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1、Chapter 4The Continuous-Time Fourier Transform,1,Chapter 41,Chapter 4 Fourier Transform,factor,Synthesis equation,Analysis equation,Fourier Transform Pair,4.1 Representation of Aperiodic Signals :The Continuous-Time Fourier Transform,2,Chapter 4,The Fourier coefficients of are proportional to sample
2、s of the Fourier transform of one period of,Consider a periodic signal,Defining,Chapter 4 Fourier Transform,3,The Fourier coefficients,Chapter 4 Fourier Transform,4.1.3 Fourier Transforms of Typical Signals,F,F,4,Chapter 4,Chapter 4 Fourier Transform,5,Chapter 4,4.2 The Fourier Transforms for Period
3、ic Signals,Chapter 4 Fourier Transform,6,4.2 The Fourier Transforms f,More generally,Periodic square wave,Chapter 4 Fourier Transform,7,More generally Periodic square,Periodic impulses train,Chapter 4 Fourier Transform,8,-0 0 0 20Per,Chapter 4 Fourier Transform,4.3 Properties of the Fourier Transfor
4、ms,4.3.1 Linearity,Chapter 4 Fourier Transform,4.3.2 Time Shifting,9,Chapter 4,Chapter 4 Fourier Transform,10,Example 4.90 1 2,4.3.3 Conjugation and Conjugate Symmetry,Chapter 4 Fourier Transform,11,4.3.3 Conjugation and Conjug,Chapter 4 Fourier Transform,12,Chapter 4,4.3.4 Differentiation and Integ
5、ration,1. Differentiation,Chapter 4 Fourier Transform,2. Integration,13,4.3.4 Differentiation and In,Chapter 4 Fourier Transform,14,-2 0 2 t1,4.3.5 Time and Frequency Scaling,Let,Chapter 4 Fourier Transform,Example,15,4.3.5 Time and Frequency Sca,交换,4.3.6 Duality（对偶性）,Example,Chapter 4 Fourier Trans
6、form,16,交换4.3.6 Duality（对偶性）Example,F,F,Example 4.13,Chapter 4 Fourier Transform,17,FFFExample 4.13 Chapter 4,Example 4.14,4.3.7 Differentiation in Frequency Domain,Chapter 4 Fourier Transform,18,Example 4.144.3.7 Differentia,Example 1,More generally,Chapter 4 Fourier Transform,19,Example 1 More gen
7、erally Chap,Example 2,Chapter 4 Fourier Transform,20,Example 2-2 -1 0,Example 3,Chapter 4 Fourier Transform,21,Example 3 Chapter 4,4.3.8 Frequency Shifting,Chapter 4 Fourier Transform,4.3.9 Parsevals Relation,22,4.3.8 Frequency Shifting Cha,Solution of Infinite Differentiation,Chapter 4 Fourier Tran
8、sform,23,Solution of Infinite Different,Example 1,F,Example 2,Chapter 4 Fourier Transform,24,Example 1 FExample 2 Chapter 4,Example 3,Chapter 4 Fourier Transform,25,Example 3 Chapter 4, is real even function.,Chapter 4 Fourier Transform,26,Example 4 -1 0 1,4.4 The Convolution Property,Chapter 4 Four
9、ier Transform,27,4.4 The Convolution Property,The usefulness of the Convolution Property,Example 4.19,Solution,Chapter 4 Fourier Transform,28,The usefulness of the Convolut,Example 4.20,F,F,Chapter 4 Fourier Transform,29,Example 4.20FF Chapter 4,4.5 The Multiplication property (modulation property)（
10、调制特性）,Chapter 4 Fourier Transform,30,4.5 The Multiplication prope,Example 4.23 Determine the Fourier transform of the signal,Chapter 4 Fourier Transform,31,Example 4.23 Chapter 4,Chapter 4 Fourier Transform,32,ExampleFigure (a)Figure (b) Ch,-7W -5W -3W 0 3W 5W 7W ,-5W -3W 0 3W 5W ,-8W -6W -2W 0 2W 6
11、W 8W ,-2W 0 2W ,Chapter 4 Fourier Transform,33,-7W -5W -3W 0 3,4.6 Frequency-domain analysis of LTI systemsLTI系统的频域分析,1. Stable System,Chapter 4 Fourier Transform,34,4.6 Frequency-domain analysi,2. Linear Constant-Coefficients Differential Equations,FT,A ratio of polynomials in,Chapter 4 Fourier Tra
12、nsform,35,2. Linear Constant-Coefficien,Chapter 4 Fourier Transform,36,Example 4.25Consider a stable,Chapter 4 Fourier Transform,37,Example 4.25Consider the LTI s,Chapter 4 Fourier Transform,38,Example Consider an LTI system,Homework: 4.3 4.4 4.10 4.11 4.14 4.15 4.24 4.25 4.32 4.35 4.36 4.37* 4.43*,Chapter 4 Fourier Transform,39,Homework: Chapter 4,Problems for Fourier Analysis,40,Problems for Fourier Analysis,
