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Step function product

  1. Aug 19, 2010 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant equations

    3. 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?
  2. jcsd
  3. Aug 19, 2010 #2


    Staff: Mentor

    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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