Is the Resultant of Combining Unit Step Functions Still a Unit Step Function?

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Discussion Overview

The discussion centers on the behavior of unit step functions when combined through addition or subtraction. Participants explore whether the resultant function maintains the properties of a unit step function, particularly focusing on the value at discontinuities and the overall magnitude of the resultant function.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions if subtracting two delayed unit step functions results in a unit step function and asks about the value at the last point, suggesting it could be 0 or 1.
  • Another participant suggests that different segments of the input functions need to be dealt with separately, implying complexity in the combination of step functions.
  • One participant recommends drawing the functions to visualize the addition and subtraction, indicating that a pictorial representation could clarify the outcome.
  • Repeated inquiries about the existence of a discontinuity at the last point when subtracting two unit step functions highlight confusion about the behavior of the resultant function.
  • A participant emphasizes that the determination of the last point depends on the specific step functions being analyzed, suggesting that graphical representation would aid in understanding the resultant behavior.

Areas of Agreement / Disagreement

Participants express differing views on the behavior of the resultant function when combining unit step functions, with no consensus reached on whether the resultant is still a unit step function or the nature of discontinuities.

Contextual Notes

Limitations include the need for specific definitions of the step functions involved and the potential for varying interpretations of the resultant function based on graphical representation.

veralika
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if you subtract two delayed unit step functions, is the resultant a unit step function too? what is the value at the last point? 0 or 1? similarly, if you add 2 unit step functions will the magnitude of the resultant funtion be 1 or 2?
 
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not exactly, you need to deal with different segements of you input function separately.
 
Just draw them out and do the additions and subtractions that way. The step function is rather simple so a quick pictoral representation should show you your answer.
 
Born2bwire said:
Just draw them out and do the additions and subtractions that way. The step function is rather simple so a quick pictoral representation should show you your answer.

i still don't get it. could u just tell me that when u subtract 2 unit step functions, will there or will there not be a discontinuity at the last point?
 
veralika said:
i still don't get it. could u just tell me that when u subtract 2 unit step functions, will there or will there not be a discontinuity at the last point?

What is the last point? This depends completely on what the actual step functions are that you are operating on. Just draw the step functions out on a graph, one above the other and it should be apparent how the resultant plot should look like when you add or subtract the two.
 

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