電子科大信號系統(tǒng)英文版課件Chapter4 FourierTransform-B

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)

2、Example( 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 conti

3、nuous time Fourier 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

4、number of maxima and 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

5、4.4 4.5Example (1)Example (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

6、transformExample 4.9thenIf4.3.2 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) If 4 The continuous

7、time Fourier transformthen(2) IfExample 4.12 4 The continuous time Fourier 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 Parseval

8、s Relationthen IfExample 4.14 4 The continuous time Fourier transform4.4 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 Mul

9、tiplication PropertyThe multiplication(modulation) property:Example 4.21 4.22 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 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:F