Why Does Changing Intervals and Arguments Affect Convolution Integrals?

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SUMMARY

The discussion centers on the effects of changing intervals and arguments in convolution integrals, particularly when convolving two pulses defined from -1 to +1. It is established that altering the integration limits results in the H function no longer being equal to 1 within the new interval, as the '1' part of the H function is excluded. The convolution integral evaluates to zero outside the defined range of the pulses, which clarifies the confusion regarding the transition indicated by the red arrow.

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  • Understanding of convolution integrals
  • Familiarity with pulse functions
  • Knowledge of the Heaviside step function (H function)
  • Basic principles of integration limits
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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
 
Last edited:
Engineering news on Phys.org
sorry wrong forum
 
The reason the integration limits change is because you're convolving two pulses that are only defined from -1 to +1, so the convolution is just 0 for all intervals other than -1 to +1.
 

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