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 Title
 FRACTAL INTERPOLATION.
 Creator

Ramesh, Gayatri, Mohapatra, Ram, University of Central Florida
 Abstract / Description

This thesis is devoted to a study about Fractals and Fractal Polynomial Interpolation. Fractal Interpolation is a great topic with many interesting applications, some of which are used in everyday lives such as television, camera, and radio. The thesis is comprised of eight chapters. Chapter one contains a brief introduction and a historical account of fractals. Chapter two is about polynomial interpolation processes such as Newton's, Hermite, and Lagrange. Chapter three focuses on...
Show moreThis thesis is devoted to a study about Fractals and Fractal Polynomial Interpolation. Fractal Interpolation is a great topic with many interesting applications, some of which are used in everyday lives such as television, camera, and radio. The thesis is comprised of eight chapters. Chapter one contains a brief introduction and a historical account of fractals. Chapter two is about polynomial interpolation processes such as Newton's, Hermite, and Lagrange. Chapter three focuses on iterated function systems. In this chapter I report results contained in Barnsley's paper, Fractal Functions and Interpolation. I also mention results on iterated function system for fractal polynomial interpolation. Chapters four and five cover fractal polynomial interpolation and fractal interpolation of functions studied by Navascués. Chapter five and six are the generalization of Hermite and Lagrange functions using fractal interpolation. As a concluding chapter we look at the current applications of fractals in various walks of life such as physics and finance and its prospects for the future.
Show less  Date Issued
 2008
 Identifier
 CFE0002472, ucf:47698
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0002472
 Title
 DESIGN AND HARDWARE IMPLEMENTATION OF A NOVEL SCRAMBLING SECURITY ALGORITHM FOR ROBUST WIRELESS LOCAL AREA NETWORKS.
 Creator

Jagetia, Mohit, Kocak, Taskin, University of Central Florida
 Abstract / Description

The IEEE802.11 standard for wireless networks includes a Wired Equivalent Privacy (WEP) protocol, which is a popular wireless secure communication stream cipher protocol approach to network security used to protect linklayer communications from eavesdropping and other attacks. It allows user to communicate with the user; sharing the public key over a network. It provides authentication and encrypted communications over unsecured channels. However, WEP protocol has an inherent security flaw....
Show moreThe IEEE802.11 standard for wireless networks includes a Wired Equivalent Privacy (WEP) protocol, which is a popular wireless secure communication stream cipher protocol approach to network security used to protect linklayer communications from eavesdropping and other attacks. It allows user to communicate with the user; sharing the public key over a network. It provides authentication and encrypted communications over unsecured channels. However, WEP protocol has an inherent security flaw. It is vulnerable to the various attacks, various experiments has proved that WEP fails to achieve its security goals. This thesis entails designing, evaluating and prototyping a wireless security infrastructure that can be used with the WEP protocol optionally, thus reducing the security vulnerabilities. We have studied the flaws of WEP and the reasons for their occurrence, and we provide the design and implementation of a novel scheme in Matlab and VHDL to improve the security of WEP in all aspects by a degree of 1000. The architecture was designed with a consideration for least increment in hardware, thus achieving power and cost efficiency. It also provides flexibility for optional implementation with the available technology by being able to be bypassed by the technology, which allows for nonreplacement of existing hardware, common on both, the WEP and the proposed protocols, on the fly.
Show less  Date Issued
 2004
 Identifier
 CFE0000062, ucf:46079
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0000062
 Title
 Improved Interpolation in SPH in Cases of Less Smooth Flow.
 Creator

Brun, Oddny, Wiegand, Rudolf, Pensky, Marianna, University of Central Florida
 Abstract / Description

ABSTRACTWe introduced a method presented in Information Field Theory (IFT) [Abramovich et al.,2007] to improve interpolation in Smoothed Particle Hydrodynamics (SPH) in cases of less smoothflow. The method makes use of wavelet theory combined with Bsplines for interpolation. The ideais to identify any jumps a function may have and then reconstruct the smoother segments betweenthe jumps. The results of our work demonstrated superior capability when compared to a particularchallenging SPH...
Show moreABSTRACTWe introduced a method presented in Information Field Theory (IFT) [Abramovich et al.,2007] to improve interpolation in Smoothed Particle Hydrodynamics (SPH) in cases of less smoothflow. The method makes use of wavelet theory combined with Bsplines for interpolation. The ideais to identify any jumps a function may have and then reconstruct the smoother segments betweenthe jumps. The results of our work demonstrated superior capability when compared to a particularchallenging SPH application, to better conserve jumps and more accurately interpolate thesmoother segments of the function. The results of our work also demonstrated increased computationalefficiency with limited loss in accuracy as number of multiplications and execution timewere reduced. Similar benefits were observed for functions with spikes analyzed by the samemethod. Lesser, but similar effects were also demonstrated for real life data sets of less smoothnature.SPH is widely used in modeling and simulation of flow of matters. SPH presents advantagescompared to grid based methods both in terms of computational efficiency and accuracy, inparticular when dealing with less smooth flow. The results we achieved through our research is animprovement to the model in cases of less smooth flow, in particular flow with jumps and spikes.Up until now such improvements have been sought through modifications to the models' physicalequations and/or kernel functions and have only partially been able to address the issue.This research, as it introduced wavelet theory and IFT to a field of science that, to ourknowledge, not currently are utilizing these methods, did lay the groundwork for future researchiiiideas to benefit SPH. Among those ideas are further development of criteria for wavelet selection,use of smoothing splines for SPH interpolation and incorporation of Bayesian field theory.Improving the method's accuracy, stability and efficiency under more challenging conditionssuch as flow with jumps and spikes, will benefit applications in a wide area of science. Justin medicine alone, such improvements will further increase real time diagnostics, treatments andtraining opportunities because jumps and spikes are often the characteristics of significant physiologicaland anatomic conditions such as pulsatile blood flow, peristaltic intestine contractions andorgans' edges appearance in imaging.
Show less  Date Issued
 2016
 Identifier
 CFE0006446, ucf:51451
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006446
 Title
 Modified Pal Interpolation and Sampling Bilevel Signals with Finite Rate of Innovation.
 Creator

Ramesh, Gayatri, Mohapatra, Ram, Vajravelu, Kuppalapalle, Li, Xin, Sun, Qiyu, University of Central Florida
 Abstract / Description

Sampling and interpolation are two important topics in signal processing. Signal processing is a vast field of study that deals with analysis and operations of signals such as sounds, images, sensor data, telecommunications and so on. It also utilizes many mathematical theories such as approximation theory, analysis and wavelets. This dissertation is divided into two chapters: Modified P(&)#225;l Interpolation and Sampling Bilevel Signals with Finite Rate of Innovation. In the first chapter,...
Show moreSampling and interpolation are two important topics in signal processing. Signal processing is a vast field of study that deals with analysis and operations of signals such as sounds, images, sensor data, telecommunications and so on. It also utilizes many mathematical theories such as approximation theory, analysis and wavelets. This dissertation is divided into two chapters: Modified P(&)#225;l Interpolation and Sampling Bilevel Signals with Finite Rate of Innovation. In the first chapter, we introduce a new interpolation process, the modified P\'al interpolation, based on papers by P(&)#225;l, J(&)#243;o and Szab(&)#243;, and we establish the existence and uniqueness of interpolation polynomials of modified P(&)#225;l type.The paradigm to recover signals with finite rate of innovation from their samples is a fairly recent field of study. In the second chapter, we show that causal bilevel signals with finite rate of innovation can be stably recovered from their samples provided that the sampling period is at or above the maximal local rate of innovation, and that the sampling kernel is causal and positive on the first sampling period. Numerical simulations are presented to discuss the recovery of bilevel causal signals in the presence of noise.
Show less  Date Issued
 2013
 Identifier
 CFE0005113, ucf:50760
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005113
 Title
 In Quest of Bernstein Inequalities Rational Functions, AskeyWilson Operator, and Summation Identities for Entire Functions.
 Creator

Puwakgolle Gedara, Rajitha, Li, Xin, Mohapatra, Ram, Ismail, Mourad, Xu, Mengyu, University of Central Florida
 Abstract / Description

The title of the dissertation gives an indication of the material involved with the connecting thread throughout being the classical Bernstein inequality (and its variants), which provides an estimate to the size of the derivative of a given polynomial on a prescribed set in the complex plane, relative to the size of the polynomial itself on the same set. Chapters 1 and 2 lay the foundation for the dissertation. In Chapter 1, we introduce the notations and terminology that will be used...
Show moreThe title of the dissertation gives an indication of the material involved with the connecting thread throughout being the classical Bernstein inequality (and its variants), which provides an estimate to the size of the derivative of a given polynomial on a prescribed set in the complex plane, relative to the size of the polynomial itself on the same set. Chapters 1 and 2 lay the foundation for the dissertation. In Chapter 1, we introduce the notations and terminology that will be used throughout. Also a brief historical recount is given on the origin of the Bernstein inequality, which dated back to the days of the discovery of the Periodic table by the Russian Chemist Dmitri Mendeleev. In Chapter 2, we narrow down the contents stated in Chapter 1 to the problems we were interested in working during the course of this dissertation. Henceforth, we present a problem formulation mainly for those results for which solutions or partial solutions are provided in the subsequent chapters.Over the years Bernstein inequality has been generalized and extended in several directions. In Chapter \ref{Bernineq}, we establish rational analogues to some Bernsteintype inequalities for restricted zeros and prescribed poles. Our inequalities extend the results for polynomials, especially which are themselves improved versions of the classical Erd\"{o}sLax and Tur\'{a}n inequalities. In working towards proving our results, we establish some auxiliary results, which may be of interest on their own. Chapters \ref{AWonpolynomials} and \ref{AWonentire} focus on the research carried out with the AskeyWilson operator applied on polynomials and entire functions (of exponential type) respectively.In Chapter 4, we first establish a Riesztype interpolation formula on the interval $[1,1]$ for the AskeyWilson operator. In consequence, a sharp Bernstein inequality and a Markov inequality are obtained when differentiation is replaced by the AskeyWilson operator. Moreover, an inverse approximation theorem is proved using a Bernsteintype inequality in $L^2$space. We conclude this chapter with an overconvergence result which is applied to characterize all $q$differentiable functions of Brown and Ismail. Chapter \ref{AWonentire} is devoted to an intriguing application of the AskeyWilson operator. By applying it on the Sampling Theorem on entire functions of exponential type, we obtain a series representation formula, which is what we called an extended Boas' formula. Its power in discovering interesting summation formulas, some known and some new will be demonstrated. As another application, we are able to obtain a couple of Bernsteintype inequalities.In the concluding chapter, we state some avenues where this research can progress.
Show less  Date Issued
 2018
 Identifier
 CFE0007237, ucf:52220
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0007237
 Title
 DESIGN OF POLYNOMIALBASED FILTERS FOR CONTINUOUSLY VARIABLE SAMPLE RATE CONVERSION WITH APPLICATIONS IN SYNTHETIC INSTRUMENTATION AND SOFTWARE DEFINED RADIO.
 Creator

Hunter, Matthew, Mikhael, Wasfy, University of Central Florida
 Abstract / Description

In this work, the design and application of PolynomialBased Filters (PBF) for continuously variable Sample Rate Conversion (SRC) is studied. The major contributions of this work are summarized as follows. First, an explicit formula for the Fourier Transform of both a symmetrical and nonsymmetrical PBF impulse response with variable basis function coefficients is derived. In the literature only one explicit formula is given, and that for a symmetrical even length filter with fixed basis...
Show moreIn this work, the design and application of PolynomialBased Filters (PBF) for continuously variable Sample Rate Conversion (SRC) is studied. The major contributions of this work are summarized as follows. First, an explicit formula for the Fourier Transform of both a symmetrical and nonsymmetrical PBF impulse response with variable basis function coefficients is derived. In the literature only one explicit formula is given, and that for a symmetrical even length filter with fixed basis function coefficients. The frequency domain optimization of PBFs via linear programming has been proposed in the literature, however, the algorithm was not detailed nor were explicit formulas derived. In this contribution, a minimax optimization procedure is derived for the frequency domain optimization of a PBF with timedomain constraints. Explicit formulas are given for direct input to a linear programming routine. Additionally, accompanying Matlab code implementing this optimization in terms of the derived formulas is given in the appendix. In the literature, it has been pointed out that the frequency response of the ContinuousTime (CT) filter decays as frequency goes to infinity. It has also been observed that when implemented in SRC, the CT filter is sampled resulting in CT frequency response aliasing. Thus, for example, the stopband sidelobes of the DiscreteTime (DT) implementation rise above the CT designed level. Building on these observations, it is shown how the rolloff rate of the frequency response of a PBF can be adjusted by adding continuous derivatives to the impulse response. This is of great advantage, especially when the PBF is used for decimation as the aliasing band attenuation can be made to increase with frequency. It is shown how this technique can be used to dramatically reduce the effect of alias build up in the passband. In addition, it is shown that as the number of continuous derivatives of the PBF increases the resulting DT implementation more closely matches the ContinuousTime (CT) design. When implemented for SRC, samples from a PBF impulse response are computed by evaluating the polynomials using a socalled fractional interval, µ. In the literature, the effect of quantizing µ on the frequency response of the PBF has been studied. Formulas have been derived to determine the number of bits required to keep frequency response distortion below prescribed bounds. Elsewhere, a formula has been given to compute the number of bits required to represent µ to obtain a given SRC accuracy for rational factor SRC. In this contribution, it is shown how these two apparently competing requirements are quite independent. In fact, it is shown that the wordlength required for SRC accuracy need only be kept in the µ generator which is a single accumulator. The output of the µ generator may then be truncated prior to polynomial evaluation. This results in significant computational savings, as polynomial evaluation can require several multiplications and additions. Under the heading of applications, a new Wideband Digital Downconverter (WDDC) for Synthetic Instruments (SI) is introduced. DDCs first tune to a signal's center frequency using a numerically controlled oscillator and mixer, and then zoomin to the bandwidth of interest using SRC. The SRC is required to produce continuously variable output sample rates from a fixed input sample rate over a large range. Current implementations accomplish this using a prefilter, an arbitrary factor resampler, and integer decimation filters. In this contribution, the SRC of the WDDC is simplified reducing the computational requirements to a factor of three or more. In addition to this, it is shown how this system can be used to develop a novel computationally efficient FFTbased spectrum analyzer with continuously variable frequency spans. Finally, after giving the theoretical foundation, a real Field Programmable Gate Array (FPGA) implementation of a novel Arbitrary Waveform Generator (AWG) is presented. The new approach uses a fixed DigitaltoAnalog Converter (DAC) sample clock in combination with an arbitrary factor interpolator. Waveforms created at any sample rate are interpolated to the fixed DAC sample rate in realtime. As a result, the additional lower performance analog hardware required in current approaches, namely, multiple reconstruction filters and/or additional sample clocks, is avoided. Measured results are given confirming the performance of the system predicted by the theoretical design and simulation.
Show less  Date Issued
 2008
 Identifier
 CFE0002292, ucf:47844
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0002292
 Title
 Influence of Topographic Elevation Error On Modeled Storm Surge.
 Creator

Bilskie, Matthew, Hagen, Scott, Wang, Dingbao, Chopra, Manoj, University of Central Florida
 Abstract / Description

The following presents a method for determining topographic elevation error for overland unstructured finite element meshes derived from bare earth LiDAR for use in a shallow water equations model. This thesis investigates the development of an optimal interpolation method to produce minimal error for a given element size. In hydrodynamic studies, it is vital to represent the floodplain as accurately as possible since terrain is a critical factor that influences water flow. An essential step...
Show moreThe following presents a method for determining topographic elevation error for overland unstructured finite element meshes derived from bare earth LiDAR for use in a shallow water equations model. This thesis investigates the development of an optimal interpolation method to produce minimal error for a given element size. In hydrodynamic studies, it is vital to represent the floodplain as accurately as possible since terrain is a critical factor that influences water flow. An essential step in the development of a coastal inundation model is processing and resampling dense bare earth LiDAR to a DEM and ultimately to the mesh nodes; however, it is crucial that the correct DEM grid size and interpolation method be employed for an accurate representation of the terrain. The following research serves two purposes: 1) to assess the resolution and interpolation scheme of bare earth LiDAR data points in terms of its ability to describe the bare earth topography and its subsequent performance during relevant tide and storm surge simulations.
Show less  Date Issued
 2012
 Identifier
 CFE0004520, ucf:49265
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004520