Persistent Homology and Discrete Fourier Transform
portes grátis
Persistent Homology and Discrete Fourier Transform
An Application to Topological Musical Data Analysis
Callet-Feltz , Victoria
Springer International Publishing AG
04/2025
250
Dura
9783031822353
Pré-lançamento - envio 15 a 20 dias após a sua edição
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1 Introduction.- Part I The two-dimensional Discrete Fourier Transform.- 2 The DFT for modeling basic musical structures.- 3 Generalization of theoretical results.- Part II Persistent homology on musical bars.- 4 Mathematical background.- 5 Musical scores and filtration.- Part III Musical applications.- 6 The DFT as a metric on the set of notes and chord.- 7 Harmonization of Pop songs.- 8 Classification of musical style.- 9 A different approach: the Hausdorff distance.- 10 Conclusion and perspectives for future research.
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Persistent homology;Discrete Fourier Transform;Topological Data Analysis;Automatic musical style classification;Tonnetz;Simplicial theory;Barcodes;Musical analysis;Musical textures;Hausdorff distance ;Hexachordal Theorem;Lewin's Lemma
1 Introduction.- Part I The two-dimensional Discrete Fourier Transform.- 2 The DFT for modeling basic musical structures.- 3 Generalization of theoretical results.- Part II Persistent homology on musical bars.- 4 Mathematical background.- 5 Musical scores and filtration.- Part III Musical applications.- 6 The DFT as a metric on the set of notes and chord.- 7 Harmonization of Pop songs.- 8 Classification of musical style.- 9 A different approach: the Hausdorff distance.- 10 Conclusion and perspectives for future research.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
