Why is the Dirac delta used when sampling continuous signals?

1. What is the purpose of the Dirac delta function?
2. Is the Dirac delta function continuous?
3. What is the sampling property of the delta function?
4. What is delta sampling?

What is the purpose of the Dirac delta function?

The Dirac delta is used to model a tall narrow spike function (an impulse), and other similar abstractions such as a point charge, point mass or electron point. For example, to calculate the dynamics of a billiard ball being struck, one can approximate the force of the impact by a Dirac delta.

Is the Dirac delta function continuous?

The Dirac delta function, often referred to as the unit impulse or delta function, is the function that defines the idea of a unit impulse in continuous-time. Informally, this function is one that is infinitesimally narrow, infinitely tall, yet integrates to one.

What is the sampling property of the delta function?

The Dirac delta function, δ(x), is a handy tool for sampling theory. It has zero width, infinite height, and unit area. For sampling, the delta function has two important properties. = 1/T.

What is delta sampling?

Delta sampling is used for expressions with counters that are identified based on delta (difference) from one sample to the next. Delta sampling requires the application to do continuous sampling, because it uses the value of the last sample.