Analog Implementation of Fractional-Order Elements and Their Applications

With advancements in the theory of fractional calculus and also with widespread engineering application of fractional-order systems, analog implementation of fractional-order integrators and differentiators have received considerable attention. This is due to the fact that this powerful mathematical tool allows us to describe and model a real-world phenomenon more accurately than via classical “integer” methods. Moreover, their additional degree of freedom allows researchers to design accurate and more robust systems that would be impractical or impossible to implement with conventional capacitors. Throughout this thesis, a wide range of problems associated with analog circuit design of fractional-order systems are covered: passive component optimization of resistive-capacitive and resistive-inductive type fractional-order elements, realization of active fractional-order capacitors (FOCs), analog implementation of fractional-order integrators, robust fractional-order proportional-integral control design, investigation of different materials for FOC fabrication having ultra-wide frequency band, low phase error, possible low- and high-frequency realization of fractional-order oscillators in analog domain, mathematical and experimental study of solid-state FOCs in series-, parallel- and interconnected circuit networks. Consequently, the proposed approaches in this thesis are important considerations in beyond the future studies of fractional dynamic systems

Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature

Gravitational wave snapshots of generic extreme mass ratio inspirals

Using black hole perturbation theory, we calculate the gravitational waves produced by test particles moving on bound geodesic orbits about rotating black holes. The orbits we consider are generic - simultaneously eccentric and inclined. The waves can be described as having radial, polar, and azimuthal "voices", each of which can be made to dominate by varying eccentricity and inclination. Although each voice is generally apparent in the waveform, the radial voice is prone to overpowering the others. We also compute the radiative fluxes of energy and axial angular momentum at infinity and through the event horizon. These fluxes, coupled to a prescription for the radiative evolution of the Carter constant, will be used in future work to adiabatically evolve through a sequence of generic orbits. This will enable the calculation of inspiral waveforms that, while lacking certain important features, will approximate those expected from astrophysical extreme mass ratio captures sufficiently well to aid development of measurement algorithms on a relatively short timescale.Comment: Minor changes in response to comments from readers, referees, and editors. Final version, as it will appear in Physical Review D. Raw data and a small program which will convert the data into waveforms lasting for arbitrary lengths of time can be found at http://gmunu.mit.edu/sdrasco/snapshot