Winter 2021 STAT 31460

Course: STAT 31460=CAAM 31460

Title: Applied Fourier Analysis

Instructor(s): Benjamin Palacios

Teaching Assistant(s): TBA

Class Schedule: Sec 1: MW 4:10 PM–5:30 PM (Remote)

Textbook(s): Mallatt, A Wavelet Tour of Signal Processing: The Sparse Way (3rd ed)

Description: Decompositions of functions into frequency components via the Fourier transform, and related sparse representations, are fundamental tools in applied mathematics. These ideas have been important in applications to signal processing, imaging, and the quantitative and qualitative analysis of a broad range of mathematical models of data (including modern approaches to machine learning) and physical systems. Topics to be covered in this course include an overview of classical ideas related to Fourier series and the Fourier transform, wavelet representations of functions and the framework of multiresolution analysis, and applications throughout computational and applied mathematics.

Prerequisite(s): Graduate student in the Physical Sciences Division or consent of instructor.