An Introduction to Fourier Analysis with Applications to Music

Journal of Humanistic Mathematics

Needell, Deanna¹  Lenssen, Nathan¹ 

[1] Claremont McKenna College

关键词: music;    mathematics;    Fourier analysis;    chord detection;    chromagram;   

DOI  :  10.5642/jhummath.201401.05

学科分类：卫生学

来源: Cleveland Clinic Educational Foundation

【 摘 要 】

In our modern world, we are often faced with problems in which a traditionally analog signal is discretized to enable computer analysis. A fundamental tool used by mathematicians, engineers, and scientists in this context is the discrete Fourier transform (DFT), which allows us to analyze individual frequency components of digital signals. In this paper we develop the discrete Fourier transform from basic calculus, providing the reader with the setup to understand how the DFT can be used to analyze a musical signal for chord structure. By investigating the DFT alongside an application in music processing, we gain an appreciation for the mathematics utilized in digital signal processing.

【 授权许可】

Unknown