How is $\delta(at+b)=\frac{1}{|a|}\delta(t+b/a)$?

1. What does the delta function do?
2. Why Dirac delta is not a function?
3. Is delta function continuous?
4. What is delta function in signals and systems?

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.

Why Dirac delta is not a function?

The integral of this function is zero for all α in the Lebesgue sense. There is clearly no function, defined in the classical sense, that has properties (1) and (2). latter is a special case of the former when f(x) = 1. This is sometimes called the “sifting” property of the Dirac delta function.

Is 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 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.