Department or Program
Mathematics
Abstract
My thesis investigates wavelet theory and methods underlying recent applications to time series analysis, particularly in the field of ecology. I begin by acquainting the reader with the mathematics of signal processing and time series analysis. From there, my thesis develops in modest detail some standard Fourier methods, including Fourier transforms and spectral approaches to time series analysis. Wavelets are then introduced with the Haar wavelet and an application to data compression, which frames the subsequent discussion regarding multiresolution analysis. Then, the continuous and discrete wavelet transforms are discussed before introducing the discrete lifting transform, a more flexible version of the discrete wavelet transform suited for the analysis of time series data characterized by irregular samples. In the latter portion of my thesis, I survey several specific wavelet methods derived from ecological research articles, with attention given to the detection of scale-specific inferences and the construction of wavelet-revised mathematical models.
Level of Access
Restricted: Campus/Bates Community Only Access
First Advisor
Greer, Meredith
Date of Graduation
5-2017
Degree Name
Bachelor of Arts
Recommended Citation
Fitzgerald, Gregory, "A Survey of Wavelet Theory and Methods Suited for Times Series Analysis" (2017). Honors Theses. 208.
https://scarab.bates.edu/honorstheses/208
Number of Pages
93
Components of Thesis
Main document
