信号与系统奥本海姆原版PPT第四章.ppt

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1、 4 The continuous time Fourier transform4.1 Representation of Aperiodic signals:The Continuous time Fourier Transform4.1.1 Development of the Fourier transform representation of the continuous time Fourier transform4.The Continuous time Fourier Transform 4 The continuous time Fourier transform(1)Exa

2、mple(From Fourier series to Fourier transform)4 The continuous time Fourier transform(2)Fourier transform representation of Aperiodic signalFor periodic signal :For aperiodic signal x(t):4 The continuous time Fourier transformT 4 The continuous time Fourier transformWhen T,So 4 The continuous time F

3、ourier transformFourier transform:Relation between Fourier series and Fourier transform:or 4 The continuous time Fourier transform 4 The continuous time Fourier transform4.1.2 Convergence of Fourier transformDirichlet conditions:(1)x(t)is absolutely integrable.(2)x(t)have a finite number of maxima a

4、nd minima within any finite interval.(3)x(t)have a finite number of discontinuity within any finite interval.Furthermore,each of these discontinuities must be finite.4 The continuous time Fourier transform4.1.3 Examples of Continuous time Fourier TransformExample 4.1 4.2 4.3 4.4 4.5Example(1)Example

5、(2)4 The continuous time Fourier transform4.2 The Fourier Transform for Periodic SignalPeriodic signal:thusExample 4.6 4.7 4.8 4 The continuous time Fourier transform4.3 Properties of the Continuous time Fourier TransformthenIf4.3.1 Linearity 4 The continuous time Fourier transformExample 4.9thenIf4

6、.3.2 Time Shifting 4 The continuous time Fourier transform4.3.3 Conjugation and Conjugate Symmetrythen(1)Ifthen(2)If 4 The continuous time Fourier transformthen(3)If 4 The continuous time Fourier transform4.3.4 Differentiation and Integrationthen(1)Ifthen(2)IfExample 4.12 4 The continuous time Fouri

7、er transform4.3.5 Time and Frequency Scalingthen IfEspecially,4 The continuous time Fourier transform4.3.6 Dualitythen IfExample 4.13 4 The continuous time Fourier transform 4 The continuous time Fourier transform4.3.7 Parsevals Relationthen IfExample 4.14 4 The continuous time Fourier transform4.4

8、The Convolution Propertyh(t)H(j)x(t)y(t)=x(t)*h(t)X(j)Y(j)=X(j)H(j)Consider a LTI system:Example 4.15 4.16 4.17 4.19 4.204.4.1 Examples 4 The continuous time Fourier transform 4 The continuous time Fourier transform4.5 The Multiplication PropertyThe multiplication(modulation)property:Example 4.21 4.

9、22 4.23s(t)p(t)r(t)4 The continuous time Fourier transform 4 The continuous time Fourier transform4.5.1 Frequency-Selective Filtering with Variable Center FrequencyA Bandpass Filter:4 The continuous time Fourier transform 4 The continuous time Fourier transform4.6 Tables of Fourier Properties and of

10、 Basic Fourier Transform PairsTable 4.1Table 4.2 4 The continuous time Fourier transform4.7 System Characterized by Linear Constant-Coefficient Differential EquationConstant-coefficient differential equation:Fourier transform:Define:Example 4.24 4.25 4.26 4 The continuous time Fourier transformProblems:4.3 4.4(a)4.10 4.11 4.14 4.15 4.24 4.25 4.32(a)(b)4.35 4.36