New Methods in Wavelet Analysis for Applications of the Wavelet Transform
Abstract
Common in signal processing (SP) is the detection of events. For instance, seismologists seek to detect abnormalities in an electromagnetic (EM) signal to detect the occurrence of an earthquake. 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 used to remove the rough portions of a signal representing noise such that events are more obvious in a signal. This research applies and improves wavelet analysis methods across multiple domains and applications of signals since Wavelet analysis smooths 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 17, 2021
- Accession Number
- AD1148724
Entities
People
- Jeffrey D. Williams
Organizations
- Air Force Institute of Technology