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摘要信号分解合成过程、周期信号的对称性与谐波成分的关系加深了对周期连续信号分解与合成的理解展示了用MATLAB编写周期连续信号分解与合成的演示程序的优点关键词：
Abstract
In order to facilitate the periodic signal analysis and processing, often make complicated cycle of signal decomposition, periodic signal will be decomposed into sine and cosine signals and other such basic linear combination of these basic signals through the unit in the time domain and frequency domain characteristics analysis of signal characteristics to achieve the purpose of understanding. This article focuses on the Fourier series to the inference process to arrive at periodic signal decomposition and composition of the basic principles. Matlab simulation software using the powerful numerical analysis and graphical capabilities of the periodic square wave signal and the periodic triangular wave signal decomposition and synthesis of presentations and intuitive to understand the observation period signal decomposition and synthesis process, periodic signal and harmonic components of the symmetry relations, and the error of which the extent and quantitative analysis of the Gibbs phenomenon, which can make the simulation results and theoretical analysis comparing the cycle of continuous deepening of the understanding of signal decomposition and composition, Fourier series describes the synthesis of signal decomposition implementation, while also demonstrated the preparation of periodic continuous signal using MATLAB decomposition and synthesis of the advantages of the demonstration program
Key words: Periodic signal; Decomposition; Synthesis; Gibbs phenomenon
目 录1绪论. 1
2信号的分解与合成. 2
2.1信号分解为正交函数 2
2.1.1正交函数集 2
2.1.2信号分解为正交函数 3
2.2周期信号的信号分解与合成 5
2.2.1周期连续信号的特点 6
2.2.2周期为T的信号的三角形式傅里叶级数表示的一般形式 6
3 MATLAB的仿真实现. 8
3.1基于MATLAB方波信号的分解与合成 8
3.1.1方波信号的傅立叶级数 8
3.1.2方波信号的分解仿真 9
3.1.3方波信号的合成仿真 10
3.1.4方波信号的频谱 11
3.1.5方波信号的误差分析 12
3.1.6吉布斯现象 13
3.2基于MATLAB三角波信号的分解与合成 13
3.2.1三角波的傅立叶级数 13
3.2.2三角波的分解仿真 15
3.2.3三角波的合成仿真 15
3.2.4三角波的频谱 17
3.2.5三角波的误差分析 18
3.3结论 18
参考文献 20
附录 21
谢辞 25
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