-phase digital IIR filtering is re-examined using Kalman filter/smoother. The paper shows that every zero-phase digital IIR filter can be viewed as a special case of an optimal smoothing Wiener filter. Based on the fact that the formulations of the optimum filter by Wiener and Kalman are equivalent in steady state, we present a Kalman filter/smoother framework to the design and implementation of digital IIR filters. As an example, the zero-phase digital Butterworth filter is designed using Kalman smoother and compared with the traditional design (forward filtering and backward smoothing) method.

Design of digital IIR filter: A research survey

This paper presents an overview on advancement made in designing of a digital infinite impulse response (IIR) filter. The design problem of an IIR filter was found to be challenging due to presence of poles in its transfer function. This makes the phase response of an IIR transfer function nonlinear and its magnitude response is also drifted due to quantization of coefficient values of denominator polynomials, which leads towards instability. Therefore, numerous efforts were made in order to acquire an optimal filter response using several optimization methods. Design problem of an IIR filter with various constraints was developed and solved using gradient based techniques, which resulted in optimal passband response with nearly linear phase or in some cases, absolute linearity was also achieved. However, the obtained solutions were sub-optimal in many cases due to transferring the multimodal design problem of an IIR filter into convex optimization. The solution was also affected due to the quantization of filter coefficients and in case of absolute linear phase response; a strong hick in magnitude response at beginning of transition edge frequency was obtained. To overcome the sub-optimality, researchers used evolutionary algorithms (EAs) for designing of an IIR filter. In time domain, system identification (SI) was adopted, whereas various error functions were developed in frequency domain for obtained magnitude responses close to desired response. This approach resulted in an optimal IIR filter response, however phase response linearity was not improved. Thus, EA approach was appropriated for lower order IIR filters. The design of various IIR filters like lowpass filter (LPF), highpass filter (HPF), bandpass filter (BPF) and bandstop filter (BSP) using an all-pass infinite impulse response (APF-IIR) was also reported. This approach is most appropriate, because the filter response is stable, nearly linear and magnitude response was also accurate. However, there is high error at the band edges of passband. Therefore, literature reveals that an APF based approach is most appropriate for various magnitude response filters.

Infinite impulse response systems modeling by artificial intelligent optimization methods

Artificial Intelligent Optimization (AIO) algorithms learn from the past searches via using a group of individuals or agents. These Artificial Intelligence-based optimizing techniques are able to solve complex optimization problems with complicated constraints. They find the optimal in the low possible number of iterations, where optimal means the best from all possibilities selected from a special point of view. This paper presents a research on employing AIO methods with aim to Infinite Impulse Response (IIR) system modeling for design and optimization of IIR digital filters. The proposed methods cover a variety of AIO methods; algorithm based on evolution strategy (genetic algorithm) and heuristic algorithms (particle swarm optimization, population-based; gravitational search algorithm, and inclined planes system optimization, both population-based and based on Newton’s laws). In this paper, the IIR system modeling is solved as a constrained single-objective optimization problem in the Mean Squared Error (MSE) fitness function and is evaluated for two different benchmark IIR plants with high and low orders. To evaluate performance, efficiency and efficacy of the methods, two important criteria are used: “Indicator of Success (IoS)” and “Degree of Reliability (DoR)”. In addition, the effect of decreasing population size (search agents) is analyzed on the performance and efficiency of the algorithms. Simulation results clarify the success of the research in terms of the MSE, IoS and DoR.

A System Identification Based Approach for Design of IIR Digital Filters with Robust Stability

Design problem of infinite impulse response (IIR) filters is generally a non-linear optimization problem due to the presence of denominator polynomial. Additionally, the stability condition (positi...

Design of digital IIR filter with low quantization error using hybrid optimization technique

In this paper, a hybrid optimization technique based on particle swarm optimization (PSO) and artificial bee colony (ABC) algorithm is presented for the optimal design of infinite impulse response (IIR) filter with low quantization effect. In this method, different variants of PSO have been exhaustively tested, and the time varying coefficients-PSO (TVC-PSO) is used to formulate a new hybrid technique for better exploitation and exploration, which is further modified by sorting and replacement mechanism of Scout Bee from ABC algorithm. For designing IIR filter, an objective function is constructed that satisfies the absolute error including peak ripples in passband and stopband regions in frequency domain, while stability of designed filter is confirmed by exploiting the lattice form structure during iterative computation that also reduces computation complexity. Several attributes such as passband error $$(e_{\mathrm{p}})$$ , stopband error $$(e_{\mathrm{s}})$$ , and stopband attenuation $$(A_{\mathrm{s}})$$ are used to measure the performance of proposed algorithm. The simulation results presented in this paper evidence that this technique can be effectively used for designing digital IIR filter with higher filter taps, and low quantization effect for fixed number of bits.

Integrated Cat Swarm Optimization and Differential Evolution Algorithm for Optimal IIR Filter Design in Multi-Objective Framework

This paper proposes an integrated optimization technique which combines the features of the cat swarm optimization (CSO) algorithm with the traditional differential evolution (DE) algorithm and applies it for the optimal design of digital infinite impulse response (IIR) filters. Traditional design methods treat the digital IIR filter design as a single-objective optimization problem by taking into account the minimization of magnitude response error only and lack in considering the linear phase response error and the order of the filter. The aim of this paper was to design an IIR filter in multi-objective framework by equally considering the minimization of magnitude response error, the linear phase response error and the order of the filter. Firstly, the CSO algorithm is applied for digital IIR filter design. In order to start with a better solution set, the opposition-based learning strategy is then incorporated. To further improve the performance of CSO for designing stable digital IIR filters, the DE optimization algorithm is combined with CSO hence producing an integrated algorithm called multi-objective cat swarm and differential evolution algorithm (MOCSO-DE) which has the capability to explore and exploit the solution search space locally as well as globally. The developed integrated algorithm is effectively applied for the designing of the digital IIR low-pass (LP), high-pass (HP), band-pass (BP) and band-stop (BS) filters. To evaluate the effectiveness of the developed integrated algorithm, the computational results are compared with some well-established algorithms and it is observed that the developed algorithm is superior or at least comparable to other algorithms in getting better magnitude response and linear phase response together with lowest filter order and can also be implemented for the higher-order filter designs.

A modified imperialist competitive algorithm for digital IIR filter design

There are two major types of digital filters in terms of structure: infinite impulse response (IIR) and finite impulse response (FIR). Digital IIR filters often provide a much better performance and less computational cost than FIR filters and have become the target of growing interest. Since the problem of the error surface of designing digital IIR filters is generally nonlinear and multimodal, global optimization techniques are required in order to avoid local minima. In this paper, an evolutionary method has been proposed to design digital IIR filters. This method is based on Imperialist Competitive Algorithm (ICA) and by adding a step to the existing steps of ICA, performance of it has been improved in searching solution space and convergence to the global minima. Obtained results from simulation using proposed method and other algorithms show that the proposed method is suitable for designing digital IIR filter.

A new greedy search method for the design of digital IIR filter

A new greedy search method is applied in this paper to design the optimal digital infinite impulse response (IIR) filter. The greedy search method is based on binary successive approximation (BSA) and evolutionary search (ES). The suggested greedy search method optimizes the magnitude response and the phase response simultaneously and also finds the lowest order of the filter. The order of the filter is controlled by a control gene whose value is also optimized along with the filter coefficients to obtain optimum order of designed IIR filter. The stability constraints of IIR filter are taken care of during the design procedure. To determine the trade-off relationship between conflicting objectives in the non-inferior domain, the weighting method is exploited. The proposed approach is effectively applied to solve the multiobjective optimization problems of designing the digital low-pass (LP), high-pass (HP), bandpass (BP), and bandstop (BS) filters. It has been demonstrated that this technique not only fulfills all types of filter performance requirements, but also the lowest order of the filter can be found. The computational experiments show that the proposed approach gives better digital IIR filters than the existing evolutionary algorithm (EA) based methods.

Design of Digital IIR Filters using Integrated Cat Swarm Optimization and Differential Evolution

This paper aims to establish a solution methodology for the optimal design of digital infinite impulse response (IIR) filters by integrating the features of cat swarm optimization (CSO) and differential evolution algorithm (DE). DE is a population based stochastic optimization technique which optimizes real valued functions. It requires negligible control parameter tuning but sometimes causes instability problem. CSO is a heuristic optimization algorithm based on the observations and imitation of the natural behavior of cats. CSO algorithm possesses local as well as global search capabilities. Although, CSO possesses better capability to search optimal point but it requires a higher computation time because the local and global searches are carried out independently in each iteration. A hybrid algorithm is proposed using the CSO algorithm and the DE optimization algorithm for the robust and stable design of digital IIR filter. To start with a better solution set, opposition based learning strategy is incorporated. The proposed method explores and exploits the search space locally as well as globally. The design criterion undertakes the minimization of magnitude approximation error and ripple magnitudes of both pass-band and stop-band satisfying the stability requirements. The developed hybrid algorithm is effectively applied for designing the digital low-pass, high-pass, band-pass and band-stop filters. The computational results demonstrate that the proposed algorithm is capable of creating designs that are competitive with reference to other design processes and can efficiently be applied for higher order filter design.

AN OPTIMAL DESIGN OF IIR DIGITAL FILTER USING PARTICLE SWARM OPTIMIZATION

In this article, a novel approach for infinite-impulse response (IIR) digital filters using particle swarm optimization (PSO) is presented. IIR filter is essentially a digital filter with recursive responses. Because the error surface of digital IIR filters is generally nonlinear and multimodal, so global optimization techniques are required in order to avoid local minima. This study is based on a heuristic way to design IIR filters. PSO is a powerful global optimization algorithm introduced in combinatorial optimization problems. This study finds the optimum coefficients of the IIR digital filter through PSO. It is found that the calculated values are more optimal than the FDA tool and GA available for the design of the filter in MATLAB. Design of low-pass and high-pass IIR digital filters is proposed in order to provide an estimate of the transition band. The simulation results of the employed examples show an improvement on the transition band. The stability of designed filters is described by the position of Pole-Zeros.

Design of Digital IIR Filter with Conflicting Objectives

Infinite impulse response (IIR) filter design is a highly constrained multiobjective optimization problem involving conflicting objectives. In this paper, particle swarm optimization (PSO) is purposed to efficiently and effectively handle multiple conflicting objectives of IIR filter design. The weighted sum approach is used to minimize magnitude response and phase response of digital IIR filter simultaneously. The value of weights are searched using PSO along with filter coefficients thus assigning different weight vector to each individual particle. The order of the filter is controlled by a control gene whose value is also optimized along with the filter coefficients to obtain optimum order of designed IIR filter. The proposed algorithm shows competitive results with improved diversity and convergence

An application of swarm intelligence for the design of IIR digital filters

This paper presents the swarm intelligence (SI)-based particle swarm optimisation (PSO) in context of designing infinite-impulse response (IIR) digital filters. IIR filters are the part of digital filters with recursive responses. Since the error surface of IIR digital filters is generally non-linear and multimodal, global optimisation techniques are required in order to avoid local minima. The particle swarm optimisation algorithm is then applied for calculating optimal coefficients of IIR digital filters and comparison is done preferably with filter design tool and other heuristic techniques. The simulation results of benchmark filter are discussed in this paper and can be efficiently used for IIR digital filter design.

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.

Fixed-point digital IIR filter design using two-stage ensemble evolutionary algorithm

The research on optimal design of infinite-impulse response (IIR) filter design based on various optimization techniques, including evolutionary algorithms (EAs), has gained much attention in recent years. Previously, the parameters of digital IIR filters are encoded with floating-point representations. It is known that a fixed-point representation can effectively save computational resources and is more convenient for direct realization on hardware. Inherently, compared with the floating-point representation, the fixed-point representation would make the search space miss much useful gradient information and therefore, surely rises new challenges for continuous EAs. In this paper, we first analyze the fitness landscape properties of optimal digital IIR filter design. Based on the fitness landscape investigation, a two-stage ensemble evolutionary algorithm (TEEA) is applied to digital IIR filter design with fixed-point representation. In order to fully evaluate the performance of TEEA, we experimentally compare it with five state-of-the-art EAs on four types of digital IIR filters with different settings. Based on the experimental results, we can conclude that TEEA has higher convergence speed, better exploration, and higher success rate. In order to benchmark TEEA further, we apply it to some more difficult problems with shorter word length or higher order. We can find that TEEA can provide satisfying performance on these hard tasks as well.

Two-stage ensemble memetic algorithm: Function optimization and digital IIR filter design

The research on optimal design of infinite-impulse response (IIR) filters based on optimization techniques has gained much attention in recent years. However, due to the limited performance of the applied optimization techniques, the orders of the filters, which can be obtained, are very low in the previous research. Memetic algorithms (MAs) are widely recognized to have better convergence capability than their conventional counterparts. However, the universality of the MAs, e.g. the ability of solving diverse kinds of digital IIR filter designs, is still limited. In this paper, we design a Two-Stage ensemble Memetic Algorithm (TSMA) framework to more appropriately synthesize the strengths of the evolutionary global search and local search techniques. In the first optimization stage, a competition is held among the candidate local search techniques. Its major idea is to choose the best local search technique and to obtain good initial state. Inheriting the good information of the first stage, the second optimization stage is to implement effective adaptive MA to pursue high-quality solution. The experimental studies presented in this paper contain three aspects: (1) the benefits of the TSMA framework are experimentally investigated by comparing TSMA with its sub-optimizers and recent effective evolutionary algorithms (EAs) on 26 test functions; then (2) TSMA is compared with 4 MAs on the CEC05 functions to comprehensively show the advantages of TSMA; and (3) the TSMA and 6 state-of-the-art algorithms are applied to design high-order digital infinite-impulse response (IIR) filters. The experimental results definitely demonstrate the excellent effectiveness, efficiency and reliability of TSMA on both function optimization and digital IIR filter design tasks.

Improved Methods for the Design of Variable Fractional-Delay IIR Digital Filters

In this paper, both methods of magnitude-oriented design and delay-oriented design for variable fractional-delay (VFD) infinite impulse response (IIR) filters are proposed. In the former, the objective error function is formed by including root-mean-square error function of variable frequency response and the stability error constrained function, such that the designed filters are stable. As for the second part of this paper, it is desirable to minimize the root-mean-square error of variable group-delay response while the magnitude response and stability can be preserved. Hence, except those stated above, the root-mean-square error function of variable group-delay response is further included in the objective error function. However, these induced problems are highly nonlinear, so iterative methods are proposed to overcome them. Several design examples are presented to demonstrate the features of these design methods, including concerns among VFD finite impulse response (FIR) filters, VFD allpass filters and VFD IIR filters as well as the designed results of both methods.

Minimax Phase Error Design of IIR Digital Filters With Prescribed Magnitude and Phase Responses

Infinite impulse response (IIR) digital filters with prescribed magnitude and phase responses have been used in many applications. To approximate the prescribed magnitude and phase responses, we propose a new approach to the design of general IIR filters by minimizing the maximum phase error subject to a prescribed or simultaneously minimized maximum magnitude error, where the phase error and magnitude error are controlled by two elliptic constraints respectively with major and minor axes along the desired frequency response. The sequential constrained least-squares method and Levy-Sanathanan-Koerner strategy are used to convert the nonconvex constraints into convex ones, resulting in a series of convex optimization subproblems. Design examples and comparisons with recent methods demonstrate the flexibility and effectiveness of the proposed methods.

Genetic Algorithm for the Design of Optimal IIR Digital Filters

This paper presents the design of Optimal Infinite-Impulse Response (IIR) digital filters using Genetic Algorithm (GA). IIR filter is essentially a digital filter with Recursive responses. Since the error surface of digital IIR filters is generally nonlinear and multimodal, global optimization techniques are required in order to avoid local minima. This paper presents heuristic way for the designing IIR filters. GA is a powerful global optimization algorithm introduced in combinatorial optimization problems. The paper finds the optimum Coefficients of IIR digital filter through GA. Design of Lowpass and High pass IIR digital filter is proposed to provide estimate of transition band. It is found that the calculated values are more optimal than fda tool available for the design of filter in MATLAB. The simulation result of the employed examples shows an improvement on transition band and mean-square-error (MSE). The position of pole-zero is also presented to describe stability and results are compared with Simulated Annealing (SA) method.

The design and implementation of a digital infinite impulse response (IIR) Lowpass Butterworth filter– impulse response (IIR) Lowpass Butterworth filter– A comparison of Matlab and Bilinear transformation methods

This research compares two IIR digital filter design and implementation methods– viz MATLAB direct method and Bilinear transformation method. Programs to design and implement Butterworth IIR lowpass digital filters were developed and executed using both methods. In the design, at Fpass of 1Hz, Fstop of 2.414 Hz, using MATLAB method the 3 dB frequency is at 1.605 Hz while using the Bilinear transformation method the 3 dB frequency is at 1.395 Hz. At Fpass of 0.7839Hz, Fstop of 2.007 Hz, using MATLAB method the 3 dB frequency is at 1.181 Hz while using the Bilinear method the 3 dB frequency is at 1.001 Hz. From the design it was observed that the Butterworth filter has maximally flat passband in its frequency response and a poor roll-off at its bandstop which is in line with predicted theory. The Butterworth filters designed using Bilinear transformation were more stable with a monotonically decreasing gain response due to its poor roll-off which may be associated to discrete component performance. The magnitude of the passband decreases as the order of the filter increases. The designs also show that higher order filters have sharper skirts and may be used in phase modulated wave (PMW) applications. Keywords: Matlab, Bilinear transformation methods, Keywords filter design.