Date of Award
Doctor of Philosophy (PhD)
Department of Operational Sciences
Raymond R. Hill, PhD
A commonality in the many applications and domains where signal processing (SP)is applied is the detection of events. Detection in SP requires the identification of the occurrence of an event, within a signal, and distinguishing the occurrence from no event. In a classical application of SP, seismologists seek to detect abnormalities in an electromagnetic (EM) signal to detect or not detect the occurrence of an earthquake, represented as an anomalous EM pulse. Since many signals are noisy, such as those produced by a seismograph, it can be challenging to distinguish a significant EM pulse from incident noise. In SP, smoothing is often used to remove the rough portions of a signal representing noise such that events are more obvious in a signal. Of the many SP smoothing techniques, this research applies and improves wavelet analysis methods across multiple domains and applications of signals. Wavelet analysis has been proven, in many applications, to smooth signals while preserving important signal artifacts such as a large EM pulse representing an earthquake. Further, there are several useful properties of wavelet analysis such as time localization and sparsity which improve detection ability in SP. In this dissertation, we explore several applications, and domains of SP such as classical data, functional data, and graph data. We improve event detection such as outliers and introduce new methods to detect and remove noise across these domains to improve SP analysis.
DTIC Accession Number
Williams, Jeffrey D., "New Methods in Wavelet Analysis for Applications of the Wavelet Transform" (2021). Theses and Dissertations. 5086.