So the most important basic function that you want to discuss is unit

impulse function, so which can be defined with a rectangular function as shown here.

So this rectangular function, so P delta tao t is our rectangular function,

with height is 1 over delta tau and

the width is delta tau, from here to here.

So if we take delta tau to be 0, so make this delta tau infinitely small.

So this area is just 1, because the width is delta tau,

and the height is 1 over delta tau.

So the area is going to be 1, and

if we take limitation of delta tau to be infinitely small, 0.

And then what will happen to this rectangular function?

And then its width is going to be infinitely small, but

its height is going to go to the infinity.

But the area of this signal is not 0, so it's going to be 1.

So area is 1.

So this function is called unit impulse function, or

delta function, or it can be called many different names.

But it's typically denoted as this delta t.

And also typically presented by this arrow, and we represent the value.

So this value is the area of this arrow.

So arrow does not have area, typically.

So line does not have area.

But this looks like line, but it has an area.

So that's a little bit confusing to understand initially.

So this is conceptual function, so that does not literally exist.

So infinite at t = 0, 0 when t is not 0,

the sum of total area is 1.

So it's often called Dirac delta function, denoted as delta t.

So any post that has area 1 and is too short and too high to be displayed,

can be used to define this delta function, or unit impulse function.

The division of delta t doesn't have to be based on a rectangular shape, or

it can be used as a Gaussian or sinc.

Also mathematical function, that does not use this in the real world and

it's useful to understand the concept of sampling.