Math 412: Music + Topology

Abstract

In this mini assignment you will explore an application of "sliding windows and persistence" on time series data (see Jose Perea's paper for more theory). Specifically, you will look at how to transform musical audio data into a high dimension point cloud/curve which can be probed with TDA methods. You will make use of a visualization program called LoopDitty to gain some intuition about what points in various persistence diagrams might mean. Please follow the directions below and submit an electronic writeup to chris.tralie@gmail.com with the answers to all of the questions and any observations you have. Enjoy!