The Discretetime Unit Impulse Sequence 1 0 n

The Discrete-time Unit Impulse Sequence 1 0 n 1

Impulse Function volt time 2

Delayed Unit Impulse 3

The Unit Step Sequence 1 0 n 4

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

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

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

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

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

0 0 n n n 10

The Sampling Property of the Unit Impulse. 11

0 n n 12

The Continuous-time Unit Step 1 0 t 13

The Continuous-time Unit Impulse Function. 0 t 14

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

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

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

Unit and scaled Impulse 1 0 t k 18

Scaled impulse and relationship of unit step & impulse. 19

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

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

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