Thread: 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!

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.