Need help, a question about energy!!!

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Jade.nguyen1

Joined Oct 6, 2021
1
I'm taking signal and system class and this is a question about energy. I need to take integral of the signal to calculate the energy, but I'm stuck on the unit rectangle function. Please help me with it!!!Screen Shot 2021-10-06 at 3.15.58 PM.png
Screen Shot 2021-10-06 at 3.21.05 PM.png
 
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Papabravo

Joined Feb 24, 2006
17,245
If I understand the meaning of the unit rectangle, it permits you to change the limits of integration and replace the rectangle function with a constant value of 1 between the limits of integration. Now it is just an ordinary definite integral.

EDIT: I'm not certain if the actual value of 1/2 at the limit(s) is important or not. My sense is that the answer is no, but I could be wrong. I think if the limits are 2+ and 4-, where 2+ is infinitesimally larger than 2 and 4- is infinitesimally smaller than 4, you will get the correct result using one of the possible definitions for the rect(t) function.

From the Wikipedia article:
Alternative definitions of the function define \( \text {rect}\left(\pm {\frac {1}{2}}\right) \) to be 0, 1, or undefined.
 
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dcbingaman

Joined Jun 30, 2021
495
I am a little confused by the question. We are taking it from negative infinity? Taking e to the power of a negative t gives a positive value that grows infinitely large as t becomes more and more negative. If this represents energy in joules as a function of time. Then if I go back say to t=-1,000,000,000 to t=0, I will get an insanely large amount of energy. In fact I can get as much as I want by simply making -t larger and larger?
 

MrChips

Joined Oct 2, 2009
24,610
I'm taking signal and system class and this is a question about energy. I need to take integral of the signal to calculate the energy, but I'm stuck on the unit rectangle function. Please help me with it!!!
Thread title police here.
Every thread starter Needs Help!!!
Can you please come up with a more informative title next time?
 
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