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1、电子科大课堂讲义课堂版信号第四章讲义 Still waters run deep.流静水深流静水深,人静心深人静心深 Where there is life,there is hope。有生命必有希望。有生命必有希望 Chapter 4 Fourier Transformfactor Synthesis equationAnalysis equationFourier Transform PairSpectrum（频谱）（频谱）of 4.1 Representation of Aperiodic Signals:The Continuous-Time Fourier Transform2The
2、 Fourier coefficients of are proportional to samples of the Fourier transform of one period of Consider a periodic signal Defining Chapter 4 Fourier Transform3 Chapter 4 Fourier Transform4.1.3 Fourier Transforms of Typical SignalsFF4 Chapter 4 Fourier Transform54.2 The Fourier Transforms for Periodi
3、c Signals Chapter 4 Fourier Transform6More generally Periodic square wave Chapter 4 Fourier Transform7 -0 0 0 20Periodic impulses train Chapter 4 Fourier Transform8 Chapter 4 Fourier Transform4.3 Properties of the Fourier Transforms 4.3.1 Linearity Chapter 4 Fourier Transform4.3.2 Time Shifting 9Exa
4、mple 4.90 1 2 3 4 t Chapter 4 Fourier Transform-2 -1 0 1 2 t Example104.3.3 Conjugation and Conjugate Symmetry Chapter 4 Fourier Transformreal evenreal evenreal oddPurely imaginary odd11 Chapter 4 Fourier Transform124.3.4 Differentiation and Integration1.Differentiation Chapter 4 Fourier Transform2.
5、Integration13-2 0 2 t1-1-2 0 2 t(1)(-2)(1)Example Chapter 4 Fourier Transform144.3.5 Time and Frequency ScalingLet Chapter 4 Fourier TransformExample 15交换交换4.3.6 Duality（对偶性）（对偶性）Example Chapter 4 Fourier Transform16FFFExample 4.13 Chapter 4 Fourier Transform17Example 4.144.3.7 Differentiation in Fr
6、equency Domain Chapter 4 Fourier Transform18Example 1 More generally Chapter 4 Fourier Transform19Example 2-2 -1 0 1 2 t-2 -1 0 1 2 t-2 -1 0 1 2 t Chapter 4 Fourier Transform20Example 3 Chapter 4 Fourier Transform214.3.8 Frequency Shifting Chapter 4 Fourier Transform4.3.9 Parsevals Relation22Solutio
7、n of Infinite Differentiation Chapter 4 Fourier Transform23Example 1 FExample 2 Chapter 4 Fourier Transform24Example 3 Chapter 4 Fourier Transform25Example 4 Consider a signal with Fourier Transform Evaluate the following frequency-domain expressions:-1 0 1 2 3 t is real even function.Chapter 4 Four
8、ier Transform264.4 The Convolution Property Chapter 4 Fourier Transform27The usefulness of the Convolution PropertyExample 4.19Solution Chapter 4 Fourier Transform28Example 4.20FF Chapter 4 Fourier Transform294.5 The Multiplication property(modulation property)（调制特性）（调制特性）Chapter 4 Fourier Transform
9、30Example 4.23 Determine the Fourier transform of the signal Chapter 4 Fourier Transform31ExampleIn Figure(a),a system is shown with input and outputThe input signal has the Fourier transform shown in Figure(b)Determine and sketch .Figure(a)Figure(b)Chapter 4 Fourier Transform32-7W -5W -3W 0 3W 5W 7
10、W -5W -3W 0 3W 5W -8W -6W -2W 0 2W 6W 8W -2W 0 2W Chapter 4 Fourier Transform334.6 Frequency-domain analysis of LTI systemsLTI系统的频域分析系统的频域分析1.Stable System Chapter 4 Fourier Transform342.Linear Constant-Coefficients Differential EquationsFTA ratio of polynomials in Chapter 4 Fourier Transform35Examp
11、le 4.25Consider a stable LTI system Chapter 4 Fourier Transform36Example 4.25Consider the LTI system with input Chapter 4 Fourier Transform37Example Consider an LTI system Chapter 4 Fourier Transform38Homework: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 Transform39Problems for Fourier Analysis Consider an LTI system with unit impulse response 2.If the input is determine the output 1.Determine the frequency response of the whole system.40