Understanding Convolution Integral Changes and the Effect on H Function

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SUMMARY

The discussion focuses on the effects of changing intervals in the convolution integral and its impact on the H function. Specifically, it highlights that altering the interval results in the H function no longer being equal to 1, as the '1' portion is removed. The participants clarify that within the interval 0 <= t <= 1, the expression H(t+1) - H(t-1) equals 1, while outside this interval, it equals 0. The conversation emphasizes the importance of understanding these transitions for accurate mathematical modeling.

PREREQUISITES
  • Understanding of convolution integrals
  • Familiarity with the Heaviside step function (H function)
  • Knowledge of interval notation in mathematics
  • Basic calculus concepts related to integration
NEXT STEPS
  • Study the properties of the Heaviside step function in detail
  • Learn about convolution integrals and their applications in signal processing
  • Explore interval changes and their effects on mathematical functions
  • Investigate simplification techniques in integral calculus
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Mathematicians, engineers, and students studying signal processing or control systems who seek to deepen their understanding of convolution integrals and the Heaviside function.

nhrock3
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cant understand the red arrow transition
i changes the intervals and i cuts half of the arguent inside the integral
i can't see why
?

regarding the interval change
the H function is 1 in a certain interval
so if they change the integrval then its no longer H inside
because we have taken the '1' part of the H
??

regarding the cutting in half the argument inside the integral
i have no idea
 
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On the interval 0 <= t <= 1, we have H(t+1) - H(t-1) = 1. Outside that interval, H(t+1) - H(t-1) = 0. The steps the author skips here are just simplifying steps. Can you get the rest from here? I hope this helps.
 
thanks
:)
 

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