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Mastering Laplace Transform: Analysis of Signals and Systems

Explore Laplace transform definitions, properties, convolution, LTI system analysis, inverse transform, and more in MATLAB. Gain insights into complex frequency analysis, pole-zero positions, stability, and solutions to differential equations.

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Mastering Laplace Transform: Analysis of Signals and Systems

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  1. Signals and SystemsUsing MATLABLuis F. Chaparro

  2. Chapter 3 - The Laplace Transform

  3. What is in this chapter? • Definition of Laplace transform • Properties of Laplace transform • Inverse Laplace transform • Convolution sum and Laplace • Analysis of LTI systems using Laplace transform • Convolution integral • System interconnection 3

  4. Signals and LTI systems 4

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  12. One-sided Laplace Transform 12

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  15. 15

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  17. 17

  18. 18

  19. Linearity 19

  20. 20

  21. 21

  22. Derivative 22

  23. 23

  24. 24

  25. Time Shifting 25

  26. 26

  27. Convolution integral 27

  28. Inverse Laplace Transform 28

  29. 29

  30. 30

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  47. What have we accomplished? • Complex frequency analysis of signals • Significance of location of poles and zeros • Convolution integral computation and transfer function • BIBO stability and pole location • Solution of differential equations, transient and steady state responses, zero-input and zero-state responses Where do we go from here? • Steady-state analysis using Fourier for periodic and aperiodic signals • Significance of complex exponentials as inputs of LTI systems • Sinusoidal representation of periodic signals • Connection of Laplace and Fourier transforms 47

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