Definition of sampling using delta or indicator function?

1. What does the delta function do?
2. What is Delta function in signals and systems?
3. How does a Dirac delta function differ from a unit step function?
4. Is the indicator function continuous?

What does the delta function do?

The Dirac delta function is an important mathematical object that simplifies calculations required for the studies of electron motion and propagation. It is not really a function but a symbol for physicists and engineers to represent some calculations.

What is Delta function in signals and systems?

The delta function is a normalized impulse, that is, sample number zero has a value of one, while all other samples have a value of zero. For this reason, the delta function is frequently called the unit impulse. The second term defined in Fig. 6-1 is the impulse response.

How does a Dirac delta function differ from a unit step function?

The definition of Dirac delta function states that it gives a value of ∞ at t=0 and 0 elsewhere. But, the definition of unit impulse function states that it gives a value of 1 at t=0 and 0 elsewhere.

Is the indicator function continuous?

Very often we come across indicator functions denoting class membership. These functions in their native form are neither continuous nor differentiable.