HOW is the height of a continuous impulse train 1?

Thread Starter

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.
 

Thread Starter

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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Thread Starter

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 :D:D
 

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 :D:D
I used to work in industrial automation controls, but I have been retired since 2014 after a career spanning half a century.
 

Thread Starter

Vikram50517

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

To More Clarifications from you !

:DD
 
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