Matching Items (5)
Filtering by
- All Subjects: MATLAB
- Creators: Trichopoulos, Georgios
Description
Chebfun is a collection of algorithms and an open-source software system in object-oriented Matlab that extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. The success of this strategy is based on the mathematical fact that smooth functions can be represented very efficiently by polynomial interpolation at Chebyshev points or by trigonometric interpolation at equispaced points for periodic functions. More recently, the system has been extended to handle bivariate functions and vector fields. These two new classes of objects are called Chebfun2 and Chebfun2v, respectively. We will show that Chebfun2 and Chebfun2v, and can be used to accurately and efficiently perform various computations on parametric surfaces in two or three dimensions, including path trajectories and mean and Gaussian curvatures. More advanced surface computations such as mean curvature flows are also explored. This is also the first work to use the newly implemented trigonometric representation, namely Trigfun, for computations on surfaces.
ContributorsPage-Bottorff, Courtney Michelle (Author) / Platte, Rodrigo (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Using object-oriented programming in MATLAB, a collection of functions, named Fourfun, has been created to allow quick and accurate approximations of periodic functions with Fourier expansions. To increase efficiency and reduce the number of computations of the Fourier transform, Fourfun automatically determines the number of nodes necessary for representations that are accurate to close to machine precision. Common MATLAB functions have been overloaded to keep the syntax of the Fourfun class as consistent as possible with the general MATLAB syntax. We show that the system can be used to efficiently solve several differential equations. Comparisons with Chebfun, a similar system based on Chebyshev polynomial approximations, are provided.
ContributorsMcleod, Kristyn Noelle (Author) / Platte, Rodrigo (Thesis director) / Gelb, Anne (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor)
Created2014-05
Description
This work focuses on the analysis and design of large-scale millimeter-wave andterahertz (mmWave/THz) beamforming apertures (e.g., reconfigurable reflective surfaces–
RRSs). As such, the small wavelengths and ample bandwidths of these frequencies enable
the development of high-spatial-resolution imaging and high-throughput wireless
communication systems that leverage electrically large apertures to form high-gain
steerable beams.
For the rigorous evaluation of these systems’ performance in realistic application
scenarios, full-wave simulations are needed to capture all the exhibited electromagnetic
phenomena. However, the small wavelengths of mmWave/THz bands lead to enormous
meshes in conventional full-wave simulators. Thus, a novel numerical decomposition
technique is presented, which decomposes the full-wave models in smaller domains with
less meshed elements, enabling their computationally efficient analysis. Thereafter, this
method is leveraged to study a novel radar configuration that employs a rotating linear
antenna with beam steering capabilities to form 3D images. This imaging process requires
fewer elements to carry out high-spatial-resolution imaging compared to traditional 2D
phased arrays, constituting a perfect candidate in low-profile, low-cost applications.
Afterward, a high-yield nanofabrication technique for mmWave/THz graphene
switches is presented. The measured graphene sheet impedances are incorporated into
equivalent circuit models of coplanar switches to identify the optimum mmWave/THz
switch topology that would enable the development of large-scale RRSs.ii
Thereon, the process of integrating the optimized graphene switches into largescale mmWave/THz RRSs is detailed. The resulting RRSs enable dynamic beam steering
achieving 4-bits of phase quantization –for the first time in the known literature–
eliminating the parasitic lobes and increasing the aperture efficiency. Furthermore, the
devised multi-bit configurations use a single switch-per-bit topology retaining low system
complexity and RF losses. Finally, single-bit RRSs are modified to offer single-lobe
patterns by employing a surface randomization technique. This approach allows for the use
of low-complexity single-bit configurations to suppress the undesired quantization lobes
without residing to the use of sophisticated multi-bit topologies.
The presented concepts pave the road toward the implementation and proliferation
of large-scale reconfigurable beamforming apertures that can serve both as mmWave/THz
imagers and as relays or base stations in future wireless communication applications.
ContributorsTheofanopoulos, Panagiotis (Author) / Trichopoulos, Georgios (Thesis advisor) / Balanis, Constantine (Committee member) / Aberle, James (Committee member) / Bliss, Dan (Committee member) / Groppi, Christopher (Committee member) / Arizona State University (Publisher)
Created2021
Description
This Creative Project was carried out in coordination with the capstone project, Around the Corner Imaging with Terahertz Waves. This capstone project deals with a system designed to implement Around the Corner, or Non Line-of-Sight (NLoS) Imaging. This document discusses the creation of a GUI using MATLAB to control the Terahertz Imaging system. The GUI was developed in response to a need for synchronization, ease of operation, easy parameter modification, and data management. Along the way, many design decisions were made ranging from choosing a software platform to determining how variables should be passed. These decisions and considerations are discussed in this document. The resulting GUI has measured up to the design criteria and will be able to be used by anyone wishing to use the Terahertz Imaging System for further research in the field of Around the Corner or NLoS Imaging.
ContributorsWood, Jacob Cannon (Author) / Trichopoulos, Georgios (Thesis director) / Aberle, James (Committee member) / Electrical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
The purpose of this project is to analyze the MIT OpenCourseWare coffee can radar design and modify it to be better suited for drone based synthetic aperture radar (SAR) applications while maintaining the low-cost aspect of the original design. The MIT coffee can radar can function as a ranged radar, a Doppler radar, or as SAR. Through simulations and research, the suggestions for how to modify the radar resulted in swapping the coffee can monopole antennas for patch antenna arrays or helical ordinary end-fire antennas, adding an Arduino for automatic recording of output pulses, and switching from a breadboard construction to a PCB to shrink form factor and keep costs and construction time low.
ContributorsRivera, Danielle (Author) / Trichopoulos, Georgios (Thesis director) / Aberle, James (Committee member) / Department of Information Systems (Contributor) / Electrical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2020-12