# Need help, a question about energy!!!

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!!!

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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?

#### dcbingaman

Joined Jun 30, 2021
495
Now that I have looked up the Rect function on Wikipedia that Papabravo brought up, it makes a little more sense.

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#### Papabravo

Joined Feb 24, 2006
17,245
Zero is more powerful than a number that approaches -∞, even exponentially.

#### 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!!!