The Discrete Fourier Transform and Applications in Audio Signal Analysis by Matt Wisotsky ’23, Mathematics Colloquium, Monday, February 6, 1 – 1:45 pm, North Science Building 113, Wachenheim.
Abstract: Fourier analysis is a pervasive subject in many areas of mathematics, and it has applications ranging from quantum mechanics to forensics to digital imaging and sound processing. We will first make rigorous the theory of the Fourier series and the related Fourier transform, motivating them from the perspective of functional analysis. We will then consider the particular applications of Fourier analysis to acoustics and audio signal analysis. Finally, we will demonstrate some of these applications by constructing a square wave as well as listening to varying levels of audio compression.