chapter3 Frequency Spectrum of Signal Fourier Transform Analysis of networks 《 Principles of Circuit Analysis》 s3-1 Frequency Spectrum of periodic signals: Fouri Chapter 3: Fourier Transform Analysis 3-2 Frequency Spectrum of non-periodie signals: ourier transform 2009-10-20 53-3 Basic theorem of frequency analysis 83-4 Outputs of constant-parameter linear circuits Content What is concerned in this lecture 5 3-1 Frequency Spectrum of periodic signals: Fourier Series Why choosing sinusoidal function as the orthogonal function system of periodic signals I. Complete Orthogonal System(mathematics, Dirichlet What is the relationship between the signals time- 2. Fourier series domain and frequency-domain characteristic 3. The relationship between symmetry of periodie signals and Spectral characteristic of common periodie signals Fourier Series From the analysis of periodic signals Introduction of the analysis of non-periodic 5. Virtual value and average power of periodic signals( for sel signals study 6. Non-sinusoidal periodic circuits Gust know it, no new conceptions 8 31 Frequeney spectrum f period ic sigmaIs--Complete Orthogonal System S 3.1 Frequency Spectrum of periodic sigmals--Complete Orthogonal System IIt has been proved in mathematics O Dirichlet condition for convergence of periodical signals: compost ty points of the fire( in which there can kind )f(t), can be near combinations of Comple Orthogonal System. This Complete Orthogonal System 1. f(t-f(t+T)is single-valued continuous function of t: 2. f(t)has finite discontinuity point in one period; x.. Taylor series 3. f(t)has finite extremal point in one period; .Bessel funetions J(x),,(x), J,(x), 4. The integral of f(0 If(t)Idt exists. ◆ trigonometric functi 1,cos(ot),cos(2ωt),cos(not)…北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 第？讲： 复习 北京大学 wwhu 北京大学 《Principles of Circuit Analysis》 Chapter 3: Fourier Transform Analysis Lecture 1 2009-10-20 Interest Focus Persistence Originality 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 第三章：信号的频谱 §3－1 Frequency Spectrum of periodic signals: Fourier Series §3－2 Frequency Spectrum of non-periodic signals: Fourier Transform §3－3 Basic theorem of frequency analysis §3－4 Outputs of constant-parameter linear circuits chapter3 Frequency Spectrum of Signals （Fourier Transform Analysis of networks） chapter3 Frequency Spectrum of Signals （Fourier Transform Analysis of networks） 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 Content §3－1 Frequency Spectrum of periodic signals: Fourier Series 1. Complete Orthogonal System (mathematics, Dirichlet conditions) 2. Fourier Series 3. The relationship between symmetry of periodic signals and Fourier Series 4. Spectral characteristic of common periodic signals 5. Virtual value and average power of periodic signals (for self￾study) 6. Non-sinusoidal periodic circuits (just know it, no new conceptions) 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 What is concerned in this lecture # Why choosing sinusoidal function as the orthogonal function system of periodic signals # What is the relationship between the signal’s time￾domain and frequency-domain characteristic # Spectral characteristic of common periodic signals # From the analysis of periodic signals ÆIntroduction of the analysis of non-periodic signals 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 ‰It has been proved in mathematics: Any single-valued continuous function (in which there can be finite discontinuity points of the first kind.) f(t), can be decomposed into linear combinations of Complete Orthogonal System. This Complete Orthogonal System composes a linear space. e.g.: ◆power functions ◆Bessel functions ◆trigonometric functions J (x),J (x), J (x),... 0 1 2 x ,x ,x ,..., x ,... 1 2 3 n 1,cos(ωt),cos(2ωt),...cos(nωt),... Taylor series Cylindrical wave decomposition §3-1 Frequency Spectrum of periodic signals--Complete Orthogonal System 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 1. f(t)= f(t+T) is single-valued continuous function of t; 2. f(t) has finite discontinuity point in one period; 3. f(t) has finite extremal point in one period; 4. The integral of f(t) exists. ◆Dirichlet condition for convergence of periodical signals： ∫ t +T t 0 0 |f(t)|dt §3-1 Frequency Spectrum of periodic signals--Complete Orthogonal System