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1、1,Chapter 4 The Continuous-Time Fourier Transform,2,factor,Synthesis equation,Analysis equation,Fourier Transform Pair,4.1 Representation of Aperiodic Signals : The Continuous-Time Fourier Transform,3,The Fourier coefficients of are proportional to samples of the Fourier transform of one period of,C
2、onsider a periodic signal,Defining,4,4.1.3 Fourier Transforms of Typical Signals,5,6,4.2 The Fourier Transforms for Periodic Signals,7,More generally,Periodic square wave,8,Periodic impulses train,9,4.3 Properties of the Fourier Transforms,4.3.1 Linearity,4.3.2 Time Shifting,10,11,4.3.3 Conjugation
3、and Conjugate Symmetry,12,13,4.3.4 Differentiation and Integration,1. Differentiation,2. Integration,14,15,4.3.5 Time and Frequency Scaling,Let,Example,16,交换,4.3.6 Duality（对偶性）,Example,17,Example 4.13,18,Example 4.14,4.3.7 Differentiation in Frequency Domain,19,Example 1,More generally,20,Example 2,
4、21,Example 3,22,4.3.8 Frequency Shifting,4.3.9 Parsevals Relation,23,Solution of Infinite Differentiation,24,Example 1,Example 2,25,Example 3,26, is real even function.,27,4.4 The Convolution Property,28,The usefulness of the Convolution Property,Example 4.19,Solution,29,Example 4.20,30,4.5 The Mult
5、iplication property (modulation property) （调制特性）,31,Example 4.23 Determine the Fourier transform of the signal,32,33,34,4.6 Frequency-domain analysis of LTI systems LTI系统的频域分析,1. Stable System,35,2. Linear Constant-Coefficients Differential Equations,FT,A ratio of polynomials in,36,37,38,39,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*,40,