基于matlab的信号合成与分解

- I - 摘 要 为了便于进行周期信号的分析与处理，常要把复杂的周期信号进行分解，即将周期 信号分解为正余弦等此类基本信号的线性组合，通过对这些基本信号单元在时域和频域 特性的分析来达到了解信号特性的目的。本文主要阐述了傅立叶级数的推演过程，从而 得出周期信号的分解与合成的基本原理。并利用Matlab仿真软件强大的数值分析和图形 功能来对周期方波信号与周期三角波信号的分解与合成进行演示，直观明了的观察周期 信号分解与合成过程、周期信号的对称性与谐波成分的关系，以及对其中的误差程度和 吉布斯现象做定量的分析，从而可以进行仿真结果与理论分析结论的对比，加深了对周 期连续信号分解与合成的理解，描述了傅立叶级数分解合成信号的实现性，同时也展示 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：周期信号；分解；合成；吉布斯现象- II - 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 programKey words: Periodic signal; Decomposition; Synthesis; Gibbs phenomenon- III - 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 ( ) f t 3 MATLAB的仿真实现8 3.1基于 MATLAB方波信号的分解与合成