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The Discrete-time Unit Impulse Sequence

The Discrete-time Unit Impulse Sequence. 1. n. 0. Impulse Function. volt. time. Delayed Unit Impulse. The Unit Step Sequence. 1. n. 0. Relationship between Unit Impulse & Unit Step Sequences. Discrete-time unit impulse is the first difference of the discrete-time unit step.

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The Discrete-time Unit Impulse Sequence

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  1. The Discrete-time Unit Impulse Sequence 1 n 0

  2. Impulse Function volt time

  3. Delayed Unit Impulse

  4. The Unit Step Sequence 1 n 0

  5. Relationship between Unit Impulse & Unit Step Sequences Discrete-time unit impulse is the first difference of the discrete-time unit step.

  6. Relationship between Unit Impulse & Unit Step Sequences Discrete-time unit step is the running sum of the discrete-time unit impulse or unit sample.

  7. 1 0 n Interval of summation m n 0 Interval of summation m 0 n

  8. Alternative way of expressing the unit step as the summation (superposition) of delayed unit impulse

  9. Interval of summation k n<0 0 Interval of summation k 0

  10. n 0 n 0 n

  11. The Sampling Property of the Unit Impulse.

  12. n 0 n

  13. The Continuous-time Unit Step 1 0 t

  14. The Continuous-time Unit Impulse Function. 0 t

  15. Relationship between continuous-time unit step and unit impulse.

  16. Integration of Unit Impulse to get Unit Stup 1 t<0 0 Interval of integration 1 0

  17. Discontinuity at t=0, poses problem of differentiation. 1 0

  18. Unit and scaled Impulse 1 t 0 k t 0

  19. Scaled impulse and relationshipof unit step & impulse.

  20. Relationship of Unit and Impulse Interval of integration 1 0 t<0 Interval of integration 1 0

  21. x(t) t 0 x(0) t 0

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