Applied Harmonic Analysis

Catalog description

Applied Harmonic Analysis studies the theory and modern extensions of Fourier analysis, with an emphasis on its role in data representation and analysis across diverse fields such as engineering, medicine, and finance. Applications include signal and image processing, data denoising and compression, and image reconstruction. Topics include Fourier series, the Fourier transform, the discrete and fast Fourier transforms (DFT/FFT), interpolation and sampling theory, wavelet analysis, and the discrete wavelet transform with applications. The course emphasizes the mathematical foundations underlying these methods, as well as the derivation and implementation of practical algorithms.