Persistent Homology and Discrete Fourier Transform by Victori... - 9783031822353

Persistent Homology and Discrete Fourier TransformAn Application to Topological Musical Data Analysis\nAuthor(s): Victoria Callet-Feltz\nFormat: Hardback\nPublisher: Springer International Publishing AG, Switzerland\nImprint: Springer International Publishing AG\nISBN-13: 9783031822353, 978-3031822353\nSynopsis\nThis book proposes contributions to various problems in the field of topological analysis of musical data: the objects studied are scores represented symbolically by MIDI files, and the tools used are the discrete Fourier transform and persistent homology. The manuscript is divided into three parts: the first two are devoted to the study of the aforementioned mathematical objects and the implementation of the model. More precisely, the notion of DFT introduced by Lewin is generalized to the case of dimension two, by making explicit the passage of a musical bar from a piece to a subset of Z/tZZ/pZ, which leads naturally to a notion of metric on the set of musical bars by their.