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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...

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 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.

We treat the design problem of second-degree IIR digital differentiators. The design problem (cost function) is formulated in the quadratic form without any frequency sampling. Since the cost function is the quadratic form, the solution is unique and the optimization scheme does not require any recursive optimization. Hence, the procedure of the design for the second-degree differentiators is very easy. Also, the second-degree differentiators obtained by our method have a robust stability since the maximum pole radius can be prescribed. Finally, we show a design example in order to demonstrate the effectiveness of the proposed method.

In this paper the design of 2-dimensional finite impulse response (2-D FIR) digital differentiator (DD) with quadrantally odd symmetric impulse response is presented. The L 1 -method is developed to design the 2-D system and minimize the L 1 -error. The design problem of 2-D FIR-DD is formulated as an optimization problem in order to compute the system coefficients with quadrantally odd symmetric properties. Finally, the design examples of 2-D differentiator of different order is demonstrated and analyzed in terms of the L 1 -error and elapsed time. The proposed 2-D FIR L 1 -DD is also compared with the existing 2-D differentiators designed using metaheuristic techniques and is observed to yield least L 1 -error.

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 novel wideband recursive digital integrator and differentiator is presented. The integrator is obtained by interpolating three digital integration techniques and the new differentiator is obtained by modifying its transfer function appropriately. Both the integrator and the differentiator are of third order and highly accurate, thus suitable for real-time applications. Copyright © 2010 John Wiley & Sons, Ltd.

A modification to the weighted least-squares algorithm is proposed to minimize the relative error in the response of a digital differentiator (DD) and is applied to the design of fifth-order DD. Simulation results are given to demonstrate the performance of the method for both even and odd length DDs. The design procedure to satisfy prescribed specifications is also discussed.

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.

A new method is proposed for the experimental determination of the longitudinal and lateral hydrodynamic coefficients of a low-speed UUV. The technique presented is a development of the classical free-decay test. A body is excited with a mechanism of springs, and system identification techniques are carried out on measured data, with the intention of evaluating the added mass and linear damping of the body in decoupled longitudinal and lateral models. Simulated results are presented in order to estimate the potential accuracy of these new methods.

Simplified formulas of weighting coefficients of maximally linear FIR digital differentiators have been derived.

In this paper, two methods for designing digital full-band FIR differentiators are presented. First of them, named Immediate, represents the efficient and general method for brusque designing the first and higher degree digital full-band FIR differentiators of even and odd order, with simultaneous approximation of the prescribed magnitude and group delay responses, using originally modified eigenfilter method. The proposed method presents an approach for the FIR differentiator frequency response approximation directly in the complex, and not in the real domain. The second method, named Intermediary, represents the efficient approach for oblique designing only the second and higher degree digital full-band FIR differentiators of odd order. The comparison of the characteristics and results of these two presented methods is performed. In order to illustrate the presented methods effectiveness, the numerical design examples of the first second degree full-band digital differentiators are given, too.

We introduce the design scheme of frequency-selective digital differentiators which is the hybrid class between frequency-selective filter (band-pass filter) and differentiator. The response of the frequency-selective digital differentiators is more flexible than that of frequency-selective Alter or full-band differentiators. Hence, the frequency-selective digital differentiators are often more beneficiated than full-band differentiators in some applications. The features of the proposed method are as follows. First, the design problem can be formulated in the quadratic form without any frequency sampling. Second, thanks to the quadratic form, the solution is unique and the optimization scheme does not require any iterative optimization in order to get the solution. Accordingly, the procedure of the design of the frequency-selective differentiators is very simple. Also, the frequency-selective differentiators obtained by the proposed method have a robust stability since the maximum pole radius can be prescribed. To demonstrate the effectiveness of the proposed method, we show the numerical examples in the cases of low-pass differentiator and high-pass differentiator.

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.

Design of maximally flat Hilbert Transformers is proposed. Taylor configuration is suggested to realize a linear phase FIR digital filter. This approach is comparatively simpler than the other known ones. Four relations (two recursive and two explicit) for computation of weights required in the design are derived. The paper also brings out relation between digital Hilbert Transformers and digital differentiators as well as with digital notch filters. Applications of the suggested design are also given.

The electromagnetic suspension system is the most important subsystem in maglev. The feedback of air-gap change rate is very important for the stability of the system. Air-gap change rate can be achieved through four types, using analog differentiator with filters, analog low-noise differentiator, digital differentiator with filters and digital low-noise differentiator. In this paper, an electromagnetic suspension system is modeled and simulated by Maltab using the four methods mentioned above. Experiments are implemented using the latter three methods. According to the waveforms obtained from the simulations and experiments, the advantages and weaknesses of the different methods are pointed out. The results indicate that the digital low-noise differentiator is the most relatively economical and practical method in the electromagnetic suspension system.

This work presents new IIR digital differentiators of first and higher orders based on optimizing the Al-Alaoui integrator using Simulated Annealing, Genetic Algorithms, and Fletcher and Powell Optimization. The work notes the idea that inverting an optimized integrator does not necessarily lead to an optimized differentiator since the work starts with the differentiators as opposed to starting with the integrators which is not the norm in previous works. The proposed differentiators are compared with many available differentiators and are proven to be of considerable accuracy. These differentiators are afterwards inverted and transformed into digital integrators of same orders.

In the above titled paper (ibid., vol. 3, no. 3, pp. 322-329, Sep. 2013), equations (17a) and (17b) should have appeared as presented here.

A new efficient algorithm for calculating the weighting coefficients of maximally linear, FIR digital differentiators is presented. Simple closed-form explicit and recursive formulas are derived in a very straightforward manner. Moreover, a simple recursive equation is established, relating coefficients of two digital differentiators of adjacent ranks.

In this paper, a new approximation is proposed to design fractional order digital differentiator using fractional delay filters. New approximation improves the design accuracy of conventional fractional differencing for wideband compared to existing approximations. Proposed new approximation is applied to see relatively small error for wideband.

An efficient design of digital differentiators (DD), with a variable frequency range of operation at low and midband frequencies, has been proposed. Implemented as a Taylor structure, a DD designed for orderN can be made to function as a universal configuration giving optimal transfer functions for all possible ordersN, without changing the coefficients.

Digital differentiators (DDs) which are maximally linear at the spot frequency omega = pi /p, p in (positive integers) are proposed for operation over a narrow band of frequencies. The suggested DDs, besides giving zero phase error over the entire band of frequencies (- pi >

A Hopfield-type neural network is proposed for the design of nonrecursive digital differentiators and Hilbert transformers. Given the amplitude response, the all-analog network computes the filter coefficients in real time. The network is simulated and a few examples are included to show that this is an efficient way of solving the approximation problem and has a high potential for implementation in analog VLSI.

A new design of a recursive wideband digital differentiator is obtained by optimising the pole-zero locations of existing recursive wideband digital differentiators. Further, a new integrator design is also obtained by inverting the transfer function of the proposed digital differentiator design with suitable modifications. The beauty of these designs is that they are only of second-order recursive systems and have not more than 0.48% relative error in magnitude responses almost over the full Nyquist band, thus being suitable for real-time circuit applications.

New compact and simple formulas for the design of digital differentiators based on the least squares method are proposed. The new expressions allow a very fast and precise computation of the filter coefficients. Furthermore, using the proposed analytical solution, the need to solve the system of linear equations for the case of fullband differentiators is avoided.

Two methods for the design of nonrecursive digital differentiators based on standard optimization methods are described. The methods are used in conjunction with the prediction technique for the differentiator order described by A. Antoniou and C. Charalambous (Proc. IEE, vol.128, pt.E, no.5, p.190-6, Sept. 1981) to design several differentiators, assuming first a prescribed bandwidth and various prescribed maximum in-band errors and then a prescribed maximum in-band error and various prescribed bandwidths. The methods are also used to design a wideband differentiator. The designs obtained satisfy the prescribed specifications in all cases. The results show that the even-order digital differentiators require lower order for the same prescribed specifications and that the error function with weighting yields better results in terms of relative error, as expected. >

A simple way of calculating the weighting coefficients for the maximum flat digital FIR differentiator is presented. A relation with interpolating polynomials is also established.

Optimal, maximally accurate digital differentiators (DDS) are derived for the low-frequency range. Exact coefficients used in the proposed DDs can be readily computed from explicit formulas, whereas the optimal (minimas RE) DDs require and optimization program to derive the coefficients. The lower the frequency of differentiation, the better is the performance of the proposed differentiators, making them suitable for many typical applications. >

Recursive as well as explicit mathematical formulas have been derived for the weighting coefficients of maximally linear, FIR digital differentiators for low frequencies.