Step Express
Step Express
How to express this function in terms of the unit step functions?
I have a function that I need as a unit step function so I can perform a laplace transformation. One problem, I find unit step functions very difficult for some reason:
f(t) = t when 0 ≤ t < 1
f(t) = 2 - t when t ≥ 1
I can draw the graph but I cannot put it into a linear unit step function. Please help, Thanks!
f(t) = t u(t) – t u(t-1) + (2-t) u(t-1)
The first term on the right turns it on at time t = 0
The second term turns it off at time t = 1
The last term turns on the new form of f at time t = 1
Expanding,
f(t) = t u(t) – t u(t-1) + 2 u(t-1) – t u(t-1)
= t u(t) + (2 – 2t) u (t-1)
= t u(t) – 2(t-1) u(t-1)
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