Design of optimal band-stop FIR filter using L1-norm based RCGA

AbstractIn this paper, an optimal design of linear phase digital finite impulse response (FIR) band stop (BS) filter using the L1-norm based real-coded genetic algorithm (L1-RCGA) is presented. Although RCGA has proved its ability to overcome the drawbacks associated with conventional gradient-based optimization methods of filter design, it is applied here with a novel fitness function based on the L1-norm. This leads to a global optimal solution along with the improvement in filter design with same specifications. The designed filter pursues a better response in terms of flat passband, high stopband attenuation and fast convergence. The simulation results justify that the proposed FIR BS filter using L1-RCGA outperforms the existing optimization techniques, the L1-method and particle swarm optimization (PSO) and the conventional methods such as least-squares (LS) approach, Kaiser window method and the Parks McClellan (PM) algorithm. A detailed analysis is performed to evaluate the performance of the designed filters

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

NATURAL ALGORITHMS IN DIGITAL FILTER DESIGN

Digital filters are an important part of Digital Signal Processing (DSP), which plays vital roles within the modern world, but their design is a complex task requiring a great deal of specialised knowledge. An analysis of this design process is presented, which identifies opportunities for the application of optimisation. The Genetic Algorithm (GA) and Simulated Annealing are problem-independent and increasingly popular optimisation techniques. They do not require detailed prior knowledge of the nature of a problem, and are unaffected by a discontinuous search space, unlike traditional methods such as calculus and hill-climbing. Potential applications of these techniques to the filter design process are discussed, and presented with practical results. Investigations into the design of Frequency Sampling (FS) Finite Impulse Response (FIR) filters using a hybrid GA/hill-climber proved especially successful, improving on published results. An analysis of the search space for FS filters provided useful information on the performance of the optimisation technique. The ability of the GA to trade off a filter's performance with respect to several design criteria simultaneously, without intervention by the designer, is also investigated. Methods of simplifying the design process by using this technique are presented, together with an analysis of the difficulty of the non-linear FIR filter design problem from a GA perspective. This gave an insight into the fundamental nature of the optimisation problem, and also suggested future improvements. The results gained from these investigations allowed the framework for a potential 'intelligent' filter design system to be proposed, in which embedded expert knowledge, Artificial Intelligence techniques and traditional design methods work together. This could deliver a single tool capable of designing a wide range of filters with minimal human intervention, and of proposing solutions to incomplete problems. It could also provide the basis for the development of tools for other areas of DSP system design

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

MIMO Radar Waveform Optimization With Prior Information of the Extended Target and Clutter

The concept of multiple-input multiple-output (MIMO) radar allows each transmitting antenna element to transmit an arbitrary waveform. This provides extra degrees of freedom compared to the traditional transmit beamforming approach. It has been shown in the recent literature that MIMO radar systems have many advantages. In this paper, we consider the joint optimization of waveforms and receiving filters in the MIMO radar for the case of extended target in clutter. A novel iterative algorithm is proposed to optimize the waveforms and receiving filters such that the detection performance can be maximized. The corresponding iterative algorithms are also developed for the case where only the statistics or the uncertainty set of the target impulse response is available. These algorithms guarantee that the SINR performance improves in each iteration step. Numerical results show that the proposed methods have better SINR performance than existing design methods

Digital Filter Design Using Multiobjective Cuckoo Search Algorithm

Digital filters can be divided into finite impulse response (FIR) digital filters and infinite impulse response (IIR) digital filters. Evolutionary algorithms are effective techniques in digital filter designs. One such evolutionary algorithm is Cuckoo Search Algorithm (CSA). The CSA is a heuristic algorithm which emulates a special parasitic hatching habit of some species of cuckoos and have been proved to be an effective method with various applications. This thesis compares CSA with Park-McClellan algorithm on linear-phase FIR Type-1 lowpass, highpass, bandpass and bandstop digital filter design. Furthermore, a multiobjective Cuckoo Search Algorithm (MOCSA) is applied on general FIR digital design with a comparison to Non-dominated Sorting Genetic Algorithm III (NSGA-III). Finally, a constrained multiobjective Cuckoo Search Algorithm is presented and used for IIR digital filter design. The design results of the constrained MOCSA approach compares favorably with other state-of-the-art optimization methods. CSA utilizes Levy flight with wide-range step length for the global walk to assure reaching the global optimum and the approach of local walk to orientate the direction toward the local minima. Furthermore, MOCSA incorporates a method of Euclidean distance combing objective-based equilibrating operations and the searching for the optimal solution into one step and simplifies the procedure of comparison

Optimisation of multiplier-less FIR filter design techniques

This thesis is concerned with the design of multiplier-less (ML) finite impulse response (FIR) digital filters. The use of multiplier-less digital filters results in simplified filtering structures, better throughput rates and higher speed. These characteristics are very desirable in many DSP systems. This thesis concentrates on the design of digital filters with power-of-two coefficients that result in simplified filtering structures. Two distinct classesof ML FIR filter design algorithms are developed and compared with traditional techniques. The first class is based on the sensitivity of filter coefficients to rounding to power-of-two. Novel elements include extending of the algorithm for multiple-bands filters and introducing mean square error as the sensitivity criterion. This improves the performance of the algorithm and reduces the complexity of resulting filtering structures. The second class of filter design algorithms is based on evolutionary techniques, primarily genetic algorithms. Three different algorithms based on genetic algorithm kernel are developed. They include simple genetic algorithm, knowledge-based genetic algorithm and hybrid of genetic algorithm and simulated annealing. Inclusion of the additional knowledge has been found very useful when re-designing filters or refining previous designs. Hybrid techniques are useful when exploring large, N-dimensional searching spaces. Here, the genetic algorithm is used to explore searching space rapidly, followed by fine search using simulated annealing. This approach has been found beneficial for design of high-order filters. Finally, a formula for estimation of the filter length from its specification and complementing both classes of design algorithms, has been evolved using techniques of symbolic regression and genetic programming. Although the evolved formula is very complex and not easily understandable, statistical analysis has shown that it produces more accurate results than traditional Kaiser's formula. In summary, several novel algorithms for the design of multiplier-less digital filters have been developed. They outperform traditional techniques that are used for the design of ML FIR filters and hence contributed to the knowledge in the field of ML FIR filter design

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