# HOW is the height of a continuous impulse train 1?

#### Vikram50517

Joined Jan 4, 2020
81
WE all know that the height of a continuous time impulse function is infinity . Then how come does each individual pulses of an impulse train is 1?

#### Papabravo

Joined Feb 24, 2006
19,551
"1" is the area under the impulse. That is the integral from -∞ to +∞ of a unit impulse is 1. This is a mathematical abstraction which of course cannot be realized in practice by any physical circuit. It can however be approximated.

#### Vikram50517

Joined Jan 4, 2020
81
"1" is the area under the impulse. That is the integral from -∞ to +∞ of a unit impulse is 1. This is a mathematical abstraction which of course cannot be realized in practice by any physical circuit. It can however be approximated.
Can u give me an idea on how it can be approximated

#### Papabravo

Joined Feb 24, 2006
19,551
Can u give me an idea on how it can be approximated
Sure. Start with a normal distribution having a mean of zero and a variance of 1. The integral from -∞ to +∞ is one. Now in the limit as the variance goes to zero the height of the distribution approaches ∞. At any point along the way it represents an approximation of the unit impulse..

$$f(x,\mu,\sigma)\;=\;\cfrac{1}{\sigma\sqrt{2\pi}}e^\cfrac{-(x-\mu)^2}{2\sigma^2}$$

$$\text{For }x=\mu=0, \text{and }\sigma=0.1, \text{the height will be }\approx 4$$

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#### Vikram50517

Joined Jan 4, 2020
81
Thanks a lot for the intuition!

Just out of curiosity as you had answered several of my questions, do you work somewhere as a signal processing engineer

#### Papabravo

Joined Feb 24, 2006
19,551
Thanks a lot for the intuition!

Just out of curiosity as you had answered several of my questions, do you work somewhere as a signal processing engineer
I used to work in industrial automation controls, but I have been retired since 2014 after a career spanning half a century.

#### Vikram50517

Joined Jan 4, 2020
81
Oh my god ! Great !!. Iam just starting my career! Great to get clarified on my doubts from you!

To More Clarifications from you !

D

#### Papabravo

Joined Feb 24, 2006
19,551
Raising a glass to return that fine toast.