Tarun Kumar Rawat

Optimal design of FIR fractional order differentiator using cuckoo search algorithm

A novel weighted least square (WLS) fitness function is adopted.The proposed method outperforms the GA in terms magnitude and phase error.The proposed method is superior to the interpolation based methods.Fast convergence rate is achieved. In this paper, a new meta-heuristic optimization algorithm, called cuckoo search algorithm (CSA) is applied to determine the optimal coefficients of the finite impulse response-fractional order differentiator (FIR-FOD) problem. CSA is based on lifestyle and unique parasitic behavior in egg laying and breeding of some cuckoo species along with Levy flight behavior of some birds and fruit flies. The CSA is capable of solving linear and nonlinear optimization problems. The proposed CSA method prevents the local minima problem encountered in conventional FIR-FOD design method. A novel weighted least square (WLS) fitness function is adopted to improve the response of the FOD to a great extent. The proposed CSA based method has alleviated from inherent drawbacks of premature convergence and stagnation unlike genetic algorithm (GA). To verify the effectiveness of the proposed FIR-FOD based on the cuckoo search algorithm, different set of initial population is tested by simulation. Simulation results affirm that the proposed fractional order differentiator design approach using CSA outperforms the genetic algorithm in terms design accuracy (magnitude and phase error), fast convergence rate and optimal solution. The simulation results confirmed that the proposed FOD using CSA outperforms the FOD designed using evolutionary algorithm like GA and conventional FOD design methods such as radial basis function (RBF) interpolation method and DCT interpolation method.

Optimal fractional delay-IIR filter design using cuckoo search algorithm

This paper applied a novel global meta-heuristic optimization algorithm, cuckoo search algorithm (CSA) to determine optimal coefficients of a fractional delay-infinite impulse response (FD-IIR) filter and trying to meet the ideal frequency response characteristics. Since fractional delay-IIR filter design is a multi-modal optimization problem, it cannot be computed efficiently using conventional gradient based optimization techniques. A weighted least square (WLS) based fitness function is used to improve the performance to a great extent. FD-IIR filters of different orders have been designed using the CSA. The simulation results of the proposed CSA based approach have been compared to those of well accepted evolutionary algorithms like Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The performance of the CSA based FD-IIR filter is superior to those obtained by GA and PSO. The simulation and statistical results affirm that the proposed approach using CSA outperforms GA and PSO, not only in the convergence rate but also in optimal performance of the designed FD-IIR filter (i.e., smaller magnitude error, smaller phase error, higher percentage improvement in magnitude and phase error, fast convergence rate). The absolute magnitude and phase error obtained for the designed 5th order FD-IIR filter are as low as 0.0037 and 0.0046, respectively. The percentage improvement in magnitude error for CSA based 5th order FD-IIR design with respect to GA and PSO are 80.93% and 74.83% respectively, and phase error are 76.04% and 71.25%, respectively.

Optimal Design of 2D FIR Filters with Quadrantally Symmetric Properties Using Fractional Derivative Constraints

In this article, an optimal design of two-dimensional finite impulse response (2D FIR) filter with quadrantally even symmetric impulse response using fractional derivative constraints (FDCs) is presented. Firstly, design problem of 2D FIR filter is formulated as an optimization problem. Then, FDCs are imposed over the integral absolute error for designing of the quadrantally even symmetric impulse response filter. The optimized FDCs are applied over the prescribed frequency points. Next, the optimized filter impulse response coefficients are computed using a hybrid optimization technique, called hybrid particle swarm optimization and gravitational search algorithm (HPSO-GSA). Further, FDC values are also optimized such that flat passband and stopband frequency response is achieved and the absolute

Design of a Variable Fractional Delay Filter Using Comprehensive Least Square Method Encompassing All Delay Values

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Adaptive infinite impulse response system identification using modified-interior search algorithm with Lèvy flight

L1-error is minimized. Finally, four design examples of 2D low-pass, high-pass, band-pass and band-stop filters are demonstrated to justify the design accuracy in terms of passband error, stopband error, maximum passband ripple, minimum stopband attenuation and execution time. Simulation results have been compared with the other optimization algorithms, such as real-coded genetic algorithm, particle swarm optimization and gravitational search algorithm. It is observed that HPSO-GSA gives improved results for 2D FIR-FDC filter design problem. In comparison with other existing techniques of 2D FIR filter design, the proposed method shows improved design accuracy and flexibility with varying values of FDCs.

Optimal design of Weighted Least Square based fractional delay FIR filter using Genetic Algorithm

ABSTRACT In this article, we propose the use of power function and least squares method for designing of a fractional order digital differentiator. The input signal is transformed into a power function by using Taylor series expansion, and its fractional derivative is computed using the Grunwald–Letnikov (G–L) definition. Next, the fractional order digital differentiator is modelled as a finite impulse response (FIR) system that yields fractional order derivative of the G–L type for a power function. The FIR system coefficients are obtained by using the least squares method. Two examples are used to demonstrate that the fractional derivative of the digital signals is computed by using the proposed technique. The results of the third and fourth examples reveal that the proposed technique gives superior performance in comparison with the existing techniques.

Window based design of fractional order FIR digital differentiator using type- III discrete cosine transform

The work presented in this paper is concerned with the designing of a variable fractional delay (VFD) FIR filter using least square method encompassing all delay values p. First, the frequency response, e-jωp, of the VFD filter is approximated using power series expansion of an exponential function and then, it is represented in terms of frequency response of the differentiator. Next, the proposed least square method adopts a novel cost function which includes all the fractional delay values. Finally, design and application examples are given to illustrate that the proposed least square method have better design accuracy and significantly reduction in magnitude error with the same degree of complexity than existing least square methods.

Minimum multiplier implementation of a comb filter using lattice wave digital filter

In this paper, a novel design of fractional order differentiator (FOD) based on lattice wave digital filter (LWDF) is proposed which requires minimum number of multiplier for its structural realization. Firstly, the FOD design problem is formulated as an optimization problem using the transfer function of lattice wave digital filter. Then, three optimization algorithms, namely, genetic algorithm (GA), particle swarm optimization (PSO) and cuckoo search algorithm (CSA) are applied to determine the optimal LWDF coefficients. The realization of FOD using LWD structure increases the design accuracy, as only N number of coefficients are to be optimized for Nth order FOD. Finally, two design examples of 3rd and 5th order lattice wave digital fractional order differentiator (LWDFOD) are demonstrated to justify the design accuracy. The performance analysis of the proposed design is carried out based on magnitude response, absolute magnitude error (dB), root mean square (RMS) magnitude error, arithmetic complexity, convergence profile and computation time. Simulation results are attained to show the comparison of the proposed LWDFOD with the published works and it is observed that an improvement of 29% is obtained in the proposed design. The proposed LWDFOD approximates the ideal FOD and surpasses the existing ones reasonably well in mid and high frequency range, thereby making the proposed LWDFOD a promising technique for the design of digital FODs.