Date of Graduation

5-2017

Level of Access

Restricted: Campus/Bates Community Only Access

Degree Name

Bachelor of Arts

Department or Program

Mathematics

Number of Pages

93

First Advisor

Greer, Meredith

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, which attention given to the detection of scale-specific inferences and the construction of wavelet-revised mathematical models.

Components of Thesis

Main document

Restricted

Available to Bates community via local IP address or Bates login.

Share

COinS