Matching Items (3)
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- All Subjects: Saddlepoint Approximation
- Creators: Cochran, Douglas
- Creators: Kosut, Oliver
- Member of: Barrett, The Honors College Thesis/Creative Project Collection
- Resource Type: Text
Description
Multiple-channel detection is considered in the context of a sensor network where data can be exchanged directly between sensor nodes that share a common edge in the network graph. Optimal statistical tests used for signal source detection with multiple noisy sensors, such as the Generalized Coherence (GC) estimate, use pairwise measurements from every pair of sensors in the network and are thus only applicable when the network graph is completely connected, or when data are accumulated at a common fusion center. This thesis presents and exploits a new method that uses maximum-entropy techniques to estimate measurements between pairs of sensors that are not in direct communication, thereby enabling the use of the GC estimate in incompletely connected sensor networks. The research in this thesis culminates in a main conjecture supported by statistical tests regarding the topology of the incomplete network graphs.
ContributorsCrider, Lauren Nicole (Author) / Cochran, Douglas (Thesis director) / Renaut, Rosemary (Committee member) / Kosut, Oliver (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
Description
Lossy compression is a form of compression that slightly degrades a signal in ways that are ideally not detectable to the human ear. This is opposite to lossless compression, in which the sample is not degraded at all. While lossless compression may seem like the best option, lossy compression, which is used in most audio and video, reduces transmission time and results in much smaller file sizes. However, this compression can affect quality if it goes too far. The more compression there is on a waveform, the more degradation there is, and once a file is lossy compressed, this process is not reversible. This project will observe the degradation of an audio signal after the application of Singular Value Decomposition compression, a lossy compression that eliminates singular values from a signal’s matrix.
ContributorsHirte, Amanda (Author) / Kosut, Oliver (Thesis director) / Bliss, Daniel (Committee member) / Electrical Engineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
Radar systems seek to detect targets in some search space (e.g. volume of airspace, or area on the ground surface) by actively illuminating the environment with radio waves. This illumination yields a return from targets of interest as well as highly reflective terrain features that perhaps are not of interest (called clutter). Data adaptive algorithms are therefore employed to provide robust detection of targets against a background of clutter and other forms of interference. The adaptive matched filter (AMF) is an effective, well-established detection statistic whose exact probability density function (PDF) is known under prevalent radar system model assumptions. Variations of this approach, however, lead to tests whose PDFs remain unknown or incalculable. This project will study the effectiveness of saddlepoint methods applied to approximate the known pdf of the clairvoyant matched filter, using MATLAB to complete the numerical calculations. Specifically, the approximation was used to compute tail probabilities for a range of thresholds, as well as compute the threshold and probability of detection for a specific desired probability of false alarm. This was compared to the same values computed using the known exact PDF of the filter, with the comparison demonstrating high levels of accuracy for the saddlepoint approximation. The results are encouraging, and justify further study of the approximation as applied to more strained or complicated scenarios.
ContributorsRhoades, Rachel (Author) / Richmond, Christ (Thesis director) / Cochran, Douglas (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Electrical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05