Browsing by Subject "Fourier analysis"
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Item A study of the effect of pitch interval during pitch identification on the electroencephalogram using Fast Fourier Transform(Texas Tech University, 1975-12) Wang, Cecilia ChuThe major concern in this study was to investigate brain wave alterations as evidenced on the electroencephalogram during a specific task of pitch discrimination. Another objective is to provide guidelines for future reference in the research of the brain in relation to music. The author sincerely hopes that the study will encourage both musicians and scientists in joint pursuits, especially in the area of neurophysiology.Item Combinatorial and probabilistic techniques in harmonic analysis(2012-05) Lewko, Mark J., 1983-; Vaaler, Jeffrey D.; Beckner, William; Pavlovic, Natasa; Rodriguez-Villegas, Fernando; Zuckerman, DavidWe prove several theorems in the intersection of harmonic analysis, combinatorics, probability and number theory. In the second section we use combinatorial methods to construct various sets with pathological combinatorial properties. In particular, we answer a question of P. Erdos and V. Sos regarding unions of Sidon sets. In the third section we use incidence bounds and bilinear methods to prove several new endpoint restriction estimates for the Paraboloid over finite fields. In the fourth and fifth sections we study a variational maximal operators associated to orthonormal systems. Here we use probabilistic techniques to construct well-behaved rearrangements and base changes. In the sixth section we apply our variational estimates to a problem in sieve theory. In the seventh section, motivated by applications to sieve theory, we disprove a maximal inequality related to multiplicative characters.Item Digital image processing and spatial frequency analysis of Texas roadway environment(Texas Tech University, 1999-12) Tang, ZhenA report presented on the acquisition, storage, processing and analysis of digital images of both fireants activities and small target visibility, beginning with the general introduction of background knowledge in digital image representation, covering acquisition, storage, enhancement and finally development of methods to extract information of interest from the digital images. Fast Fourier transform and digital image processing techniques are reviewed and utilized.Item Holographic Representations of Optical Systems.(Texas Tech University, 1975-05) Deen, Lewis MonroeNot Available.Item Some inequalities in Fourier analysis and applications(2014-05) Kelly, Michael Scott; Vaaler, Jeffrey D.We prove several inequalities involving the Fourier transform of functions which are compactly supported. The constraint that the functions have compact support is a simplifying feature which is desirable in applications, but there is a trade-off in control of other relevant quantities-- such as the mass of the function. With applications in mind, we prove inequalities which quantify these types of trade-offs.Item Using Fourier Analysis To Generate Believable Gait Patterns For Virtual Quadrupeds(2013-01-16) Cureton, SpencerAchieving a believable gait pattern for a virtual quadrupedal character requires a significant time investment from an animator. This thesis presents a prototype system for creating a foundational layer of natural-looking animation to serve as a starting point for an animator. Starting with video of an actual horse walking, joints are animated over the footage to create a rotoscoped animation. This animation represents the animal?s natural motion. Joint angle values for the legs are sampled per frame of the animation and conditioned for Fourier analysis. The Fast Fourier Transform provides frequency information that is used to create mathematical descriptions of each joint?s movement. A model representing the horse?s overall gait pattern is created once each of the leg joints has been analyzed and defined. Lastly, a new rig for a virtual quadruped is created and its leg joints are animated using the gait pattern model derived through the analysis.