Musical Analysis and Synthesis in Matlab
Musical Analysis and Synthesis in Matlab
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Matlab 中的音乐分析与合成
DOI：
10.2307/4146853
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发表时间：
2004
影响因子：
--
通讯作者：
Mark R. Petersen
中科院分区：
文献类型：
--
作者：
Mark R. Petersen
本文介绍了可用于偏微分方程和傅里叶级数入门课程的音乐示例和计算机工具，学生在该课程中使用热和波方程。从音乐的角度研究傅立叶级数提供了对基本数学概念和乐器物理学的深刻见解。Matlab中提供的工具允许学生轻松分析录制声音的波形和谐波，并合成自己的声音。这些实验是一种启发思维的方式，可以理解波形是如何由傅里叶级数基函数的总和组成的，以及它与频域的关系。我曾经合作过的许多学生都有特殊的音乐兴趣，并继续用自己的乐器进行实验。被拨动的琴弦PDE入门课程中的标准问题之一是具有Dirichlet边界条件的波动方程，
This article presents musical examples and computer tools that could be used in an introductory pde and Fourier Series class, where students work with the heat and wave equations. The study of Fourier series from a musical perspective offers great in- sight into basic mathematical concepts and the physics of musical instruments. Tools available in Matlab allow students to easily analyze the wave forms and harmonics of recorded sounds and to synthesize their own. These experiments are a thought pro- voking way to understand how a wave form is composed of a summation of Fourier Series basis functions and how this relates to the frequency domain. Many students I have worked with have special musical interests and go on to conduct experiments with their own instruments. The plucked string. One of the standard problems in an introductory pde course is the wave equation with Dirichlet boundary conditions,