Define a rectangular pulse p(t) = u(t+1)-u(t-1) =
{
1, -1≤ t ≤1
0, otherwise
1. An LTI system has an impulse response h(t) = tu(t-5). If the input
is x(t) = t²[u(t-1) - u(t-3)], find the output.
2. Determine whether the contintuous-time LTI systems characterized by
the following impulse responses are causal or non-causal, stable or non-
stable.
(a) h(t) = e^tu(-t)
(b) h(t) = (-t)e-tu(-t)
(c) h(t) = e-12t
(d) h(t) = p(t/2).
(e) h(t) = d(t) + e-stu(t)
3. Are the LTI systems with the following impulse responses invertible?
If invertible, find the inverse system.
(a) h(t) = 3d(t+3)
(b) h(t)=(t-3) + (t - 5).
4. Consider a circuit with a voltage source, v(t), a resistor with resistance
R, and a capacitor with capacitance C connected in serise. If the input
of the system is the voltage source v(t), and the output of the system
is the voltage across the capacitor, v(t). Write the system equation in
the form of a differential equation.
