Convolution with time shifted step function.

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Convolution involving the time-shifted step function x(t) = u(t-1) can be approached by adjusting the limits of integration from 0 to t, changing them to 1 to t. This adjustment is valid because the unit-step function serves primarily to modify the integration limits. The discussion emphasizes that the unit-step function's role is to define the active region of the convolution. Understanding this concept is crucial for correctly performing convolution with shifted functions. Properly applying these limits ensures accurate results in signal processing contexts.
seang
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How do you go about convolving when x(t) = u(t-1)? Can you just make the limits of integration 1 to t instead of 0 to t?
 
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Yes this is what it does, the only use of the unit-step function inside the integral is to change the limits
 

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