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Math Help - Expressing x(t) and h(t) in terms of unit step function

  1. #1
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    Expressing x(t) and h(t) in terms of unit step function

    It seems that I am on a conflict, because I have read few things, but it seems that I am rather confused now.
    We have these two functions:


    So I believe that the answer should be something like this : x(t) = 1 u(t) , and h(t)= t u(t). I am really not sure if it right . Anyone could verify it or provide me with some path ? Thanks!
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  2. #2
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    Re: Expressing x(t) and h(t) in terms of unit step function

    Hi Duskfall.

    I assume you are using the definition u(t) = 1 for all t >= 0, and u(t) = 0 for all t < 0.

    Then x(t) = u(t)*u(T-t) and h(t) = t*u(t)*u(2T-t). The extra factors u(T-t) and u(2T-t) in a sense "turn off" the functions at the appropriate values of t for each function, T for x(t) and 2T for h(t).

    Hope this helps.
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