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In this paper, new designs of infinite impulse response digital integrators are presented. Transfer functions of the digital integrators are derived after utilizing the concept of multirate techniq...

Clinically, electrocardiogram (ECG) is a powerful tool for determining the health and functioning of the human heart. Faster detection and diagnosis of heart functioning would aid cardiologists to provide appropriate treatment to the patients (subjects). In this paper, the concept of fractional-order calculus is employed for noise cancellation and artifacts removal in ECG signal as fractional-order differentiator proved to provide more peculiar details about signals than an integer-order differentiator. In the proposed method, R-peaks are detected using Riesz fractional-order digital differentiator (RFODD) based on the differencing method. The differentiation operation enhances the high-frequency components of the signal. So, QRS complex which is a high-frequency component in ECG is accentuated and the R-peaks are detected using appropriate threshold technique. The proposed method is tested on Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) arrhythmia database, and the experimental results of the proposed method have achieved a sensitivity of 99.95%, positive predictivity of 99.949% and an error rate of 0.095%. ECG waveforms are analyzed on various fractional orders of RFODD, and their performance parameters, i.e., sensitivity, positive predictivity and error rate, are also calculated.

Optimal designs of finite impulse response (FIR) digital filters with prescribed magnitude and phase responses have found many applications in signal processing. To deal with the nonconvexity of the constraint region in the phase-error and magnitude-error constrained design, a new error constraint method based on a modified annulus sector (MAS) is proposed. With the new constraint method, the phase-error and magnitude-error constrained least squares, phase-error constrained minimax, and iterative reweighted phase-error constrained minimax designs of FIR filters are studied. Analyses and design examples demonstrate the higher accuracy of the MAS constraint and better filter performance by the constraint method than existing constraint methods. An application in the design of digital differentiators with flatness constraints is also provided.

Detection of QRS complex is an important step for the analysis of heart rate variability. It has been proved that the algorithms based on the use of differentiation are efficient and hence can be used for the real-time analysis. At the same time, fractional order digital differentiators are gaining their interest in many areas of research. In this paper, an attempt is made to detect QRS complex by making use of the proposed transfer functions of digital differentiators. The transfer functions in s domain are obtained by making use of the Continued Fraction Expansion Method. The Bilinear Transform and Al-Alaoui Transform are used for the purpose of discretization. These filters are used for the detection of QRS complexes. The result has been proven to be comparable to the conventional techniques.

This article proposes an IIR full-band digital differentiator (FBDD) design methodology by using a competitive metaheuristic optimisation technique called crow search algorithm (CSA). The CSA based FBDD design attains the most accurate characteristics to the ideal FBDD as compared to the standard optimisation methods such as differential evolution (DE) and real-coded genetic algorithm (RGA). Moreover, the CSA based FBDD design results sensibly surpass state-of-the-art reported FBDD design approaches.

In this paper, two designs of first-order digital differentiators are investigated. In the first design, hybrid filter approximation is used to approximate the fractional delay-based differentiator. The second design involves the direct optimization of the first-order FIR Lagrange filter approximation. Both first-order designs are compared with the existing first-order designs in terms of absolute magnitude error to demonstrate their effectiveness.

This paper proposes a Novel least mean square algorithm using First order Al-Alaoui differentiator.The performance of the proposed Algorithm is compared with existing algorithms by taking an example. The results prove the efficacy of the proposed Algorithm.

In this paper, a new design of digital differentiator of the second order using genetic algorithm is presented. By the use of genetic algorithm, transfer function differentiator of second order is derived. Then compare the results with the ideal second-order differentiator. Result is also compared with digital IIR differentiator second order using backward difference formula which is already exist.

In this paper, the design of digital differentiator (DD) using supervised learning method on Keras framework is presented. First, the design problem of DD is converted into a supervised learning problem such that the rich learning tools of the Keras can be applied to solve the problem directly. Then, the coefficients of transfer function of DD are determined by minimizing the loss functions such as mean squared errors or mean absolute errors. Next, the optimal solution of DD design problem is obtained by the various Keras optimizers such as stochastic gradient descent (SGD) or adaptive moments (Adam) algorithms. Finally, several numerical examples are shown to demonstrate the effectiveness of the proposed design method.

In this paper, an efficient design of FIR digital differentiator using the $L_1$-optimality criterion is proposed. We present a technique based on the modified Newton method to solve the design problem so that the optimal differentiator coefficients are obtained by minimizing the absolute error. The novel $L_1$-error function leads to a flat response at low-frequencies. Extensive simulations are carried out to validate the proposed design. The superiority of the proposed design is evident by comparing it with other conventional design techniques such as, windowing, minimax and the least-squares approach.

This paper proposes work on an efficient implementation of third order differentiator which is based on the lattice wave digital filter (LWDF). For third order Lattice wave digital differentiator (LWDD), data flow graph (DFG) is represented and using an unfolding algorithm it is transformed into an efficient design. The simulation result validates that the proposed design takes less execution time to give the required result. Further simulations also suggest that as an order of unfolding increases less execution time is required.

A simple and accurate analog to digital transform (ADT) is employed, to design a first order digital differentiator, which closely approximates the analog one. This transform has a fractional parameter m that our approach design based on. The proposed digital differentiator is obtained by selecting the best parameter m such that the relative error between the analog differentiator s and its equivalent digital one is minimum. Some design examples are illustrated to show the effectiveness of the ADT design technique. The beauty of this design is that it's only of first order and suitable for real-time applications.

This paper presents a novel metaheuristic algorithm called Interior Search Algorithm (ISA), which is applied for digital differentiator design problem. ISA is based on the principles of aesthetic techniques commonly used in interior design and decoration. ISA has a very quick convergence rate and only one control parameter. The approach presented here has alleviated from the problems of premature convergence, stagnation and revisiting of the same solution over and over again, which is common in other optimization techniques. Statistical and simulation results have been compared with already existing differentiator design methods such as segment rule, genetic algorithm (GA), simulated annealing (SA), pole zero method (PZ) and particle swarm optimization (PSO). The results affirm that the proposed method outperforms its counterparts in terms of absolute magnitude error and phase error.

This paper focuses on designing two digital second order infinite impulse response (IIR) fractional order circuits-a digital differentiator and a DC blocker using optimization techniques. The Firefly Algorithm was first employed for designing a second order infinite impulse response digital fractional order differentiator and the time complexity was measured. Next the efficacy of the Firefly algorithm and Cuckoo Search Algorithm were compared in designing a new second order infinite impulse response DC Blocker by comparing the closeness to ideal response of the DC blocker. The DC blocker designed by Firefly Algorithm outperforms the existing first order recursive DC blocker as well as the one designed by the Cuckoo Search Algorithm.

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.

The Second-Order Generalized Integrator (SOGI) was used as a building block for the SOGI-Quadrature-Signal Generator (SOGI-QSG) which has been widely used for gridsynchronization, frequency estimation, and harmonic extraction over the past decade. This paper further investigates its integration and differentiation characteristics, with four new integrators and differentiators proposed. Theoretical analysis shows that the proposed SOGI-QSG based integration and differentiation methods can effectively overcome the drawbacks of the pure integrator and differentiator. The proposed four new methods are the frequency-adaptive integrator, the frequencyadaptive differentiator, the frequency-fixed integrator and the frequency-fixed differentiator respectively. The effectiveness of the proposed methods and the correctness of the theoretical analysis are finally evaluated by experimental results.

In this paper, a simple approach is proposed to design recursive digital differentiators and integrators by applying the concept of time-constant analysis. The time-constant combined with the magnitude response describes the system behavior of a digital differentiator and an integrator. Further, new recursive digital differentiator and integrator designs of first-order systems are also obtained for more accurate or comparable magnitude responses as compared to the existing designs of higher-order systems over wideband. These designs are more suitable for control systems and signal processing applications.

In this letter, a neural network implementation for the least-squares design of digital differentiators with closed-form derivations for Hopfield-related parameters are proposed. Using this technique, the optimal filter coefficients are obtained by iteratively updating the dynamic nonlinear equations of the network. Simulation results indicate that the proposed technique has the advantage of effectiveness and is suitable for hardware implementation in real time.

This paper investigates digital differentiation performed using a Kalman filter. The model employed allows noise immunity by ensuring a high frequency roll off. The differentiation technique is applied to estimating coal mine instability by monitoring the hydraulic pressure from roof supports. The Kalman filter model which implements a digital differentiator is thoroughly analyzed in this paper.