We present elementary wavelet theory, including an historical background and the role of the uncertainty principle. The application to periodicity detection is elementary to explain, and is motivated by classical problems in spectral estimation. Its origins are in the problem of epileptic seizure prediction.

This lecture deals with the theory of Fourier frames, versus the wavelet frames of the first lecture. In the finite case, we study Platonic solids and in the infinite case we solve a data acquisition problem in magnetic resonance imaging (MRI). We close by giving associated Fourier transform uncertainty principle inequalities dealing with the uncertainty principle inequality that arose in the first lecture.

This lecture presents multidimensional wavelet theory, and provides basic constructions of single dyadic orthonormal wavelets. These constructions are intimately related to fractal sets and the notion of self-similarity.

The speaker's own results in these talks represent joint work with David Colella, Matthew Fickus, Hans Heinig, Manuel Leon, Goetz Pfander, Songkiat Sumetkijakan, and Hui-Chuan Wu.