Design Of Fractional Order Differentiator Research Articles

Optimal designs of analogue and digital fractional order filters for signal processing applications

Our initial research work was focussed on employing metaheuristic optimization techniques to design optimal digital signal processing (DSP) systems such as the full band, conventional infinite impulse response differentiators and integrators meeting the accurate magnitude responses with a smaller average group delay. Since, integer order systems are a tight subset of the fractional order (FO) systems the research has been extended towards the optimal design of FO differentiators and integrators in the discrete domain with improved frequency response performances. Specific emphasis was laid on the feasibility of the designed FO differentiators in controlling a double-integrator plant. Analogue Butterworth filter with fractional stepping in the transition band has also been realized using an optimal integer-order rational transfer function. In future, we intend to design and implement generalized fractional-order filters on FPGA/DSP kit and FPAAs.

An efficient design of fractional order differentiator using hybrid Shuffled frog leaping algorithm for handling noisy electrocardiograms

ABSTRACT The Fractional Order Differentiator (FOD) along with the various integrator topologies have been introduced here in this work. There are several benefits offered which are the resistor-less realizations, the electronic adjustments of their respective traits, and capacity to operate the voltage of power supply. All these were achieved by the employment of Sinh- Domain filtering. Important information is provided by the Electrocardiogram (ECG) regarding the condition of the heart and for this work, there is an algorithm which was proposed known as the Shuffled Frog Leaping Algorithm along with the TABU Search (SFLA-TS). This optimization problem has been formulated in a way in which the approach proposed as opposed to the other techniques do not need an operator of the discretization for obtaining their digital models. The response and its frequency along with its design stability and convergence speed of a hybrid SFLA-TS were investigated thoroughly. This FOD was employed to perform the necessary signal conditioning of the ECG in this SFLA-TS algorithm. The models proposed had achieved a high level of improvement over the other designs that were state of the art with regard to their magnitude response performance index.

Design of minimum multiplier fractional order differentiator based on 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.

Design of fractional order differentiator using type-III and type-IV discrete cosine transform

In this paper, an interpolation method based on discrete cosine transform (DCT) is employed for digital finite impulse response-fractional order differentiator (FIR-FOD) design. Here, a fractional order digital differentiator is modeled as finite impulse response (FIR) system to get an optimized frequency response that approximates the ideal response of a fractional order differentiator. Next, DCT-III and DCT-IV are utilized to determine the filter coefficients of FIR filter that compute the Fractional derivative of a given signal. To improve the frequency response of the proposed FIR-FOD, the filter coefficients are further modified using windows. Several design examples are presented to demonstrate the superiority of the proposed method. The simulation results have also been compared with the existing FIR-FOD design methods such as DFT interpolation, radial basis function (RBF) interpolation, DCT-II interpolation and DST interpolation methods. The result reveals that the proposed FIR-FOD design technique using DCT-III and DCT-IV outperforms DFT interpolation, RBF interpolation, DCT-II interpolation and DST interpolation methods in terms of magnitude error.

Wideband Differentiator and Integrator With Ideal Phase Response

In this paper, we consider the design of a digital differentiator and integrator using the natural logarithm series. The proposed class of differentiators and integrators matches the ideal phase response and the magnitude response as closely as possible at low frequencies for orders lower than those reported in the literature. Furthermore, the bandwidth of the digital differentiator and integrator is extended to cover the entire Nyquist range using a simple multirate technique. In principle, the approach yields the results that are similar to those obtained by the design of fractional order differentiators and integrators.

Design of digital Riesz fractional order differentiator

In this paper, the design problems of the digital Riesz fractional order differentiator (FOD) are presented. First, the continuous-time Riesz fractional order derivative is reviewed briefly. Then, the fact that the frequency response of Riesz FOD is only the scaling even part of frequency response of the conventional FOD is shown. Based on this fact, the conventional FOD are applied to design fixed Riesz FOD including fractional differencing method, Tustin׳s method and discrete cosine transform method. Next, the fractional sample delay is used to improve the designed Riesz FOD. And, the discussion on the variable Riesz FOD design and implementation issues are made. Finally, numerical and application examples are demonstrated to show the effectiveness of the proposed digital Riesz fractional order differentiators.