Question: Sampling Function vs Impulse Train

[TecHNooB]

How come these two functions are used interchangebly? A sampling function is supposed to be a square wave with a very small duty cycle, but at least the height is still finite. A delta function has infinite height and zero width. It seems like both square wave and dirac train are used as sampling functions interchangebly.

In my signals book, an 'impulse train' or dirac train is used to sample a function. In lab, a rectangle wave with a very small duty cycle (so that it resembles an impulse train) is used to sample a function. The rectangle wave makes sense to me because the height of the rectangle waves is finite. The infinite height dirac train is what confuses me. Explain?

 

[Leros]

The dirac delta train seems more like a nice theoretical sampling function. In the real world, sampling takes a finite amount of time and is better represented by a rectangle wave.