山东交通学院
2013届毕业生毕业论文(设计)
题目：音乐信号的频域分析
院(系)别 信息科学与电气工程学院 专 业 电子信息工程 班 级 电信091 学 号 090819507 姓 名 陈 鹏 指导教师 饶中洋
二〇一三年六月
原 创 声 明
本人陈鹏郑重声明：所呈交的论文“音乐信号的频域分析”，是本人在导师饶中洋的指导下开展研究工作所取得的成果。除文中特别加以标注和致谢的地方外，论文中不包含任何其他个人或集体已经发表或撰写过的研究成果，对本文的研究做出重要贡献的个人和集体均已在文中以明确方式标明，本人完全意识到本声明的法律后果，尊重知识产权，并愿为此承担一切法律责任。
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摘 要
信号不仅在时域有表现形式，在频域、复频域等同样有表现形式。在时域难以辨别的信号可通过傅里叶变换到频域进行分析。往往在频域分析音乐信号时更容易找出它们之间各自的特点。时域信号通过傅里叶变换就可以转换到频域，特别是离散傅里叶变换近年来发展迅猛，先后出现了多种快速算法，特别是借助计算机后，使得繁杂的计算变的简单化、快速化、形象化。
但是，傅里叶变换是一种整体变换，作为频域表示的功率谱并不能告诉我们其中某种频率分量出现在什么时候及其变化情况。在许多实际应用场合，信号是非平稳的，这时，只了解信号频域的全局特性是远远不够的，最希望得到的是信号频谱随时间变化的情况。为此，需要使用时间和频率的联合函数来表示信号，这种表示简称为信号的时频表示。时频分析的主要研究对象是非平稳信号或时变信号，主要的任务是描述信号的频谱含量是怎样随时间变化的。
本文就是基于Matlab1应用短时傅里叶变换的方法对钢琴等乐器发出的单个音进行分析，然后对一段未知乐曲进行同样的频域分析，与已知音名的音的频域特点进行对比进而翻译这段音乐的乐谱。
关键词：音乐信号，时频分析，Matlab
1 本文用Matlab版本均为R2007a.
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Abstract
Not only has the form the signal in time domain, but also in frequency domain, in complex frequency domain .The signal which is not distinguished in the time domain can be analyzed by the Fourier transforming to the frequency domain. Music signal analysis in frequency domain is more likely to identify their respective characteristics between them in often. The time domain signal can be converted to the frequency domain through the Fourier exchange, especially the discrete Fourier transform is developing rapidly in recent years, there are a variety of fast algorithms, especially the help of the computer makes the complicated calculation become simple, fast and visual.
However, Fourier transform is an integral transform, power spectrum as a representation of frequency domain can not tell us some frequency components appear at any time and its changes. The signal is non-stationary in practice, if we only know the global properties of signal frequency at this time, it is far from enough, and what mostly we want is the signal spectrum varies with time. Therefore, we need to use the function between the time and frequency to express the signal, we regard this representation as time-frequency signal representation in short words. The main research object of the time-frequency analysis signals is non-stationary or time-varying signals. It is aimed at how to describe the change of the content of signal spectrum over time.
This paper makes use of the method of Matlab application of short-time based on Fourier transform to analyze any tone which is produced on the piano, and then analyze the interception of a piece of music of the same frequency which is unknown, and the compared with the sound of the frequency domain characteristics of known name and then translate this paragraph of music score.
Key words：The music signal, Time-frequency analysis, Matlab
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