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- Creators: Kosut, Oliver
- Creators: Arizona State University
- 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
Eigenvalues of the Gram matrix formed from received data frequently appear in sufficient detection statistics for multi-channel detection with Generalized Likelihood Ratio (GLRT) and Bayesian tests. In a frequently presented model for passive radar, in which the null hypothesis is that the channels are independent and contain only complex white Gaussian noise and the alternative hypothesis is that the channels contain a common rank-one signal in the mean, the GLRT statistic is the largest eigenvalue $\lambda_1$ of the Gram matrix formed from data. This Gram matrix has a Wishart distribution. Although exact expressions for the distribution of $\lambda_1$ are known under both hypotheses, numerically calculating values of these distribution functions presents difficulties in cases where the dimension of the data vectors is large. This dissertation presents tractable methods for computing the distribution of $\lambda_1$ under both the null and alternative hypotheses through a technique of expanding known expressions for the distribution of $\lambda_1$ as inner products of orthogonal polynomials. These newly presented expressions for the distribution allow for computation of detection thresholds and receiver operating characteristic curves to arbitrary precision in floating point arithmetic. This represents a significant advancement over the state of the art in a problem that could previously only be addressed by Monte Carlo methods.
ContributorsJones, Scott, Ph.D (Author) / Cochran, Douglas (Thesis advisor) / Berisha, Visar (Committee member) / Bliss, Daniel (Committee member) / Kosut, Oliver (Committee member) / Richmond, Christ (Committee member) / Arizona State University (Publisher)
Created2019
Description
There has been a substantial development in the field of data transmission in the last two decades. One does not have to wait much for a high-definition video to load on the systems anymore. Data compression is one of the most important technologies that helped achieve this seamless data transmission experience. It helps to store or send more data using less memory or network resources. However, it appears that there is a limit on the amount of compression that can be achieved with the existing lossless data compression techniques because they rely on the frequency of characters or set of characters in the data. The thesis proposes a lossless data compression technique in which the data is compressed by representing it as a set of parameters that can reproduce the original data without any loss when given to the corresponding mathematical equation. The mathematical equation used in the thesis is the sum of the first N terms in a geometric series. Various changes are made to this mathematical equation so that any given data can be compressed and decompressed. According to the proposed technique, the whole data is taken as a single decimal number and replaced with one of the terms of the used equation. All the other terms of the equation are computed and stored as a compressed file. The performance of the developed technique is evaluated in terms of compression ratio, compression time and decompression time. The evaluation metrics are then compared with the other existing techniques of the same domain.
ContributorsGrewal, Karandeep Singh (Author) / Gonzalez Sanchez, Javier (Thesis advisor) / Bansal, Ajay (Committee member) / Findler, Michael (Committee member) / Arizona State University (Publisher)
Created2021