Difference Between Dirac delta and unit impulse 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.

1. Is unit impulse function and Dirac delta function same?
2. What is the difference between delta function and Dirac delta function?
3. Is impulse the same as Delta?
4. What is difference between impulse and unit impulse?

Is unit impulse function and Dirac delta function same?

In mathematics, the Dirac delta distribution (δ distribution), also known as the unit impulse, is a generalized function or distribution over the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one.

What is the difference between delta function and Dirac delta function?

The delta function is a generalized function that can be defined as the limit of a class of delta sequences. The delta function is sometimes called "Dirac's delta function" or the "impulse symbol" (Bracewell 1999). It is implemented in the Wolfram Language as DiracDelta[x].

Is impulse the same as Delta?

IMPULSE: An impulse is the result of a force acting over a time interval. Since an impulse is usually something that takes place over a short time interval, we can say Impulse = F x Delta t. From the above expression of Newton's Second Law, Impulse = Delta P, so it also has the units of momentum.

What is difference between impulse and unit impulse?

In discrete time the unit impulse is the first difference of the unit step, and the unit step is the run- ning sum of the unit impulse. Correspondingly, in continuous time the unit im- pulse is the derivative of the unit step, and the unit step is the running integral of the impulse.