shamieh
- 538
- 0
Write the piecewise function
\[ f(t) = \begin{cases}
2t, & 0\leq t < 3 \\
6, & 3 \le t < 5 \\
2t, & t \ge 5 \\
\end{cases}
\]
in terms of unit step functions.
So here is what i;ve got just guessing , I don't think I'm correct. I really need some help. But I got:
$f(t) = 2t[u(t-0) - u(t-3)] + 6[u(t-3) - u(t-5)] + 2t[u(t-5) - u(t - \infty)]$
Which becomes
$f(t) = 2t[u(t) - u(t-3)] + 6[u(t-3) - u(t-5)] + 2t[u(t-5)]$
\[ f(t) = \begin{cases}
2t, & 0\leq t < 3 \\
6, & 3 \le t < 5 \\
2t, & t \ge 5 \\
\end{cases}
\]
in terms of unit step functions.
So here is what i;ve got just guessing , I don't think I'm correct. I really need some help. But I got:
$f(t) = 2t[u(t-0) - u(t-3)] + 6[u(t-3) - u(t-5)] + 2t[u(t-5) - u(t - \infty)]$
Which becomes
$f(t) = 2t[u(t) - u(t-3)] + 6[u(t-3) - u(t-5)] + 2t[u(t-5)]$