Speaker: Parker Allmond (UCF, Mathematics Department)
Title: Wavelets and Wavelet Transforms
Abstract: In the 1980's the concepts of wavelets began to appear across literature in mathematics, physics, and engineering. Intuitively understood as "brief" or "localized" oscillations, it was quickly realized by authors such as Morlet, Grossman, and Meyer that these wavelets could be used as the foundation for an integral transform overcoming some of the shortcomings of the classical Fourier transform. The Fourier transform gives precise frequency information about the entirety of a given signal, but definitionally contains no local information. Wavelet transforms by contrast provide a balance of frequency and time information.
This talk will give an overview of the wavelet theory, with special attention to results analogous to that of the Fourier theory. We will discuss the continuous and discrete wavelet transforms, as well as some of their applications to various fields.
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