Class of Recursive Wideband Digital Differentiators and Integrators

New designs of recursive digital differentiators are obtained by optimizing a general fourth-order recursive digital filter over different Nyquist bands. In addition, another design of recursive digital differentiator is also obtained by optimizing the specified pole-zero locations of existing recursive digital differentiator of second-order system. Further, new designs of recursive digital integrators are obtained by inverting the transfer functions of designed recursive digital differentiators with suitable modifications. Thereafter, the zero-reflection approach is discussed and then applied to improve the phase responses of designed recursive digital differentiators and integrators. The beauty of finally obtained recursive digital differentiators and integrators is that they have nearly linear phase responses over wideband and also provide the choice of suitable recursive digital differentiator and integrator according to the importance of accuracy, bandwidth and the system simplicity

Linear Phase Second Order Recursive Digital Integrators and Differentiators

In this paper, design of linear phase second order recursive digital integrators and differentiators is discussed. New second order integrators have been designed by using Genetic Algorithm (GA) optimization method. Thereafter, by modifying the transfer function of these integrators appropriately, new digital differentiators have been obtained. The proposed digital integrators and differentiators accurately approximate the ideal ones and have linear phase response over almost entire Nyquist frequency range. The proposed operators also outperform the existing operators in terms of both magnitude and phase response

Design of digital differentiators

A digital differentiator simply involves the derivation of an input signal. This work includes the presentation of first-degree and second-degree differentiators, which are designed as both infinite-impulse-response (IIR) filters and finite-impulse-response (FIR) filters. The proposed differentiators have low-pass magnitude response characteristics, thereby rejecting noise frequencies higher than the cut-off frequency. Both steady-state frequency-domain characteristics and Time-domain analyses are given for the proposed differentiators. It is shown that the proposed differentiators perform well when compared to previously proposed filters. When considering the time-domain characteristics of the differentiators, the processing of quantized signals proved especially enlightening, in terms of the filtering effects of the proposed differentiators. The coefficients of the proposed differentiators are obtained using an optimization algorithm, while the optimization objectives include magnitude and phase response. The low-pass characteristic of the proposed differentiators is achieved by minimizing the filter variance. The low-pass differentiators designed show the steep roll-off, as well as having highly accurate magnitude response in the pass-band. While having a history of over three hundred years, the design of fractional differentiator has become a ‘hot topic’ in recent decades. One challenging problem in this area is that there are many different definitions to describe the fractional model, such as the Riemann-Liouville and Caputo definitions. Through use of a feedback structure, based on the Riemann-Liouville definition. It is shown that the performance of the fractional differentiator can be improved in both the frequency-domain and time-domain. Two applications based on the proposed differentiators are described in the thesis. Specifically, the first of these involves the application of second degree differentiators in the estimation of the frequency components of a power system. The second example concerns for an image processing, edge detection application

Engineering Education and Research Using MATLAB

MATLAB is a software package used primarily in the field of engineering for signal processing, numerical data analysis, modeling, programming, simulation, and computer graphic visualization. In the last few years, it has become widely accepted as an efficient tool, and, therefore, its use has significantly increased in scientific communities and academic institutions. This book consists of 20 chapters presenting research works using MATLAB tools. Chapters include techniques for programming and developing Graphical User Interfaces (GUIs), dynamic systems, electric machines, signal and image processing, power electronics, mixed signal circuits, genetic programming, digital watermarking, control systems, time-series regression modeling, and artificial neural networks

Fractional Calculus and the Future of Science

Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton’s laws. Mandelbrot’s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton’s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton’s laws to describe the many guises of complexity, most of which lay beyond Newton’s experience, and many had even eluded Mandelbrot’s powerful intuition. The book’s authors look behind the mathematics and examine what must be true about a phenomenon’s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding

Design of Digital Integrator for Rogowski Coil Sensor

The goal of this thesis is to create a well performed digital Rogowski coil integrator on PC for later implementation on FPGA, and the final filter is applied with fixed point arithmetic. Integrator’s design and optimization based on the specification provided by the company. During the implementation, the constraints of the hardware should be taken into account, and the design method needs to be verified by simulations and practical experiments and tests. There are two design phases to implementing the filter. The first phase is software implementation, the integrator is realized by creating the MATLAB and C models. The other phase is hardware realization. By software application, the filter could be simu-lated with targeted test benches. After the software application is verified, hardware implementation could be carried out if it is necessary. In this thesis, RTL model is de-rived from the C model via translating it with VHDL. Afterward, the integrator is im-plemented on FPGA board for practical field tests. From the tests, the validity, practicability of the Rogowski integrator have to be veri-fied from the perspective of both functionality and performance. The software imple-mentation of the integrator is capable of filtering different kinds of the input signals with reasonable and acceptable outputs. Meanwhile, in the practical application, the integrator performed well when dealing with various earth fault cases. All, in brief, this Rogowski integrator has to satisfy the standard of the design specification

Applications of Mathematical Models in Engineering

The most influential research topic in the twenty-first century seems to be mathematics, as it generates innovation in a wide range of research fields. It supports all engineering fields, but also areas such as medicine, healthcare, business, etc. Therefore, the intention of this Special Issue is to deal with mathematical works related to engineering and multidisciplinary problems. Modern developments in theoretical and applied science have widely depended our knowledge of the derivatives and integrals of the fractional order appearing in engineering practices. Therefore, one goal of this Special Issue is to focus on recent achievements and future challenges in the theory and applications of fractional calculus in engineering sciences. The special issue included some original research articles that address significant issues and contribute towards the development of new concepts, methodologies, applications, trends and knowledge in mathematics. Potential topics include, but are not limited to, the following: Fractional mathematical models; Computational methods for the fractional PDEs in engineering; New mathematical approaches, innovations and challenges in biotechnologies and biomedicine; Applied mathematics; Engineering research based on advanced mathematical tools