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Signals and Systems Lecture 24

Signals and Systems Lecture 24. The Laplace Transform ROC of Laplace Transform Inverse Laplace Transform. Chapter 9 The Laplace Transform. Chapter 9 The Laplace Transform. Defining. §9.1 The Laplace Transform.

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Signals and Systems Lecture 24

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  1. Signals and SystemsLecture 24 The Laplace Transform ROC of Laplace Transform Inverse Laplace Transform

  2. Chapter 9 The Laplace Transform

  3. Chapter 9 The Laplace Transform Defining §9.1 The Laplace Transform ——Laplace Transform 1. The relationship

  4. Chapter 9 The Laplace Transform Dirichlet Condition 1 : ROC：对给定的 ，使其拉氏变换存在的σ对应的 S平面上的区域。 2. Region of Convergence（收敛域）

  5. Chapter 9 The Laplace Transform Example 9.2 pole-zero plot Example 9.1 pole-zero plot 零极点图

  6. Chapter 9 The Laplace Transform Particularly, The Fourier transform of does not exist.

  7. Chapter 9 The Laplace Transform Example 9.3

  8. Chapter 9 The Laplace Transform Example 9.3

  9. Chapter 9 The Laplace Transform Example 9.4 pole-zero plot does not exist. entire S plane

  10. Chapter 9 The Laplace Transform Zeros: Poles: ROC of X(s) 1. The direction of signals 2. The position of poles §9.2 The Properties of ROC Property 1: The ROC of X(s) consists of strips parallel to the jω-axis in the s-plane ——Depends only on σ

  11. Chapter 9 The Laplace Transform Property 3: If is of finite duration and is absolutely integrable, then the ROC is the entire s-plane. ① when Property 2: For rational Laplace transforms, the ROC does not contain any poles.

  12. Chapter 9 The Laplace Transform

  13. Chapter 9 The Laplace Transform Example 零极点 抵消 pole: zero: zeros: pole-zero plot

  14. Chapter 9 The Laplace Transform Property 4: If is right sided, finite

  15. Chapter 9 The Laplace Transform Property 5: If is left sided, Property 6: If is two sided, ROC:

  16. Chapter 9 The Laplace Transform has no Laplace transform. Example 9.7 If b>0, If b≤0,

  17. Chapter 9 The Laplace Transform Property 7: If the Laplace transform of is rational, ① is right sided, ② is left sided, Example 9.8 left sided right sided two sided

  18. Chapter 9 The Laplace Transform Basic Laplace Pairs Poles ROC none

  19. Chapter 9 The Laplace Transform ROC of X(s) 1. The direction of signals 2. The position of poles

  20. Chapter 9 The Laplace Transform 1. 2. 3.

  21. Chapter 9 The Laplace Transform Example 9.9 defining Determine the inverse Laplace transform for all possible ROC. §9.3 The Inverse Laplace Transform

  22. Summary • The Laplace Transform and its RoC • Inverse Laplace Transform

  23. Problem Set • P724 9.21 (a) (b) • P725 9.22 (a) (b)

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