Introduction to Wavelets - 525.762

This is an introductory course on wavelet analysis, with an emphasis on the fundamental mathematical principles and basic algorithms. We cover the mathematics of signal (function) spaces, orthonormal bases, frames, time-frequency localization, the windowed Fourier transform, the continuous wavelet transform, discrete wavelets, orthogonal and biorthogonal wavelets of compact support, wavelet regularity, and wavelet packets. It is designed as a broad introduction to wavelets for engineers, mathematicians, and physicists.Prerequisite: Competence with multivariable calculus, linear algebra, and a scientific programming language is required, as well as familiarity with Fourier transforms and signal processing fundamentals such as the discrete Fourier transform, convolutions, and correlations.