Can u(t-2)u(t-a) be simplified in unit step function analysis?

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SUMMARY

The expression u(t-2)u(t-a) can be simplified based on the value of 'a'. Specifically, if 'a' is less than or equal to 2, the expression simplifies to u(t-2). Conversely, if 'a' is greater than 2, the expression simplifies to u(t-a). This conclusion is derived from analyzing the behavior of the unit step function, which takes values of either 0 or 1 depending on the value of 't'. Graphical representation further confirms this simplification.

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Homework Statement


I need this to answer a question, its not a homework question itself. Can this be simplified? u(t-2)u(t-a) where u is the unit step function.


Homework Equations


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The Attempt at a Solution


I know the answer is u(t-2) if a <= 2, u(t-a) otherwise. But is there a better way to express this?
 
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Unit step functions are either 0 or 1, depending on the value of t. Look at two cases for a: a < 2 and a > 2, and sketch a graph of u(t - 2) * u(t - a) for each case. (If a = 2, the graph of u(t - 2) * u(t - a) looks exactly like the graph of u(t - 2).)
 

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