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The unit step response of an LTI system

The unit step response of an LTI system. The unit step response of an LTI system. The unit step response of an LTI system. Linear constant-coefficient difference equations. +. delay. depends on x[n]. We don’t know y[n] unless x[n] is given.

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The unit step response of an LTI system

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  1. The unit step response of an LTI system

  2. The unit step response of an LTI system

  3. The unit step response of an LTI system

  4. Linear constant-coefficient difference equations + delay depends on x[n]. We don’t know y[n] unless x[n] is given. But h[n] doesn’t depend on x[n]. We should be able to obtain h[n] without x[n]. How? • LTI system response properties, this chapter. • Discrete Fourier transform, --- Ch. 5.

  5. Linear constant-coefficient difference equations + delay When n 1, Causality

  6. Linear constant-coefficient difference equations + delay Determine A by initial condition: When n = 0, A = 1

  7. Linear constant-coefficient difference equations + delay Two ways: (1) Repeat the procedure (2)

  8. The unit step response of an LTI system, continuous time

  9. Linear constant-coefficient difference equations + depends on x(t). We don’t know y(t) unless x(t) is given. But h(t) doesn’t depend on x(t). We should be able to obtain h(t) without x(t). How? • LTI system response properties, this chapter. • Continuous time Fourier transform.

  10. Linear constant-coefficient difference equations + When t>0, Causality Determine A by initial condition:

  11. Linear constant-coefficient difference equations + Determine A by initial condition: A = 1

  12. Linear constant-coefficient difference equations +

  13. Singularity functions Define:

  14. Singularity functions

  15. Singularity functions k terms

  16. Singularity functions

  17. Singularity functions --- discrete time Define:

  18. Singularity functions --- discrete time Define:

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