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?

 

"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.

 

"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

 

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..

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

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

 

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

 

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.

 

Oh my god ! Great !!. Iam just starting my career! Great to get clarified on my doubts from you!

To More Clarifications from you !

D

 

Raising a glass to return that fine toast.