Linear Phase FIR Low Pass Filter Design Based on Firefly Algorithm

In this paper, a linear phase Low Pass FIR filter is designed and proposed based on Firefly algorithm. We exploit the exploitation and exploration mechanism with a local search routine to improve the convergence and get higher speed computation. The optimum FIR filters are designed based on the Firefly method for which the finite word length is used to represent coefficients. Furthermore, Particle Swarm Optimization (PSO) and Differential Evolution algorithm (DE) will be used to show the solution. The results will be compared with PSO and DE methods. Firefly algorithm and Parks–McClellan (PM) algorithm are also compared in this paper thoroughly. The design goal is successfully achieved in all design examples using the Firefly algorithm. They are compared with that obtained by using the PSO and the DE algorithm. For the problem at hand, the simulation results show that the Firefly algorithm outperforms the PSO and DE methods in some of the presented design examples. It also performs well in a portion of the exhibited design examples particularly in speed and quality

Adaptive notch filtering for tracking multiple complex sinusoid signals

This thesis is related to the field of digital signal processing; where the aim of this research is to develop features of an infinite impulse response adaptive notch filter capable of tracking multiple complex sinusoid signals. Adaptive notch filters are commonly used in: Radar, Sonar, and Communication systems, and have the ability to track the frequencies of real or complex sinusoid signals; thus removing noise from an estimate, and enhancing the performance of a system. This research programme began by implementing four currently proposed adaptive notch structures. These structures were simulated and compared: for tracking between two and four signals; however, in their current form they are only capable of tracking real sinusoid signals. Next, one of these structures is developed further, to facilitate the ability to track complex sinusoid signals. This original structure gives superior performance over Regalia's comparable structure under certain conditions, which has been proven by simulations and results. Complex adaptive notch filter structures generally contain two parameters: the first tracks a target frequency, then the second controls the adaptive notch filter's bandwidth. This thesis develops the notch filter, so that the bandwidth parameter can be adapted via a method of steepest ascent; and also investigates tracking complex-valued chirp signals. Lastly, stochastic search methods are considered; and particle swarm optimisation has been applied to reinitialise an adaptive notch filter, when tracking two signals; thus more quickly locating an unknown frequency, after the frequency of the complex sinusoid signal jumps

Applications of swarm, evolutionary and quantum algorithms in system identification and digital filter design

The thesis focuses on the application of computational intelligence (CI) techniques for two problems - system identification and digital filter design. In system identification, different case studies have been carried out with equal or reduced number of orders as the original system and also in identifying a blackbox model. Lowpass, Highpass, Bandpass and Bandstop FIR and Lowpass IIR filters have been designed using three algorithms using two different fitness functions. Particle Swarm Optimization (PSO), Differential Evolution based PSO (DEPSO) and PSO with Quantum Infusion (PSO-QI) algorithms have been applied in this work --Abstract, page iii

Linear Phase FIR Digital Filter Design Using Differential Evolution Algorithms

Digital filter plays a vital part in digital signal processing field. It has been used in control systems, aerospace, telecommunications, medical applications, speech processing and so on. Digital filters can be divided into infinite impulse response filter (IIF) and finite impulse response filter (FIR). The advantage of FIR is that it can be linear phase using symmetric or anti-symmetry coefficients. Besides traditional methods like windowing function and frequency sampling, optimization methods can be used to design FIR filters. A common method for FIR filter design is to use the Parks-McClellan algorithm. Meanwhile, evolutional algorithm such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO) [2], and Differential Evolution (DE) have shown successes in solving multi-parameters optimization problems. This thesis reports a comparison work on the use of PSO, DE, and two modified DE algorithms from [18] and [19] for designing six types of linear phase FIR filters, consisting of type1 lowpass, highpass, bandpass, and bandstop filters, and type2 lowpass and bandpass filters. Although PSO has been applied in this field for some years, the results of some of the designs, especially for high-dimensional filters, are not good enough when comparing with those of the Parks-McClellan algorithm. DE algorithms use parallel search techniques to explore optimal solutions in a global range. What’s more, when facing higher dimensional filter design problems, through combining the knowledge acquired during the searching process, the DE algorithm shows obvious advantage in both frequency response and computational time

Digital Filter Design Using Improved Teaching-Learning-Based Optimization

Digital filters are an important part of digital signal processing systems. Digital filters are divided into finite impulse response (FIR) digital filters and infinite impulse response (IIR) digital filters according to the length of their impulse responses. An FIR digital filter is easier to implement than an IIR digital filter because of its linear phase and stability properties. In terms of the stability of an IIR digital filter, the poles generated in the denominator are subject to stability constraints. In addition, a digital filter can be categorized as one-dimensional or multi-dimensional digital filters according to the dimensions of the signal to be processed. However, for the design of IIR digital filters, traditional design methods have the disadvantages of easy to fall into a local optimum and slow convergence. The Teaching-Learning-Based optimization (TLBO) algorithm has been proven beneficial in a wide range of engineering applications. To this end, this dissertation focusses on using TLBO and its improved algorithms to design five types of digital filters, which include linear phase FIR digital filters, multiobjective general FIR digital filters, multiobjective IIR digital filters, two-dimensional (2-D) linear phase FIR digital filters, and 2-D nonlinear phase FIR digital filters. Among them, linear phase FIR digital filters, 2-D linear phase FIR digital filters, and 2-D nonlinear phase FIR digital filters use single-objective type of TLBO algorithms to optimize; multiobjective general FIR digital filters use multiobjective non-dominated TLBO (MOTLBO) algorithm to optimize; and multiobjective IIR digital filters use MOTLBO with Euclidean distance to optimize. The design results of the five types of filter designs are compared to those obtained by other state-of-the-art design methods. In this dissertation, two major improvements are proposed to enhance the performance of the standard TLBO algorithm. The first improvement is to apply a gradient-based learning to replace the TLBO learner phase to reduce approximation error(s) and CPU time without sacrificing design accuracy for linear phase FIR digital filter design. The second improvement is to incorporate Manhattan distance to simplify the procedure of the multiobjective non-dominated TLBO (MOTLBO) algorithm for general FIR digital filter design. The design results obtained by the two improvements have demonstrated their efficiency and effectiveness

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

Particle Swarm Optimization with Quantum Infusion for the Design of Digital Filters

In this paper, particle swarm optimization with quantum infusion (PSO-QI) has been applied for the design of digital filters. In PSO-QI, Global best (gbest) particle (in PSO star topology) obtained from particle swarm optimization is enhanced by doing a tournament with an offspring produced by quantum behaved PSO, and selecting the winner as the new gbest. Filters are designed based on the best approximation to the ideal response by minimizing the maximum ripples in passband and stopband of the filter response. PSO-QI, as is shown in the paper, converges to a better fitness. This new algorithm is implemented in the design of finite impulse response (FIR) and infinite impulse response (IIR) filter

An Efficient Hybrid SIMBO-GA Approach to Design FIR Low Pass Filter

In this paper a narrative approach for designing FIR low pass filter is presented by practicing hybrid technique of Swine Influenza Model based Optimization (SIMBO) and Genetic Algorithm (GA). Premature convergence was the major difficulty faced by SIMBO algorithm individually in FIR filter design. To address this problem, a hybrid SIMBO-GA is proposed in this paper. GA is used to help SIMBO escape from local optima and prevent premature convergence. Results are presented and compared in term of magnitude response with Differential Evolution Particle Swarm Optimization (DEPSO), Genetic Lbest Particle Swarm Optimization with Dynamically Varying Neighbourhood (GLPSO DVN). A comparison of simulation results divulges that SIMBO-GA seems to be promising tool for FIR filter design. Keywords: FIR Filter, SIMBO-GA, DEPSO, LPSO, GLPSO DVN

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

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