Design Of Linear Phase FIR Filters Research Articles

Sparse Finite Impulse Response Low Pass Filter Design using Improved Firefly Algorithm

In this work, optimal sparse linear phase Finite impulse response filters are designed using swarm intelligence-based Firefly optimization algorithm. Filters are designed to meet the desired specification with fixed and variable sparsity. The objective function is formulated consisting of three parameters, i. e., maximum passband ripple, maximum stopband ripple and stopband attenuation. The effectiveness of the proposed method is evaluated in two stages. In first stage, the designed filters have been compared with non- sparse in terms of deviation in their specification. The Comparative analysis depicts that the proposed approach of sparse linear phase FIR filter design method performs better than the conventional methods without significantly deviating from the desired specification. The proposed designed filter is then implemented on xilinx ISE14.7(Vertex7) design environment and their performance is compared in terms of time delay, resource utilizaion and frequency of operation. In the second stage, designed sparse FIR filters are compared with earlier state of art sparse FIR filters design techniques.

Sparse FIR Filter Design via Partial 1-Norm Optimization

In this brief, we consider a sparse linear-phase FIR filter design problem. Recent methods assume that all the coefficients can be nullified and, thus, various 0 or 1-norm-based optimization techniques are applied on each of them. In contrast, the proposed algorithm is based on two important observations: 1) Given design specifications, some coefficients cannot be nullified, otherwise the specifications cannot be satisfied. 2) Impulse responses on neighboring positions of an FIR filter cannot vary dramatically so as to guarantee the smoothness of the corresponding magnitude responses over most of frequencies. In view of these facts, several rules are adopted in the proposed algorithm to select indices of potential zero coefficients to be used in 1-norm optimization. Simulation results have demonstrated the effectiveness of the proposed design algorithm.

FPGA based Synthesize of PSO Algorithm and its Area-Performance Analysis

Digital filters are the most significant part of signal processing that are used in enormous applications such as speech recognition, acoustic, adaptive equalization, and noise and interference reduction. It would be of great benefit to implement adaptive FIR filter because of self-optimization property, linearity and frequency stability. Designing FIR filter involves multi-modal optimization problems whereas conservative gradient optimization technique is not useful to design the filter. Hence, Particle Swarm Optimization (PSO) algorithm is more flexible and optimization technique based on population of particles in search space and alternative approach for linear phase FIR filter design. PSO improves the solution characteristic by giving a novel method for updating swarm’s position and velocity vector. Set of optimized filter coefficients will be generated by PSO algorithm. In this paper, PSO based FIR Low pass filter is efficiently designed in MATLAB and further Xilinx System Generator tool is used to efficiently design, synthesize and implement FIR filter in FPGA using SPARTEN 3E kit. For an example specifications, output of PSO algorithm is obtained that is set of optimized coefficients whose response is approximating to the ideal response. Hence, functional verification of the proposed algorithm has been performed and the error between obtained filter and ideal filter is minimized successfully. This work demonstrates the effectiveness of the PSO algorithms in parallel processing environment as compared to the Remez Exchange algorithm.

Performance of swarm based optimization techniques for designing digital FIR filter: A comparative study

In this paper, a linear phase FIR filter is designed through recently proposed nature inspired optimization algorithm known as Cuckoo search (CS). A comparative study of Cuckoo search (CS), particle swarm optimization (PSO) and artificial bee colony (ABC) nature inspired optimization methods in the field of linear phase FIR filter design is also presented. For this purpose, an improved L1 weighted error function is formulated in frequency domain, and minimized through CS, PSO and ABC respectively. The error or objective function has a controlling parameter wt which controls the amount of ripple in the desired band of frequency. The performance of FIR filter is examined through three key parameters; Maximum Pass Band Ripple (MPR), Maximum Stopband Ripple (MSR) and Stopband Attenuation (As). Comparative study and the simulation results reveal that the designed filter with CS gives better performance in terms of Maximum Stopband Ripple (MSR), and Stopband Attenuation (As) for low order filter design, and for higher order it also gives better performance in term of Maximum Passband Ripple (MPR). Superiority of the proposed technique is also shown through comparison with other recently proposed methods.

Greedy Algorithm for the Design of Linear-Phase FIR Filters with Sparse Coefficients

In this work, a greedy algorithm for the design of sparse linear-phase finite impulse response filters wherein the coefficients are successively fixed to zero individually is proposed. To meet the filter specifications, the coefficient for which the middle value of its feasible range is closest to zero is selected to be set to zero, whereas all the other unfixed coefficients are free to change. Design examples show that the proposed technique can design FIR filters with higher sparsity than that obtained by existing nonexhaustive algorithms for given specifications. To show the optimality of the algorithm, we design 100 filters, with results showing that the global optimal solution, i.e., the sparsest solution found by exhaustive search, can be achieved in most cases, but with much less computation time.

Closed-Form FIR Filter Design Based on Convolution Window Spectrum Interpolation

This paper proposes a closed-form linear phase FIR filter design concurrently possessing high efficiency and excellent transfer characteristic. This design is derived from conventional frequency sampling method through replacing its frequency-domain interpolation function with the Fourier spectrum of a convolution window. Meanwhile, this derivation inherently contains a mechanism of synthesizing all possible sub filters into one better FIR filter, which also plays the role of optimizing the transfer characteristic in nature. The above synthesizing process is equivalent to three simple steps, from which a closed-form formula of tap coefficients can be summarized. We further prove the proposed filter’s five properties, from which a modified closed-form design without any redundant parameters is also derived. Numerical results show that, the transfer performance of the proposed design is comparable to the mainstream designs (such as WLS method, Parks- McClellan method). Meanwhile, the proposed design can achieve an extremely high efficiency when designing high-order FIR filters.

Optimal linear phase FIR filter design using particle swarm optimization with constriction factor and inertia weight approach with wavelet mutation

In this paper, Particle Swarm Optimization with Constriction Factor and Inertia Weight Approach is hybridized with Wavelet Mutation (PSOCFIWA-WM) strategy for the optimal design of linear phase FIR filters. Real coded genetic algorithm (RGA), particl

Cat Swarm Optimization algorithm for optimal linear phase FIR filter design

In this paper a new meta-heuristic search method, called Cat Swarm Optimization (CSO) algorithm is applied to determine the best optimal impulse response coefficients of FIR low pass, high pass, band pass and band stop filters, trying to meet the respective ideal frequency response characteristics. CSO is generated by observing the behaviour of cats and composed of two sub-models. In CSO, one can decide how many cats are used in the iteration. Every cat has its′ own position composed of M dimensions, velocities for each dimension, a fitness value which represents the accommodation of the cat to the fitness function, and a flag to identify whether the cat is in seeking mode or tracing mode. The final solution would be the best position of one of the cats. CSO keeps the best solution until it reaches the end of the iteration. The results of the proposed CSO based approach have been compared to those of other well-known optimization methods such as Real Coded Genetic Algorithm (RGA), standard Particle Swarm Optimization (PSO) and Differential Evolution (DE). The CSO based results confirm the superiority of the proposed CSO for solving FIR filter design problems. The performances of the CSO based designed FIR filters have proven to be superior as compared to those obtained by RGA, conventional PSO and DE. The simulation results also demonstrate that the CSO is the best optimizer among other relevant techniques, not only in the convergence speed but also in the optimal performances of the designed filters.

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.

Improved Particle Swarm Optimization with wavelet mutation: Application to linear phase FIR filter design

In this paper, various swarm based algorithms like conventional Particle Swarm Optimization PSO, Improved Particle Swarm Optimization IPSO and another novel Improved Particle Swarm Optimization with Wavelet Mutation IPSOWM have been applied for the optimal design of linear phase FIR filters. Real coded genetic algorithm RGA has also been adopted for the sake of comparison. IPSO uses new definition for the velocity vector. Whereas in addition to the above-mentioned new definition added in IPSO, IPSOWM incorporates a new definition of swarm updating with the help of wavelet mutation based on wavelet theory. Wavelet mutation enhances the PSO to explore the solution space more effectively compared to the other optimization methods. IPSOWM is apparently free from getting trapped at local optima and premature convergence. Low pass LP, high pass HP, band pass BP and band stop BS FIR filters are designed with the proposed IPSOWM and other afore-mentioned algorithms individually for comparative optimization performance. A comparison of simulation results reveals the optimization efficacy of the IPSOWM over the other optimization techniques for the solution of the multimodal, non-differentiable, highly non-linear, and constrained FIR filter design problems.

Comparative Study of Target Function Definition in Linear Phase FIR Filter Design

Comparative Study of Target Function Definition in Linear Phase FIR Filter Design

Linear phase FIR filter design using particle swarm optimization and genetic algorithms

In this paper, a linear phase FIR filter is designed using particle swarm optimization (PSO) and genetic algorithms (GA). Two design cases are considered. In the first case, the filter length, passband and stopband frequencies, and the ratio of the passband and stopband ripples size are specified. In the second case, a feasible passband and stopband ripples size in addition to the other three filter specifications are specified. The later situation is not explicitly considered by the Parks–McClellan (PM) algorithm. Furthermore, the PSO and the GA are used to design optimum FIR filters for which the filter coefficients are represented using finite word length. In all cases, the design goal is successfully achieved using the PSO and compared with that obtained using the GA. For the problem at hand, it is found that the PSO outperforms the GA in some of the presented design cases.

Design of linear-phase FIR filters using support vector regression approach

The design of linear-phase FIR filters is formulated within the support vector regression (SVR) framework. A simple design example shows that, for a given filter order, the proposed SVR technique yields slightly lower passband and stopband ripples than a minimax approach.

Simple design and realisation of linear phase 2DFIR filters with diamond frequency support

A simple design method for linear-phase 2D FIR filters with diamond frequency support is proposed. The method is based on a 1D halfband linear-phase FIR filter design and offers some flexibility in the choice of specifications; the resulting realisation is efficient in terms of computational cost. A design example is also included.

Exchange algorithms that complement the Parks-McClellan algorithm for linear-phase FIR filter design

The authors describe an exchange algorithm for the frequency domain design of linear-phase FIR equiripple filters where the Chebyshev error in each band is specified. The algorithm is a hybrid of the algorithm of Hofstetter, Oppenheim and Siegel and the Parks-McClellan algorithm. The authors also describe a modification of the Parks-McClellan algorithm where either the passband or the stopband ripple size is specified and the other is minimized.

Weighted mean squared error criterion with fixed-level modification for linear-phase fIR filter design

This paper describes a new approach--a Fixed-Level Least Squares (FLLS) method for linear-phase FIR filter design. It is intended for rejection of the Gibbs phenomenon through the introduction of a set of equally spaced fixed levels in the transition band and subsequent redefinition of the approximated and weighted functions. Detailed mathematical solutions of the problem as well as many examples are given. The results in graphical form are shown as an output of the FLLS software model.

A new WLS Chebyshev approximation method for the design of FIR digital filters with arbitrary complex frequency response

In this paper, motivated by Chi-Kou's weighted least-squares (WLS) Chebyshev approximation method for the design of FIR filters with linear phase, we propose a new self-initiated iterative WLS Chebyshev approximation method for the design of FIR digital filters with arbitrary complex frequency response and real filter coefficients. The proposed method not only inherits all the advantages of Chi-Kou's method but also is computationally more efficient than Chi-Kou's method for the case of linear phase FIR filter design. On the other hand, contrast to Chit-Mason's time-domain least mean square (LMS) approximation methods, the proposed method is a frequency-domain WLS method based on similar philosophies. Several design examples are provided to demonstrate the good performance of the proposed method.

Accelerated design of linear or minimum phase FIR filters with a Chebyshev magnitude response

An accelerated version of the well known program of Parks and McClellan for the design of linear-phase FIR filters is combined with an improved cepstral procedure to find the corresponding minimum-phase solution. Among three possibilities of speeding up the program, two recently published ones are shown to be doubtful, although a third and new one proves useful. The minimum-phase part follows the method preferred from two methods proposed previously, with some improvements. Further improvements, implemented already or yet to be investigated, are given.

Design of linear-phase FIR filters using pseudo-Boolean methods

To implement a given digital filter with a finite-bit digital hardware, its design parameters have to be rounded off or truncated. The resulting filter characteristics considerably deviate from the desired ones. This effect can be reduced if the parameters are suitably chosen in the discrete-parameter-space. In this paper, this is achieved for linear-phase FIR filters by solving a system of linear pseudo-Boolean inequalities. The method is simple to use and is believed to offer a new insight into the problem. It takes much less computer time as compared to the existing search techniques, and yet has much better chances of converging to a global optimum.