Wavelet Applications to Ecological Time Series

Gregory Lee Fitzgerald, Bates College


My thesis investigates applications of wavelet analysis to ecological time series. I begin by acquainting the reader with the mathematics of signal processing and, in particular, 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 with particular appeal to ecological time series analysis. In the latter portion of my thesis, I survey several specific wavelet applications to ecology, focusing on the detection scale-specific inferences and the construction of wavelet-revised mathematical models.