1 / 19

Lecture #06

Lecture #06. Laplace Transform. Eigenfunction. A. LTI system. h(t) is the impulse response of the LTI system According to the convolution:. We define that. We identify as an eigenfunction of the LTI system and H(s) as the corresponding eigenvalue. In which s is a complex frequency.

apu
Download Presentation

Lecture #06

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Lecture #06 Laplace Transform signals & systems

  2. Eigenfunction A signals & systems

  3. signals & systems

  4. LTI system h(t) is the impulse response of the LTI system According to the convolution: We define that signals & systems

  5. We identify as an eigenfunction of the LTI system and H(s) as the corresponding eigenvalue. In which s is a complex frequency Is the Fourier transform of signals & systems

  6. Laplace transform Inverse Laplace transform signals & systems

  7. Unilateral Laplace transform for causal system signals & systems

  8. Laplace transform properties signals & systems

  9. Time convolution signals & systems

  10. If is continuous at and may different and if is not impulse function or derivative of impulse function, then Initial Value Theorem Initial-Value Theorem Example 1 signals & systems

  11. If and are Laplace transformable, if exists and if is analytic on the imaginary axis and in right half of the s-plane, then Final Value Theorem Final-Value Theorem • No any pole on the imaginary axis or in right half of s-plane. • System is stable. signals & systems

  12. Example 2 Example 3 not exist signals & systems

  13. If include impulse function at . Remark 1 Example 4 Remark 2 Example 5 signals & systems

  14. Case I simple root where Inverse Laplace transform F(s) is a strictly proper rational function Degree of denominator signals & systems

  15. Example 6 or or or signals & systems

  16. Case II complex root Inverse Laplace transform let signals & systems

  17. Example 7 signals & systems

  18. Case III repeated root Inverse Laplace transform signals & systems

  19. Example 8 signals & systems

More Related