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Signal processing with Fourier analysis, novel algorithms and applications
Title
Signal processing with Fourier analysis, novel algorithms and applications.
Creator
Syed, Alam, Foroosh, Hassan, Sun, Qiyu, Bagci, Ulas, Rahnavard, Nazanin, Atia, George, Katsevich, Alexander, University of Central Florida
Abstract / Description
Fourier analysis is the study of the way general functions may be represented or approximatedby sums of simpler trigonometric functions, also analogously known as sinusoidal modeling. Theoriginal idea of Fourier had a profound impact on mathematical analysis, physics, and engineeringbecause it diagonalizes time-invariant convolution operators. In the past signal processing was atopic that stayed almost exclusively in electrical engineering, where only the experts could cancelnoise, compress...
Show moreFourier analysis is the study of the way general functions may be represented or approximatedby sums of simpler trigonometric functions, also analogously known as sinusoidal modeling. Theoriginal idea of Fourier had a profound impact on mathematical analysis, physics, and engineeringbecause it diagonalizes time-invariant convolution operators. In the past signal processing was atopic that stayed almost exclusively in electrical engineering, where only the experts could cancelnoise, compress and reconstruct signals. Nowadays it is almost ubiquitous, as everyone now dealswith modern digital signals.Medical imaging, wireless communications and power systems of the future will experience moredata processing conditions and wider range of applications requirements than the systems of today.Such systems will require more powerful, efficient and flexible signal processing algorithms thatare well designed to handle such needs. No matter how advanced our hardware technology becomeswe will still need intelligent and efficient algorithms to address the growing demands in signalprocessing. In this thesis, we investigate novel techniques to solve a suite of four fundamentalproblems in signal processing that have a wide range of applications. The relevant equations, literatureof signal processing applications, analysis and final numerical algorithms/methods to solvethem using Fourier analysis are discussed for different applications in the electrical engineering /computer science. The first four chapters cover the following topics of central importance in thefield of signal processing: Fast Phasor Estimation using Adaptive Signal Processing (Chapter 2) Frequency Estimation from Nonuniform Samples (Chapter 3) 2D Polar and 3D Spherical Polar Nonuniform Discrete Fourier Transform (Chapter 4)iv Robust 3D registration using Spherical Polar Discrete Fourier Transform and Spherical Harmonics(Chapter 5)Even though each of these four methods discussed may seem completely disparate, the underlyingmotivation for more efficient processing by exploiting the Fourier domain signal structureremains the same. The main contribution of this thesis is the innovation in the analysis, synthesis, discretization of certain well-known problems like phasor estimation, frequency estimation, computations of a particular non-uniform Fourier transform and signal registration on the transformed domain. We conduct propositions and evaluations of certain applications relevant algorithms suchas, frequency estimation algorithm using non-uniform sampling, polar and spherical polar Fourier transform. The techniques proposed are also useful in the field of computer vision and medical imaging. From a practical perspective, the proposed algorithms are shown to improve the existing solutions in the respective fields where they are applied/evaluated. The formulation and final proposition is shown to have a variety of benefits. Future work with potentials in medical imaging, directional wavelets, volume rendering, video/3D object classifications, high dimensional registration are also discussed in the final chapter. Finally, in the spirit of reproducible research, we release the implementation of these algorithms to the public using Github.
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Date Issued
2017
Identifier
CFE0006803, ucf:51775
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0006803