Stable Infinite Impulse Response Research Articles

Reduced order infinite impulse response system identification using manta ray foraging optimization

This article presents a useful application of the Manta Ray Foraging Optimization (MRFO) algorithm for solving the adaptive infinite impulse response (IIR) system identification problem. The effectiveness of the proposed technique is validated on four benchmark IIR models for reduced order system identification. The stability of the proposed estimated IIR system is assured by incorporating a pole-finding and initialization routine in the search procedure of the MRFO algorithm and this algorithmic modification contributes to the MRFO algorithm when seeking stable IIR filter solutions. The absence of such a scheme, which is primarily the case with the majority of the recently published literature, may lead to the generation of an unstable IIR filter for unknown real-world instances (particularly when the estimation order increases). Experiments conducted in this study highlight that the proposed technique helps to achieve a stable filter even though large bounds for the design variables are considered. The convergence rate, robustness, and computational speed of MRFO for all the considered problems are investigated. The influence of the control parameters of MRFO on the design performances is evaluated to gain insight into the interaction between the three foraging strategies of the algorithm. Extensive statistical performance analyses employing various non-parametric hypothesis tests concerning the design consistency and convergence are conducted for comparison of the proposed MRFO-based approach with six other metaheuristic search procedures to investigate the efficiency. The results on the mean square error metric also highlight the improved solution quality of the proposed approach compared to the various techniques published in the literature.

Design of Fractional Order Odd-Harmonics Repetitive Controller for Discrete-Time Linear Systems with Experimental Validations.

This paper presents a simple and straightforward design of a discrete-time fractional-order odd-harmonics repetitive controller (RC). Unlike general RC designs, the proposed method utilizes an internal model with a half-period delay and a stabilizing controller with a fractional phase lead compensator. First, the odd-harmonics internal model representing odd-harmonics frequencies is constructed by using the information of the reference's basis period and the preferred tracking bandwidth. Secondly, an optimization problem synthesized from the stability condition of the RC closed-loop system is solved to obtain the fractional phase lead compensator. Finally, the fractional term of the stabilizing controller is realized by using a causal and stable infinite impulse response (IIR) filter, where the filter coefficients are computed by applying the Thiran formula. Simulation and experimental validation on a servomotor system are conducted to verify the effectiveness of the proposed design.

NANO-studio, the design environment of filter banks implemented in standard CMOS technology

The paper presents a method of optimizing frequency characteristics of filter banks in terms of their implementation in digital CMOS technologies in nanoscale. Usability of such filters is demonstrated by frequency-interleaved (FI) analog-to-digital converters (ADC). An analysis filter present in these converters was designed in switched-current technique. However, due to huge technological pitch of standard digital CMOS process in nanoscale, its characteristics substantially deviate from the required ones. NANO-studio environment presented in the paper allows adjustment, with transistor channel sizes as optimization parameters. The same environment is used at designing a digital synthesis filter, whereas optimization parameters are input and output conductances, gyration transconductances and capacitances of a prototype circuit. Transition between analog s and digital z domains is done by means of bilinear transformation. Assuming a lossless gyrator-capacitor (gC) multiport network as a prototype circuit, both for analysis and synthesis filter banks in FI ADC, is an implementation of the strategy to design filters with low sensitivity to parameter changes. An additional advantage is designing the synthesis filter as stable infinite impulse response (IIR) instead of commonly used finite impulse response (FIR) filters. It provides several dozen-fold saving in the number of applied multipliers.. The analysis and synthesis filters in FI ADC are implemented as filter pairs. An additional example of three-filter bank demonstrates versatility of NANO-studio software.

Optimal communications with infinite impulse response matched filters

Abstract Optimal communication waveforms matched to a large and practically important class of filters are investigated and shown to be chaotic. Filters of this class are defined by an infinite impulse response (IIR) and a transfer function comprising a finite number of distinct stable poles. This class contains many of the most popular and widely used filter families, including Butterworth, Chebyshev (type I), and Bessel. For such a filter, a matched basis function is derived and convolved with a random binary sequence to construct a communication waveform. It is shown that this waveform is chaotic in the sense that it is deterministic and characterized by a positive Lyapunov exponent. This result supports a recent conjecture that optimal communication waveforms matched to stable IIR filters are chaotic, and it further establishes that chaos is fundamental to modern communication theory.

A Simplified Realization of Zero Frequency Filter for Hardware Implementation

Zero frequency filtering (ZFF) is a well-explored technique for detecting glottal closure instants (GCIs) from the speech signal. The features extracted from the ZFF of the speech signal have also been used for many speech-based applications. Zero frequency resonators used in the infinite impulse response (IIR) realization of ZFF are unstable filters. Consequently, the filter output grows or decays in an unbounded manner. In the finite impulse response (FIR) realization of ZFF, the filter instability problem is address by using more adders and multipliers. In this paper, a simplified stable IIR realization of ZFF (SIIR-ZFF) is proposed for efficient hardware implementation. The SIIR-ZFF requires significantly less hardware than the earlier reported IIR-ZFF as well as FIR-ZFF. Performance of the proposed approach for the task of detecting GCIs from speech signal is found to be almost equivalent to that of the conventional IIR-ZFF. The hardware architecture for the proposed approach is designed and implemented on FPGA.

Prediction-error identification of LPV systems: A nonparametric Gaussian regression approach

In this paper, a Bayesian nonparametric approach is introduced to estimate multi-input multi-output (MIMO) linear parameter-varying (LPV) models under the general noise model structure of Box–Jenkins (BJ) type. The approach is based on the estimation of the one-step-ahead predictor of general LPV-BJ structures. Parts of the predictors associated with the input and output signals are modeled as asymptotically stable infinite impulse response (IIR) models. Then, these IIR models are identified in a completely nonparametric sense: not only the coefficients are estimated as functions, but also the whole time evolution of the impulse response w.r.t. the scheduling signal of the LPV system. In this Bayesian setting, the estimate of the one-step-ahead predictor is a realization from a zero-mean Gaussian random field, where the covariance function is a multidimensional Gaussian kernel that encodes both the possible structural dependencies and the stability of the predictor. Two different kernel formulations are presented for the LPV setting, namely a diagonal (DI) like and tuned/correlated (TC) like kernels, where the TC-like kernel is able to describe the correlation between coefficient functions associated with different time indices. The unknown hyperparameters that parameterize the DI or TC kernel are tuned by maximizing the marginal likelihood w.r.t. the observed data. Moreover, we provide a nonparametric realization scheme to recover the original process and noise IIRs from the identified one-step-ahead predictor. The performance of the presented identification approach is tested on a MIMO LPV-BJ simulation example by means of an extensive Monte-Carlo study.

Causal IIR Audio Precompensator Filters Subject to Quadratic Constraints

Infinite impulse response (IIR) Wiener precompensator design, with constraints on causality, is here also extended to incorporate general quadratic constraints. A method for finding a linear quadratic optimal, causal discrete-time multiple-input multiple-output filter subject to a set of user defined constraints is proposed and analyzed. A method for designing causal filters subject to constraints on the power gains in a large number of small frequency intervals is also proposed. The resulting set of methods provide constrained stable IIR filters with optimal parameterization. Compared to finite impulse response Wiener filtering, the computational complexity is much lower; and compared to noncausal frequency domain designs, we gain control of the time-domain properties of the compensated system. The design methods are applied to a room compensation audio problem subject to filter power gain constraint(s) and are compared to a corresponding noncausal per-frequency method. The results are presented with audio filtering and sound field control as main motivating applications but the methods extend to other areas of linear feedforward controller design and Wiener filtering.

A New Design Method for Stable IIR Filters With Nearly Linear-Phase Response Based on Fractional Derivative and Swarm Intelligence

In this paper, a new design method based on fractional derivative (FD) is proposed for designing digital stable infinite impulse response (IIR) filters with nearly linear-phase response. In this method, the design problem is formulated as a phase error optimization of an all-pass filter connected in parallel with a pure delay function. FD is employed to improve the frequency response of the filter at some reference point $(\omega _{{0}})$ in the passband. Optimal values of FD constraints and reference points in passband are determined by minimizing the sum of error in passband $(E_{p})$ and stopband $(E_{s})$ of an IIR filter, using different evolutionary techniques such as particle swarm optimization (PSO), constraint factor inertia PSO (CFI-PSO), quantum PSO, artificial bee colony algorithm, and cuckoo search technique. Comparative study provides evidence that the proposed method, based on CFI-PSO, gives the best performance amongst the employed swarm-based techniques. Experimental results show the impact of the proposed method as compared to earlier reported techniques in terms of improved response in passband and sharper transition width. However, small reduction in stopband attenuation $(A_{s})$ is observed within the allowable limit when compared to nonfractional design approaches.

High order stable infinite impulse response filter design using cuckoo search algorithm

In this paper, an efficient technique for optimal design of digital infinite impulse response (IIR) filter with minimum passband error (e p ), minimum stopband error (e s ), high stopband attenuation (A s ), and also free from limit cycle effect is proposed using cuckoo search (CS) algorithm. In the proposed method, error function, which is multi-model and non-differentiable in the heuristic surface, is constructed as the mean squared difference between the designed and desired response in frequency domain, and is optimized using CS algorithm. Computational efficiency of the proposed technique for exploration in search space is examined, and during exploration, stability of filter is maintained by considering lattice representation of the denominator polynomials, which requires less computational complexity as well as it improves the exploration ability in search space for designing higher filter taps. A comparative study of the proposed method with other algorithms is made, and the obtained results show that 90% reduction in errors is achieved using the proposed method. However, computational complexity in term of CPU time is increased as compared to other existing algorithms.

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.

Multi-objective IIR Filter Design using Nondominated Sorting Genetic Algorithm-II

Objectives: To design a stable Infinite Impulse Response (IIR) filter which minimizes the magnitude response. Methods/Statistical Analysis: The problem is perceived as a problem of optimization with many objectives. An efficient algorithm, namely Non-dominated Sorting Genetic Algorithm-II (NSGA-II), is used to solve it. To get assurance of stability, the poles of the filter are maintained inside the unit circle. Findings: As results show, the algorithm is well suited for the problem. Especially, it is very easy to design stable Low Pass (LP) and High Pass (HP) filters using this algorithm. Band Pass (BP) and Band Stop (BS) filters can also be designed by this algorithm, but sometimes it takes large number of iterations to converge. However, in offline applications, time is not an issue. Application/Improvement: The algorithm is an improvement over other researchers’ works which only minimize the magnitude response error treating the problem as a single objective one.

Chaos in optimal communication waveforms

The properties of nonlinear dynamics and chaos are shown to be fundamental to optimal communication signals subject to two practical and realistic design requirements: (i) operation in a noisy environment and (ii) simple hardware implementation. Starting with a simple electronic circuit, a linear filter receiver is presumed, and the matched optimal communication waveform that maximizes the receiver signal-to-noise performance is derived. A return map using samples from this optimal waveform is conjugate to a shift, thereby implying the waveform is chaotic. The optimal communication waveform for a second simple receiver is similarly derived, and it is found to be an exact solution to a physically realizable chaotic oscillator. Thus, a practical consequence of chaos in these waveforms is the potential for simple and efficient signal generation using chaotic oscillators. A conjecture is made that the optimal communication waveform for any stable infinite impulse response filter is similarly chaotic.

Opposition aided Cat Swarm OptimizationAlgorithm for Optimal Digital IIR High PassFilter Design

1 ABSTRACT: This paper presents a solution methodology for the designing of optimal and stable digital infinite impulse response (IIR) high pass (HP) filter by employing the cat swarm optimization (CSO) technique with oppositional learning. Because of the presence of the denominator terms, the error surface of digital IIR filters is non linear and multimodal. Therefore, the traditional designing techniques usually got trapped in the local minim. CSO is a population based global optimization technique which has global as well as local search capabilities. Here, the multicriterion optimization is used as the design criterion that undertakes the minimization of magnitude approximation error and minimization of ripple magnitudes while satisfying the stability constraints that are imposed during the design process. For the intent of starting with an improved solution set, the opposition based learning strategy is included in CSO. The developed algorithm is used to design the digital IIR high pass (HP) filter and attempts to find the optimal filter coefficients which are approximately close to the desired filter response. The computational results shows that the proposed algorithm is capable of designing the stable and optimal digital IIR HP filter structure that is better to the designs presented by other algorithms.

Epoch Extraction Using Zero Band Filtering from Speech Signal

Zero frequency filter (ZFF) is a marginally stable infinite impulse response resonant filter at 0 Hz that is used to extract the epoch locations reliably from speech signals. However, the output of such an ideal resonator is an exponentially increasing/decreasing function of time. The trend is removed from the filtered output by subtracting the average over 1---2 pitch periods to obtain zero frequency filtered signal. Alternatively in this paper, a bounded input bounded output stable realization of ZFF is proposed for epoch extraction, where the output of such a filter is not an increasing/decreasing function of time. The advantages of using such a stable filter is that the filter output is bounded and has no precision related problem associated with the output for lengthy speech files, also, the method does not require remove trend procedure that needs initial pitch estimation. The proposed approach is evaluated using CMU-Arctic database for clean and degraded conditions. Furthermore, the method is also validated in cases of singing voice and emotional speech to demonstrate the robustness for varying pitch scenarios. The proposed method is found to be robust for wide range of chosen parameters.

Digital IIR Filter Design using Real Coded Genetic Algorithm

The paper develops a technique for the robust and stable design of digital infinite impulse response (IIR) filters. As the error surface of IIR filters is generally multi-modal, global optimization techniques are required to design efficient digital IIR filter in order to avoid local minima. In this paper a real-coded genetic algorithm (RCGA) with arithmetic- average-bound-blend crossover and wavelet mutation is applied to design the digital IIR filter. A multicriterion optimization is employed as the design criterion to obtain the optimal stable IIR filter that satisfies the different performance requirements like minimizing the Lp-norm approximation error and minimizing the ripple magnitude. The proposed real-coded genetic algorithm is effectively applied to solve the multicriterion, multiparameter optimization problems of low-pass, high-pass, band-pass, and band-stop digital filters design. The computational experiments show that the proposed method is superior or atleast comparable to other algorithms and can be efficiently used for higher order filter design.

Design of Optimal L1 Stable IIR Digital filter using Hybrid Optimization Algorithm

Hybrid optimization algorithm is applied for designing stable infinite impulse response (IIR) digital filter based on L1-approximation error criterion. The proposed Hybrid method calculates the optimal filter coefficients by exploring and exploiting the search space locally as well globally. The filter designed based on L1-approximation error possesses flat passbands and stopbands in comparison to that of least square design and the minimax approach. A comparison with other design techniques is made, demonstrating that the proposed hybrid approach can obtain better digital IIR filters than the existing Genetic Algorithm (GA) based methods. KeywordsIIR filters, Hybrid search algorithm, L 1-approximation error, Stability.

CSD‐Coded Genetic Algorithm on Robustly Stable Multiplierless IIR Filter Design

A Canonic‐Signed‐Digit‐(CSD‐) coded genetic algorithm (GA) is proposed to find the optimal design of robustly stable infinite impulse response digital filter (IIR). Under the characteristics of the CSD structure, the circuit of the filter can be simplified and also the calculation speed can be raised to increase the hardware’s efficiency. However, the design of CSD has a big challenge: the CSD structure of the system parameters will be destroyed by an optimal design procedure. To solve this problem, in this research a CSD‐coded GA is proposed so that the CSD structure can be maintained. Moreover, the robustly stable IIR filters design problem is included in this paper. The robustness of the IIR filters is achieved by ensuring that all poles of the filters are located inside a disk D(α, r) contained in the unit circle, in which α is the center, r is the radius of the disk, and |α| + r < 1. Consequently, in this paper, a new and more efficient D(α, r)‐stability criterion will be derived and then embedded in GA for the design of robust IIR filters. It is worthwhile to note that to design an IIR filter simultaneously with CSD‐structured parameters and robust stability is difficult and is not well explored so far. An example will be presented to show the efficiency of the proposed strategy for design of IIR filters.

Optimal design of IIR filters using linear semi‐indefinite programming method

AbstractAn optimal design method for stable IIR (Infinite Impulse Response) filters under the min‐max criterion is proposed. The design problem considered is the complex Chebyshev approximation of a rational function including the stability constraint. We formulate this problem as a problem of real linear semi‐infinite programming problem using the real rotation theorem. The problem is solved by the three‐phase method; one of the methods is used for solving semi‐infinite programming problems. The three‐phase method includes three operations. In the first operation, some active constraint candidates are selected by the iterative simplex method. Next, the second operation integrates some degenerate constraints. In the third operation, the approximate solution obtained up to the second operation is adjusted so as to satisfy the optimality condition. The filters designed by the method are found to be more precise than those designed by the conventional method. Several design examples are presented to demonstrate the effectiveness of the proposed method. © 2011 Wiley Periodicals, Inc. Electron Comm Jpn, 94(6): 17–23, 2011; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/ecj.10330

Deconvolution filters for the analysis of dynamic measurement processes: a tutorial

Analysis of dynamic measurements is of growing importance in metrology as an increasing number of applications requires the determination of measurands showing a time-dependence. Often linear time-invariant (LTI) systems are appropriate for modelling the relation between the available measurement data and the required time-dependent values of the measurand. Estimation of the measurand is then carried out by deconvolution.This paper is a tutorial about the application of digital deconvolution filters to reconstruct a time-variable measurand from the measurement signal of a LTI measurement apparatus. The goal of the paper is to make metrologists aware of the potentialities of digital signal processing in such cases. A range of techniques is available for the construction of a digital deconvolution filter. Here we compare various approaches for a form of dynamic model that is relevant to many metrological applications and we discuss the consequences for these approaches of the different ways in which information about the LTI system may be expressed. We consider specifically the methods of minimum-phase all pass decomposition, asynchronous time reversal using the exact inverse filter and the construction of stable infinite impulse response and finite impulse response approximate inverse filters by a least squares approach in the frequency domain. The methods are compared qualitatively by assessing their numerical complexity and quantitatively in terms of their performance for a simulated measurement task.Taking into account numerical complexity and underlying assumptions of the methods, we conclude that when a continuous model of the LTI system is available, or when the starting point is a set of measurements of the frequency response of a system, application of least squares in the frequency domain for the construction of an approximate inverse filter is to be preferred. On the other hand, asynchronous time reversal filtering using the exact inverse filter appears superior when a discrete model of the LTI system is available and when causality of the deconvolution filter is not an issue.

Optimal Design of IIR Filters Using Linear Semi-Infinite Programming Method

In this paper, an optimal design method for stable IIR(Infinite Impulse Response) filters in a criterion of min-max sense is proposed. The design problem is considered one of the complex Chebyshev approximation for rational function including the stability constraint, we formulated such the problem as a real linear semi-infinite programming using the real rotation theorem. Then, the problem is solved by the three phase method that is one of the methods solving semi-infinite programming problem. The three phase method is composed of three operations. In the first operation, some candidates of active constraints are selected by the iterative simplex method. Next, the second operation integrates some degenerate constraints. In the third operation, the approximation solution obtained until second operation is adjusted so as to satisfy the optimality condition. As a result, the filters designed by the method are more precise than one designed by conventional method. Several design examples are shown to present effectiveness of the proposed method.