Fourier Analysis and Signal Processing

A wide range of computational applications involve oscillating signals in one or more dimensions. Fourier analysis techniques make it possible to analyze these signals in terms of the frequency components that make them up, forming the basis for technologies ranging from audio and video compression to sound and image processing to automatic speech and image recognition. In this course we will introduce the mathematics of Fourier series and transforms, their discretization through the Fast Fourier Transform, and associated topics such as convolutions, filters, and uncertainty relations. We will then apply these techniques to a variety of examples, including music, speech, and images. (MATH 0122 and MATH 0200 and CSCI 0201) 3 hrs. lect./lab