基于matlab的信號合成與分解

- I - 摘 要 為了便于進行周期信號的分析與處理，常要把復(fù)雜的周期信號進行分解，即將周期 信號分解為正余弦等此類基本信號的線性組合，通過對這些基本信號單元在時域和頻域 特性的分析來達到了解信號特性的目的。本文主要闡述了傅立葉級數(shù)的推演過程，從而 得出周期信號的分解與合成的基本原理。并利用Matlab仿真軟件強大的數(shù)值分析和圖形 功能來對周期方波信號與周期三角波信號的分解與合成進行演示，直觀明了的觀察周期 信號分解與合成過程、周期信號的對稱性與諧波成分的關(guān)系，以及對其中的誤差程度和 吉布斯現(xiàn)象做定量的分析，從而可以進行仿真結(jié)果與理論分析結(jié)論的對比，加深了對周 期連續(xù)信號分解與合成的理解，描述了傅立葉級數(shù)分解合成信號的實現(xiàn)性，同時也展示 了用 MATLAB 編寫周期連續(xù)信號分解與合成的演示程序的優(yōu)點 關(guān)鍵詞：周期信號；分解；合成；吉布斯現(xiàn)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 錄 1緒論.1 2信號的分解與合成.2 2.1信號分解為正交函數(shù)2 2.1.1正交函數(shù)集.2 2.1.2信號分解為正交函數(shù).3 2.2周期信號的信號分解與合成5 2.2.1周期連續(xù)信號的特點.6 2.2.2周期為T的信號 的三角形式傅里葉級數(shù)表示的一般形式.6 ( ) f t 3 MATLAB的仿真實現(xiàn)8 3.1基于 MATLAB方波信號的分解與合成

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