Musical Engineering and Discovery with Wavelet Analysis

Name: Rephael Berkooz
Major: Mathematics
Minor: Computer Science
Advisors: Dr. Pamela Pierce
This project presents a novel method for extracting musical features via signal processing and wavelet analysis. I begin by exploring the human experience of consuming music, contrasting with digital encoding and playback of music. Starting with the Fourier transform, I construct and explore different modes of encoding music information in time and frequency dimensions. This project also introduces the fundamental limitations of encoding time and frequency information. Building upon these limitations, this project constructs the mathematics of Wavelet Analysis, which allows the representation of digital music information in a format very close to our human understanding of music. Utilizing convolutions and other techniques in signal processing, this project proposes methods for extracting beats and rhythm structure. Furthermore, I propose a method for recommending music based upon these extracted musical features. This music recommendation system enables individuals to choose the degree of similarity between different repeating parts of the recommended songs, such as bass line, rhythm, and melody. My IS project has given me a new way of connecting music with different modes of mathematical analysis, all within the context of the interface between human experience and digital technology.

Rephael will be online to field comments on April 16:
noon-2pm EDT (PST 9-11am, Africa/Europe: early evening) and 4-6 pm EDT (PST 1-3pm, Africa/Europe: late evening)

Posted in I.S. Symposium 2021, Independent Study.