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Lesson 3

Linear system. Lesson 3. Signals and systems. Linear system. (1) Unit step function. Shift a. Linear system. Area=1. Amplitude. width. (2) Unit impulse function. Linear system. (3) Unit doublet function. Linear system. …. Sampling. Linear system. (4) sign function.

simon-barnes
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Lesson 3

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  1. Linear system Lesson 3 Signals and systems

  2. Linear system (1) Unit step function Shift a Meiling CHEN

  3. Linear system Area=1 Amplitude width (2) Unit impulse function Meiling CHEN

  4. Linear system (3) Unit doublet function Meiling CHEN

  5. Linear system … Sampling Meiling CHEN

  6. Linear system (4) sign function (5) Unit ramp signal Meiling CHEN

  7. Linear system (6) parabolic signal (7) sinc signal Meiling CHEN

  8. Linear system Signal Classification • Periodic and aperiodic • Even and odd • Real and complex • Continuous-time and discrete-time • Deterministic and stochastic (random) • Causal and noncausal Meiling CHEN

  9. Linear system Periodic signals Even signals odd signals Meiling CHEN

  10. Linear system Causal signals Anticausal signals Meiling CHEN

  11. Linear system Causal and noncausal system Example: distinguish between causal and noncausal systems in the following: (1) Case I Noncausal system Meiling CHEN

  12. Linear system (2) Case II Delay system causal system (3) Case III causal system At present past Meiling CHEN

  13. Linear system (4) Case IV noncausal system At present future (5) Case V noncausal system Meiling CHEN

  14. Linear system Signal operations • Simple operation : ＋、－ • Convolution : * Meiling CHEN

  15. Linear system simple operation Meiling CHEN

  16. Linear system Convolution Integral : Linear system Linear system … Meiling CHEN

  17. Linear system Linear system I.C.=0 Impulse response Transfer function of the system Linear system I.C.=0 Any input Zero state response Meiling CHEN

  18. Linear system Example : Graphical convolution (1) Meiling CHEN

  19. Linear system (2) (3) Meiling CHEN

  20. Linear system (4) (5) Meiling CHEN

  21. Linear system Ans: Meiling CHEN

  22. Linear system Laplace and convolution integral Algebra operator Meiling CHEN

  23. Linear system Example Meiling CHEN

  24. Linear system Hint: Meiling CHEN

  25. Laplace transform For causal signals pass through linear time-invariant causal systems Complex frequency Meiling CHEN

  26. Linear system Laplace transform properties Meiling CHEN

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