Infinite Impulse Response Digital Filters Research Articles

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.

Frequency‐space wavefield extrapolation using infinite impulse response digital filters: is it feasible?

ABSTRACTThe purpose of this paper is to study the possibility of performing practically stable and efficient frequency‐space (f−x) wavefield extrapolation for the application of seismic imaging and datuming via infinite impulse response (IIR) filters. The model reduction control theory was adopted to design such IIR f−x extrapolation filters. The model reduction theory reduces the order of a given order system which, in this case, involves reducing a finite impulse response (FIR) f−x extrapolation filter system into an IIR f−x extrapolation filter system. This theory relies on decomposing the states of the given filter system into strong and weakly coupled sub‐systems, and then eliminating the weakly coupled states via singular value decomposition of the Hankel and the impulse response Gramian matrices. Simulation results indicate that IIR f−x filters can be obtained, which are stable from an IIR filter design point of view. Simulations also indicate that stable seismic impulse responses and synthetics can be obtained with a reduced system model order and, hence, less computational efforts with respect to the number of complex multiplications and additions per output sample. It is hoped that this study will open new possibilities for researchers to reconsider designing IIR f−x explicit depth extrapolation filters due to their expected computational savings and wavenumber response accuracy, when compared to the FIR f−x explicit depth extrapolation filters.

Determine Optimal Coefficients of IIR Digital Filters using Simulated Annealing

This paper determines coefficients of infinite-impulse response (IIR) using Simulated Annealing (SA). 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. In this paper heuristic way for the designing IIR filters is presented. SA is a powerful global optimization algorithm introduced in combinatorial optimization problems. The paper finds the optimum Coefficients of IIR digital filter through SA. It is found that the calculated values are more optimal than fda tool availble for the design of filter in MATLAB. Design of Lowpass and High pass IIR digital filter is proposed to provide estimate of transition band. The simulation results of the employed examples shows an improvement on transition band. It is also observed that mean-square-error of designed is least as compared to fda technique. The position of the Pole-Zero describes the stability of designed filters.

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.

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.

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.

210 デジタルフィルタによる時間-周波数分析を用いた振動解析に関する基礎的検討 : 非線形振動への適用

The main purpose of the current study is to model and identify vibrations in mechanical systems subject to arbitrary external excitations. In this paper, we apply our method based on infinite impulse response digital filter technology - termed time-frequency analysis - to analyze nonlinear vibrations. Firstly, we consider transient and nonstationary forced vibrations of weekly nonlinear systems having a single degree of freedom. With the use of time-frequency analysis method, secondly, we analyze transient forced vibrations for primary and secondary resonances, which is unable to be analyzed by a fast Fourier transform (FFT) analysis. Thirdly, we discuss the passage of the system through resonance when the frequency of the excitation is varied. Moreover, the proposed analysis has the advantage over FFT analysis that we can also analyze transient and nonstationary vibration phenomena.

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.

Cultural firework algorithm and its application for digital filters design

The substance of the digital filter design is a multi-parameter optimisation problem. This paper presents a joint objective function to design finite impulse response (FIR) digital filters and infinite impulse response (IIR) digital filters, and a cultural firework (CF) algorithm is proposed to implement filter designs. The design of the filter is transformed into the constrained optimisation problem, and the cultural firework algorithm is used to search optimal value of filter design parameters in the parameter space with parallel search. The proposed cultural firework algorithm is a multi-dimensional search algorithm for optimisation of real numbers, which uses mechanisms of cultural evolution to update the locations of cultural sparks. Computer simulations have showed that FIR and IIR digital filters based on the CF algorithm are superior to previous filters based on particle swarm optimisation (PSO), quantum-behaved particle swarm optimisation (QPSO) and adaptive quantum-behaved particle swarm optimisation (AQPSO) in the convergence speed and optimisation results. The effectiveness and superiority of the CF are also demonstrated by computer simulations.

An Adaptive-Filter-Based Torque-Ripple Minimization of a Fuzzy-Logic Controller for Speed Control of IPM Motor Drives

This paper presents an adaptive-filter-based torque-ripple minimization (TRM) of a fuzzy-logic controller (FLC) for speed control of an interior permanent magnet (IPM) motor drive. A simple and effective first-order digital infinite impulse response filter is utilized to reduce the torque ripples introduced by the FLC. The gain of the filter is adapted online based on the magnitude of the torque ripple. The optimal position of the filter in the complete drive is also determined for effective TRM. The various sources of torque pulsations in a practical electric-machine drive are described. The main causes of the torque ripple in an FLC are also explained. A simulation model for closed vector control of an FLC-based IPM motor drive incorporating the proposed TRM technique is developed in Matlab/Simulink. The complete drive is also experimentally implemented using digital signal processor board DS1102 for a laboratory 1-hp IPM motor. The effectiveness of the proposed technique is investigated, both in simulation and experiment, at different operating conditions. It is found that the performance of the FLC-based IPM drive is improved significantly with the proposed TRM technique.

Digital fractional delay implementation based on fractional order system

This study presents a design method of the digital fractional delay operator z−m for 0<m<1, in a given frequency band of interest, using digital infinite impulse response (IIR) filters. The design technique is based on the approximation of the fractional order systems. First, analogue rational function approximation, for a given frequency band, of the fractional power pole (FPP) is given. Then the forward difference generating function is used to digitise the FPP to obtain a closed-form IIR digital filter, which approximates the digital fractional delay operator z−m for 0<m<1. Finally, an example is presented to illustrate the effectiveness of the proposed design method. The proposed technique has also been used to design a comb filter. The results obtained have been discussed and compared with some of the most recent work in the literature.

Mooring alignment for marine SINS using the digital filter

Strapdown inertial navigation system (SINS) is presently used in several applications related to aerospace system and marine navigation. The accurate initial attitude is essential to ensure the precise determination of the position and attitude of the moving platform, which is usually calculated using initial alignment. When the vehicle is moored, the SINS inevitably experience disturbing motion. The method of ground coarse alignment, which is based on the assumption that SINS is on a stationary carrier with limited vibration, therefore cannot be used to perform the SINS mooring alignment. In this paper, a novel method processing the gyro and accelerometer measurements with infinite impulse response (IIR) digital low-pass filter to remove the high frequency noise is investigated for marine mooring alignment. Its algorithmic principle is described in details. The results obtained from both simulation and mooring experiment show that the attitude determined by this novel method can meet the accurate alignment.

Three-Dimensional Sound Field Rendering with Digital Boundary Condition using Graphics Processing Unit

A boundary condition with arbitrary frequency characteristics called a digital boundary condition is realized by an infinite impulse response (IIR) digital filter. The digital boundary condition is integrated with a three-dimensional sound field renderer using the digital Huygens' model (DHM), then it is implemented into a Graphics Processing Unit (GPU). Numerical demonstrations are carried out for three-dimensional sound propagation in a cubic room. It is confirmed that the presented model is valid for a boundary condition with arbitrary frequency characteristics.

Minimax Design of IIR Digital Filters Using a Sequential Constrained Least-Squares Method

The minimax design of infinite impulse response (IIR) digital filters is a nonconvex optimization problem, and thus has many local minima. It is shown in this correspondence that a sequential constrained least-squares (SCLS) method has a higher possibility of obtaining better solutions than a direct minimization method when applied to the nonconvex minimax design of IIR filters. We combine the SCLS method with a Steiglitz-McBride (SM) strategy, resulting in a practical design procedure. The positive realness stability condition proposed by Dumitrescu and Niemisto is reformulated as linear inequality constraints and then incorporated in the design procedure. Simulation examples and comparisons with several existing methods demonstrate the effectiveness of the procedure and good performances of the designed filters.

Digital IIR filter design using multi-objective optimization evolutionary algorithm

The research of applying evolutionary algorithms (EAs) to digital infinite-impulse response (IIR) filter design has gained much attention in recent years. Previously, most works treated digital IIR filter design as a single objective optimization problem of minimizing the magnitude response error with supplementary conditions. While the lack of considering the linear phase response error and the order may result in the loss of control on the structural flexibility, the distortion of output, and the dependency on pre-knowledge. The aim of this paper is to develop proper IIR filter designing method that (1) can provide relatively more complete optimal solutions with equal consideration of magnitude response, linear phase response and the order of structure; (2) can simultaneously optimize the structure and coefficients of digital IIR filter to obtain relatively better linear phase response and lower order, besides the good magnitude response. To achieve these targets, the digital IIR filter design problem is treated as a multi-objective optimization problem in this paper. A new local search operator enhanced multi-objective evolutionary algorithm (LS-MOEA) is specifically proposed for such kind of multi-objective optimization problems. To evaluate the effectiveness and efficiency of LS-MOEA, we experimentally compare it with classical methods and previously effective EAs for digital IIR filter design on four typical IIR filter design cases. Experimental results show that the proposed method can effectively improve the linear phase response of the designed filter, and can obtain filter of lower order. Besides, it achieves these by relatively much lower computational cost than compared EAs.

Time-domain split-step method with variable step-sizes in vectorial pulse propagation by using digital filters

Finite impulse response (FIR) and infinite impulse response (IIR) digital filters are proposed to allow for time-domain simulation of optical pulse propagation by using the operator-splitting technique. These filters simulate polarization mode dispersion and chromatic dispersion effects with acceptable accuracy in time-domain. An analytical relation between the coefficients of these filters and the simulation step-size is established to accommodate the possibility of carrying out the time-domain split-step method with variable split-step length at virtually no computational burden. The superiority of the proposed method over the conventional frequency-domain technique is particularly demonstrated in wavelength-division multiplexing (WDM) applications.

Minimax Design of IIR Digital Filters Using SDP Relaxation Technique

This paper presents a new algorithm using semidefinite programming (SDP) relaxation to design infinite impulse response digital filters in the minimax sense. Unlike traditional design algorithms that try to directly minimize the error limit, the proposed algorithm employs a bisection searching procedure to locate the minimum error limit of the approximation error. Given a fixed error limit at each iteration, the SDP relaxation technique is adopted to formulate the design problem in a convex form. In practice, the true minimax design cannot be always obtained. Thus, a regularized feasibility problem is adopted in the bisection searching procedure. The stability of the designed filters can also be guaranteed by adjusting the regularization coefficient. Unlike other sequential design methods, the proposed algorithm tries to find a feasible solution at each iteration of the sequential design procedure within a feasible set defined by the relaxed constraints. This feasible set is not restricted within the neighborhood of a given point obtained from the previous iteration. Thus, the proposed method can avoid being trapped in the locally minimum point. Four examples are presented in this paper to demonstrate the effectiveness of the proposed method.

A New Mutated Quantum-Behaved Particle Swarm Optimizer for Digital IIR Filter Design

Adaptive infinite impulse response (IIR) filters have shown their worth in a wide range of practical applications. Because the error surface of IIR filters is multimodal in most cases, global optimization techniques are required for avoiding local minima. In this paper, we employ a global optimization algorithm, Quantum-behaved particle swarm optimization (QPSO) that was proposed by us previously, and its mutated version in the design of digital IIR filter. The mechanism in QPSO is based on the quantum behaviour of particles in a potential well and particle swarm optimization (PSO) algorithm. QPSO is characterized by fast convergence, good search ability, and easy implementation. The mutated QPSO (MuQPSO) is proposed in this paper by using a random vector in QPSO to increase the randomness and to enhance the global search ability. Experimental results on three examples show that QPSO and MuQPSO are superior to genetic algorithm (GA), differential evolution (DE) algorithm, and PSO algorithm in quality, convergence speed, and robustness.

DSP-PML algorithm for open region DNG meta-material FDTD simulations

The digital signal processing (DSP) algorithms developed for digital filters and the perfectly matched layer (PML) formulations are incorporated with the finite difference time domain (FDTD) method to model open region double-negative (DNG) meta-material electromagnetic problems. In the proposed approach, the dielectric parameters of each FDTD unit cell are interpreted as an infinite impulse response digital filter which can be implemented efficiently using the transpose direct form II. A numerical example carried out in a two-dimensional domain is included to show the validity of the proposed formulation.

Discrete finite-difference time domain impulse response filters for transparent field source implementations

Closed form discrete transfer functions are derived for finite-difference time domain (FDTD) grids in two- and three-dimensional (3D) space. The transfer functions can be used directly to synthesise the grid impulse response as part of modelling accurate and transparent embedded field sources in FDTD simulations. This approach eliminates the need for measuring grid impulse responses by end users from large and time consuming homogeneous unbounded simulations. The transfer functions were determined through designing fifth order infinite impulse response (IIR) digital filters using a combination of the Prony method and non-linear regression. It was found that the impulse response of equally spaced FDTD grids is independent of absolute values of temporal and spatial steps and rather depends only on the relative ratio of the used time step to the maximum allowed by the stability criterion. Sets of IIR filters are presented and validated for two-dimensional and 3D FDTD grids employing the standard as well as high-order FDTD update equations.