信号与系统 课件 英文版1

,4 The continuous time Fourier transform,4.1 Representation of Aperiodic signals: The Continuous time Fourier Transform,4.1.1 Development of the Fourier transform representation of the continuous time Fourier transform,4. The Continuous time Fourier Transform,4 The continuous time Fourier transform,(1) Example,( From Fourier series to Fourier transform ),4 The continuous time Fourier transform,(2) Fourier transform representation of Aperiodic signal,For periodic signal :,For aperiodic signal x(t) :,4 The continuous time Fourier transform,4 The continuous time Fourier transform,When T ,So,4 The continuous time Fourier transform,Fourier transform:,Relation between Fourier series and Fourier transform:,or,4 The continuous time Fourier transform,4 The continuous time Fourier transform,4.1.2 Convergence of Fourier transform,Dirichlet conditions: (1) x(t) is absolutely integrable. (2) x(t) have a finite 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 transform,4.1.3 Examples of Continuous time Fourier Transform,Example 4.1 4.2 4.3 4.4 4.5,Example (1),Example (2),4 The continuous time Fourier transform,4.2 The Fourier Transform for Periodic Signal,Periodic signal:,thus,Example 4.6 4.7 4.8,4 The continuous time Fourier transform,4.3 Properties of the Continuous time Fourier Transform,then,If,4.3.1 Linearity,4 The continuous time Fourier transform,Example 4.9,then,If,4.3.2 Time Shifting,4 The continuous time Fourier transform,4.3.3 Conjugation and Conjugate Symmetry,then,(1) If,then,(2) If,4 The continuous time Fourier transform,then,(3) If,4 The continuous time Fourier transform,4.3.4 Differentiation and Integration,then,(1) If,then,(2) If,Example 4.12,4 The continuous time Fourier transform,4.3.5 Time and Frequency Scaling,then,If,Especially,4 The continuous time Fourier transform,4.3.6 Duality,then,If,Example 4.13,4 The continuous time Fourier transform,4 The continuous time Fourier transform,4.3.7 Parsevals Relation,then,If,Example 4.14,4 The continuous time Fourier transform,4.4 The Convolution Property,Consider a LTI system:,Example 4.15 4.16 4.17 4.19 4.20,4.4.1 Examples,4 The continuous time Fourier transform,4 The continuous time Fourier transform,4.5 The Multiplication Property,The multiplication(modulation) property:,Example 4.21 4.22 4.23,4 The continuous time Fourier transform,4 The continuous time Fourier transform,4.5.1 Frequency-Selective Filtering with Variable Center Frequency,A Bandpass Filter :,4 The continuous time Fourier transform,4 The continuous time Fourier transform,4.6 Tables of Fourier Properties and of Basic Fourier Transform Pairs,Table 4.1Table 4.2,4 The continuous time Fourier transform,4.7 System Characterized by Linear Constant- Coefficient Differential Equation,Constant-coefficient differential equation:,Fourier