Design of Second Order Recursive Digital Integrators with Matching Phase and Magnitude Response

Location of poles and zeroes greatly affect phase response and magnitude response of a system. Recently, pole-zero optimization emerged as an effective approach to approximately match magnitude response of a system with that of an ideal one. In this brief, a methodology for the design of linear phase integrators and ones with constant phase of -90 degree is proposed. The aim of this method is to simultaneously attain multiple objectives of magnitude and phase optimization. In this method, magnitude response error is minimized under the constraint that the maximum passband phase-response error is below a prescribed level. Examples are included to illustrate the proposed design technique

Digital Filter Design Using Improved Artificial Bee Colony Algorithms

Digital filters are often used in digital signal processing applications. The design objective of a digital filter is to find the optimal set of filter coefficients, which satisfies the desired specifications of magnitude and group delay responses. Evolutionary algorithms are population-based meta-heuristic algorithms inspired by the biological behaviors of species. Compared to gradient-based optimization algorithms such as steepest descent and Newton’s like methods, these bio-inspired algorithms have the advantages of not getting stuck at local optima and being independent of the starting point in the solution space. The limitations of evolutionary algorithms include the presence of control parameters, problem specific tuning procedure, premature convergence and slower convergence rate. The artificial bee colony (ABC) algorithm is a swarm-based search meta-heuristic algorithm inspired by the foraging behaviors of honey bee colonies, with the benefit of a relatively fewer control parameters. In its original form, the ABC algorithm has certain limitations such as low convergence rate, and insufficient balance between exploration and exploitation in the search equations. In this dissertation, an ABC-AMR algorithm is proposed by incorporating an adaptive modification rate (AMR) into the original ABC algorithm to increase convergence rate by adjusting the balance between exploration and exploitation in the search equations through an adaptive determination of the number of parameters to be updated in every iteration. A constrained ABC-AMR algorithm is also developed for solving constrained optimization problems.There are many real-world problems requiring simultaneous optimizations of more than one conflicting objectives. Multiobjective (MO) optimization produces a set of feasible solutions called the Pareto front instead of a single optimum solution. For multiobjective optimization, if a decision maker’s preferences can be incorporated during the optimization process, the search process can be confined to the region of interest instead of searching the entire region. In this dissertation, two algorithms are developed for such incorporation. The first one is a reference-point-based MOABC algorithm in which a decision maker’s preferences are included in the optimization process as the reference point. The second one is a physical-programming-based MOABC algorithm in which physical programming is used for setting the region of interest of a decision maker. In this dissertation, the four developed algorithms are applied to solve digital filter design problems. The ABC-AMR algorithm is used to design Types 3 and 4 linear phase FIR differentiators, and the results are compared to those obtained by the original ABC algorithm, three improved ABC algorithms, and the Parks-McClellan algorithm. The constrained ABC-AMR algorithm is applied to the design of sparse Type 1 linear phase FIR filters of filter orders 60, 70 and 80, and the results are compared to three state-of-the-art design methods. The reference-point-based multiobjective ABC algorithm is used to design of asymmetric lowpass, highpass, bandpass and bandstop FIR filters, and the results are compared to those obtained by the preference-based multiobjective differential evolution algorithm. The physical-programming-based multiobjective ABC algorithm is used to design IIR lowpass, highpass and bandpass filters, and the results are compared to three state-of-the-art design methods. Based on the obtained design results, the four design algorithms are shown to be competitive as compared to the state-of-the-art design methods

Novel Design of Recursive Differentiator Based on Lattice Wave Digital Filter

In this paper, a novel design of third and fifth order differentiator based on lattice wave digital filter (LWDF), established on optimizing L_1-error approximation function using cuckoo search algorithm (CSA) is proposed. We present a novel realization of minimum multiplier differentiator using LWD structure leading to requirement of optimizing only N coefficients for Nth order differentiator. The gamma coefficients of lattice wave digital differentiator (LWDD) are computed by minimizing the L_1-norm fitness function leading to a flat response. The superiority of the proposed LWDD is evident by comparing it with other differentiators mentioned in the literature. The magnitude response of the designed LWDD is found to be of high accuracy with flat response in a wide frequency range. The simulation and statistical results validates that the designed minimum multiplier LWDD circumvents the existing one in terms of minimum absolute magnitude error, mean relative error (dB) and efficient structural realization, thereby making the proposed LWDD a promising approach to digital differentiator design

Discrete-time implementation and experimental validation of a fractional order PD controller for vibration suppression in airplane wings

Vibrations in airplane wings have a negative impact on the quality and safety of a flight. For this reason, active vibration suppression techniques are of extreme importance. In this paper, a smart beam is used as a simulator for the airplane wings and a fractional order PD controller is designed for active vibration mitigation. To implement the ideal fractional order controller on the smart beam unit, its digital approximation is required. In this paper, a new continuous-to-discrete-time operator is used to obtain the discrete-time approximation of the ideal fractional order PD controller. The efficiency and flexibility, as well as some guidelines for using this new operator, are given. The numerical examples show that high accuracy of approximation is obtained and that the proposed method can be considered as a suitable solution for obtaining the digital approximation of fractional order controllers. The experimental results demonstrate that the designed controller can significantly improve the vibration suppression in smart beams

Symbolic Representation for Analog Realization of A Family of Fractional Order Controller Structures via Continued Fraction Expansion

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.This paper uses the Continued Fraction Expansion (CFE) method for analog realization of fractional order differ-integrator and few special classes of fractional order (FO) controllers viz. Fractional Order Proportional-Integral-Derivative (FOPID) controller, FO[PD] controller and FO lead-lag compensator. Contemporary researchers have given several formulations for rational approximation of fractional order elements. However, approximation of the controllers studied in this paper, due to having fractional power of a rational transfer function, is not available in analog domain; although its digital realization already exists. This motivates us for applying CFE based analog realization technique for complicated FO controller structures to get equivalent rational transfer functions in terms of the controller tuning parameters. The symbolic expressions for rationalized transfer function in terms of the controller tuning parameters are especially important as ready references, without the need of running CFE algorithm every time and also helps in the synthesis of analog circuits for such FO controllers

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide

Identification of Linear / Nonlinear Systems via the Coyote Optimization Algorithm (COA)

Classical techniques used in system identification, like the basic least mean square method (LMS) and its other forms; suffer from instability problems and convergence to a locally optimal solution instead of a global solution. These problems can be reduced by applying optimization techniques inspired by nature. This paper applies the Coyote optimization algorithm (COA) to identify linear or nonlinear systems. In the case of linear systems identification, the infinite impulse response (IIR) filter is used to constitute the plants. In this work, COA algorithm is applied to identify different plants, and its performance is investigated and compared to that based on particle swarm optimization algorithm (PSOA), which is considered as one of the simplest and most popular optimization algorithms. The performance is investigated for different cases including same order and reduced-order filter models. The acquired results illustrate the ability of the COA algorithm to obtain the lowest error between the proposed IIR filter and the actual system in most cases. Also, a statistical analysis is performed for the two algorithms. Also, the COA is used to optimize the identification process of nonlinear systems based on Hammerstein models. For this purpose, COA is used to determine the parameters of the Hammerstein models of two different examples, which were identified in the literature using other algorithms. For more investigation, the fulfillment of the COA is compared to that of some other competitive heuristic algorithms. Most of the results prove the effectiveness of COA in system identification problems

Analysis of Wideband Second-Order Microwave Integrators

This chapter presents the implementation of stable, accurate, and wideband second-order microwave integrators (SOMIs). These SOMI designs are obtained by the use of various cascading combinations of transmission line sections and shunt stubs. In order to obtain the optimal values of the characteristic impedances of these line elements, the particle swarm optimization (PSO), cuckoo search algorithm (CSA) and gravitational search algorithm (GSA) are used to approximate the magnitude response of the ideal second-order integrator (SOI). Based on magnitude response, absolute magnitude error, phase response, convergence rate, pole-zero plot, and improvement graph, the performance measure criteria for the proposed SOMIs are performed. The results of the simulation and statistical analysis reveal that GSA exceeds the PSO and CSA in order to approximate the ideal SOI in all state-of-the-art eligible for wide-band microwave integrator. The designed SOMI is compact and suitable for applications covering ultra-wideband (UWB). The designed SOMI structure is also simulated on Advanced Design Software (ADS) in the form of a microstrip line on a dielectric constant 2.2 RT/Duroid substrate with a height of 0.762 mm. In the 3–15 GHz frequency range, the simulated magnitude result agrees well with the ideal one