Search

Digital differentiators enable the computation of the derivative of a continuous-time signal at discrete time instances, and they are used in many signal processing applications. This paper derives a unified filter order estimate for digital differentiators that are realized with linear-phase finite-length impulse response filters and designed in the minimax sense. The estimate is useful at the high-level system design when assessing the implementation complexity and it enables fewer designs when finding the minimal filter order required to satisfy a prescribed tolerable approximation error. The proposed unified estimate covers both wideband and lowpass differentiators of integer degrees up to ten. Furthermore, degree-individual filter order estimates are derived which improve and extend previous results. The performance of both the unified and degree-individual order estimates is evaluated through simulation examples and compared with previous estimates. [ABSTRACT FROM AUTHOR]

Inherent control delays and changeable grid operational conditions pose significant challenges to the stability of the Modular multilevel converter-based high voltage direct current (MMC-HVDC) system, inducing the risk of high-frequency resonances (HFR). This paper proposes a passivity enhancement based on the second-order digital differentiator (DD) and lead-lag compensator, ensuring reliable and robust HFR suppression performance even under the resonance frequency drift and fault earthing scenes. First, the passivity-based stability analysis is provided based on the system output impedance model, elucidating the HFR mechanisms and frequency drift problems. Second, the proposed passivity enhancement scheme's control structure and impedance reshaping principle are analyzed to verify resonance suppression ability. Third, the control parameters tuning process and direct realization of differentiator are detailed, reinforcing the stable margin and harmonic rejection ability. Finally, several case studies and simulation results are provided to validate the effectiveness of the proposed passivity-based HFR suppression scheme. • The proposed scheme integrates a second-order digital differentiator plus a lead-lag compensator. • Superior passivity and harmonic rejection ability are ensured, with frequency drift risk-solving ability. • Parameters tuning and differentiator discretization realization are elaborated. • Large phase lag and noise amplification problems are solved by impedance reshaping. [ABSTRACT FROM AUTHOR]

A fractional-order digital differentiator is employed for the calculation of a time-derivative of the applied signal. In the recent few decades, this particular concept of a fractional derivative has been gaining a lot of attention in various applications concerning engineering, technology and science that includes image processing along with automatic control. Once there has been an effective use for this continuous-time Fractional-Order Differentiator (FOD), the trend in its research is primarily toward using a discrete-time fractional differentiator. All these conventional techniques tend to make use of a unimodal function for approximating an ideal FOD. For these techniques, there is a minimization of the fitness function that is accomplished by the algorithms which are based on the gradient. The fractional-order circuits along with their systems include an emerging area that has a high level of potential in aspects such as the biomedical instrumentation, control or signal processing. A digital differentiator is a tool that is extremely helpful in the determination and estimation of time derivatives of any given signal. Irrespective of the actual type of filter chosen (the Finite Impulse Response (FIR) or the Infinite-Length Impulse Response (IIR)), it is critical to bring down the complexity of computation needed for the implementation of the filter for a certain bandwidth and error of approximation. A metaheuristic algorithm normally has some advantages in the solving of problems which are Non-Deterministic Polynomial (NP)-hard. The Shuffled Frog Leaping Algorithm (SFLA) has been a new heuristic algorithm proposed in this work for the determination of optimal coefficients of the problem of FIR-FOD. A design for fractional-order-based digital differentiator is not a very important topic in research and signal processing. [ABSTRACT FROM AUTHOR]

• If the frequency is contemplated in models, the estimates in signals are better. • The importance to increase and decrease the sampling rate in dynamic signals. • Update parameters in models achieve better performance in dynamic signals. This paper presents a method to obtain good synchronous and instantaneous estimates in position, velocity and acceleration; using a position measurement only. The proposed method shows better estimates in position, velocity and acceleration than other methods such as nonlinear tracking differentiator (TD), extended state estimation (ESO) and digital differentiator based on Taylor series (DDBTS). The proposed method allows for an increased accuracy of estimates by generating a feedback frequency obtained to the position measurement signals. The model and method proposed in this paper reduce the error when the measurement signal presents a change in frequency. The model update and adjusts simultaneously to changes in sample rates using a feedback frequency estimate. The proposed method was validated with the QNET DC Motor Control Trained (DCMCT). Since the method requires the measurement position only from an encoder, it eliminates the need for more sensors for velocity and acceleration, thus begin less costly. [ABSTRACT FROM AUTHOR]

In this paper, a novel approach to design the digital linear-phase finite impulse response (FIR) differentiator is introduced. First, the differentiator design problem is formulated using the L1-method. Then, the L1 optimality criterion is applied using the Bat algorithm (BA) and Particle swarm optimization (PSO) to further optimize the differentiator design. A novel fitness function is developed based on the L1-error norm which is unique and is liable to produce a flat response. These techniques are developed in order to minimize the non-differentiable fitness function. Finally, the simulation results have been presented for 5th-, 7th- and 11th-order FIR differentiator using the L1-method, PSO-L1 and BA-L1. The magnitude response of the designed differentiators is analyzed for different frequency bands on the basis of relative magnitude error computed with respect to the ideal response. All the reported techniques contribute toward superior results, when compared with the traditional gradient-based optimizations, such as the window method, minimax and least-squares approach. In addition, the L1-method yields better results for higher-order designs. Furthermore, the proposed designs are tested on two input signals for their efficient response. [ABSTRACT FROM AUTHOR]

Heart rate variability (HRV) analysis is considered as a preliminary diagnosis method to check the cardiac health of the human heart. The reliability of the HRV analysis system solely depends on the accuracy of the QRS complex detector. Hence, in this paper, an optimally designed digital differentiator (DD) for precise detection of QRS complex is proposed. The proposed DD is designed by using an efficient evolutionary optimization technique called gases Brownian motion optimization (GBMO) algorithm and is used in the preprocessing stage of the QRS detector. In GBMO algorithm, a balanced trade-off is maintained between both the exploration and the exploitation phases to find the global optimum solution. The electrocardiogram signal is preprocessed by using the proposed DD to generate the feature signals corresponding to the R-peaks only. The detection technique utilizes the principle of Hilbert transform and zeroes crossing detection. The proposed approach is verified against all the first channel records of MIT/BIH arrhythmia database by considering the standard QRS detection performance metrics and produces a sensitivity (Se) of 99.92%, positive predictivity (+P) of 99.92%, detection error rate (DER) of 0.1562%, QRS detection rate of 99.92%, accuracy (Acc) of 99.84%, and F score of 0.9992%. With respect to the standard performance metrics, the proposed QRS detector outperforms all the recently reported QRS detection techniques. [ABSTRACT FROM AUTHOR]

In this paper, a recently proposed metaheuristic optimization technique called hybrid flower pollination algorithm (HFPA) is applied to design wideband infinite impulse response digital differentiators (DDs) and digital integrators (DIs). In recent years, benchmark nature-inspired optimization algorithms such as particle swarm optimization (PSO), simulated annealing, and genetic algorithm have been employed for the design of wideband DDs and DIs. However, individually, these algorithms show major drawbacks such as premature convergence, thus leading to a sub-optimal solution. HFPA, however, is a hybrid approach which combines the efficient exploitation and exploration capabilities of two different metaheuristics, namely PSO and flower pollination algorithm (FPA), respectively. The HFPA-based designs have been compared with real-coded genetic algorithm, PSO, differential evolution, success-history-based adaptive differential evolution with linear population size reduction (L-SHADE), self-adaptive differential evolution (jDE), and FPA-based designs with respect to the solution quality, robustness, convergence, and optimization time. Simulation results demonstrate that among all the algorithms, the HFPA-based designs consistently achieve superior performances in the least number of function evaluations. Exhaustive experimentations are conducted to determine the best values of the control parameters of HFPA for the optimal design of DDs and DIs. The proposed designs also outperform the recently reported designs based on non-optimal, classical, and nature-inspired optimization approaches in terms of magnitude response. The lower orders of the proposed designs render them suitable for real-time applications. [ABSTRACT FROM AUTHOR]

This paper presents an efficient approach to design stable, wideband, and infinite impulse response digital integrators (DIs) and digital differentiators (DDs) of first, second, third, and fourth order using an evolutionary optimization algorithm called harmony search (HS). In recent years, although wideband DIs and DDs have been designed using metaheuristic optimization techniques such as simulated annealing, genetic algorithm, and particle swarm optimization (PSO), these algorithms lead to sub-optimal solutions because of stagnation and premature convergence. HS algorithm, however, promises an enhanced frequency response for DIs and DDs because of the better exploration and exploitation of the search space. Simulation results demonstrate the superiority of HS-based designs as compared with three well-known benchmark evolutionary optimization algorithms, namely real coded genetic algorithm (RGA), PSO, and differential evolution (DE) based designs by yielding the least values of different magnitude response error metrics. Parametric and non-parametric statistical hypothesis tests are also conducted to compare the consistency in the performance of HS-based DIs and DDs with those of the designs based on RGA, PSO, and DE. The proposed HS-based designs also outperform those of the designs based on both classical and evolutionary optimization approaches reported in recent literature in terms of the maximum absolute magnitude error metric. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

Recently, the Taylor–Fourier transform (TFT) was proposed to analyze the spectrum of signals with oscillating harmonics. The coefficients of this linear transformation were obtained through the calculation of the pseudoinverse matrix, which provides the classical solution to the normal equations of the least-squares (LS) approximation. This paper presents a filtering design technique that obtains the coefficients of the filters at each harmonic by imposing the maximally flat conditions to the polynomials defining their frequency responses. This condition can be used to solve the LS problem at each particular harmonic frequency, without the need of obtaining the whole set, as in the classical pseudoinverse solution. In addition, the filter passband central frequency can follow the fluctuations of the fundamental frequency. Besides, the method offers a reduction of the computational burden of the pseudoinverse solution. An implementation of the proposed estimator as an adaptive algorithm using its own instantaneous frequency estimate to relocate its bands is shown, and several tests are used to compare its performance with that of the ordinary TFT. [ABSTRACT FROM AUTHOR]

Novel designs of third-order recursive wideband digital integrator and differentiator are presented. The integrator is obtained by interpolating two digital integration techniques, the Schneider-Kaneshige-Groutage (SKG) rule and the Trapezoidal rule. The differentiator is obtained by inverting the transfer function of the designed integrator after necessary modifications. The proposed integrator and differentiator approximate their ideal counterparts with absolute magnitude errors less than 0.02 and 0.14, respectively, over the entire frequency spectrum. Their performance compares favorably with existing integrators and differentiators. [ABSTRACT FROM AUTHOR]

Abstract: Studies on analysis, design and applications of analog and digital differentiators and integrators of fractional order is the main objective of this paper. Time and frequency domain analysis, different ways of realization of fractance device is presented. Active and passive realization of fractance device of order using continued fraction expansion is carried out. Later, time and frequency domain analysis of fractance based circuits is considered. The variations of rise time, peak time, settling time, time constant, percent overshoot with respect to fractional order is presented. Digital differentiators and integrators of fractional order can be obtained by using direct and indirect discretization techniques. The s to z transforms used for this purpose are revisited. In this paper by using indirect discretization technique fractional order differentiators and integrators of order and are designed. These digital differentiators and integrators are implemented in real time using TMS320C6713 DSP processor and tested using National instruments education laboratory virtual instrumentation system (NIELVIS). The designed fractional order differentiators have been used for the detection of QRS sequences as well as the occurrence of Sino Atrial Rhythms in an ECG signal and also for the detection of edges in an image. The obtained results are in comparison with the conventional techniques. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the variable fractional-order (VFO) differintegrator is designed based on IIR-typed Farrow structure. The stability of the designed VFO IIR differintegrator is achieved by incorporating a constrained function into the objective error function. But the minimization of the original objective error function is a highly nonlinear problem, so an iterative quadratic method is proposed to overcome it. Comparing with the design based on FIR-typed Farrow structure, several designed examples, including a VFO differintegrator, a pure VFO differentiator and a pure VFO integrator, are presented to demonstrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: In the paper, a new method is proposed for the design of variable fractional-order (VFO) FIR differintegrators. Comparing with the existing methods, the elements of relevant matrices can be determined just by the given specification, which makes the method easier. An iterative technique is also incorporated to adjust the weighting function, such that the peak absolute error of variable frequency response can be reduced drastically. Several design examples, including a VFO differintegrator, two VFO differentiators and a VFO integrator, are presented to demonstrate the effectiveness and flexibility of the proposed method. [Copyright &y& Elsevier]

In this correspondence, we propose a fractional bilinear transform used in analog-to-digital (A/D) conversion. This transfer function is derived by means of fractional delay filters. According to this transformation, first-order differentiator can be easily designed. Next, some design examples are illustrated to show the linear frequency mapping property when doing A/D conversion. Finally, the designed tow-order digitat differentiator is compared with the existing differentiators. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the design of fractional order Simpson digital integrator is investigated. First, the conventional transfer function of second-order IIR Simpson integrator is factorized into product of first-order factors. Then, each factor of product is fractionalized by taking fractional power and using binomial series expansion. Next, truncating the length of series expansion, the transfer functions of FIR and IIR fractional order Simpson integrators are obtained. It is shown that the IIR fractional integrator is always stable. Finally, design examples are demonstrated to illustrate the performance of the proposed method and some further improvement using fractional delay is also discussed. [Copyright &y& Elsevier]

This paper proposes an approach based on a weighted L 1 -norm optimization criterion and employs it in conjunction with salp swarm algorithm (SSA) to design 2nd- to 4th-order wideband infinite impulse response (IIR) digital differentiators (DDs). Integration of the proposed fitness function and SSA allows both the magnitude and phase responses to be improved. An extensive simulation is carried out to explore the performance of the proposed approach. First, a comparative study with widely used methods, namely, real-coded genetic algorithm (RCGA) and particle swarm optimization (PSO), is performed to examine accuracy, robustness, consistency and efficiency. Afterwards, the magnitude and phase responses of the proposed digital differentiators are compared with those of the existing designs in the literature. New wideband IIR digital integrators (DIs) are derived by inverting transfer functions of their respective digital differentiators and then compared with the existing designs in the literature in terms of the magnitude and phase responses. Simulation and statistical results reveal that the superiority of the proposed approach is statistically significant and demonstrate that the proposed digital differentiators and integrators significantly outperform all state-of-the-art designs in terms of the magnitude response as measured by the absolute relative error (A R E) with almost linear phase responses in wideband frequency regions. [ABSTRACT FROM AUTHOR]