Question

Compute u (t) convolved with itself?

(a) y(t)=t.u(t)

(b) y(t)=u(t)

(c) y(t)=t^2.u(t)

(d) y(t)=t.u(t-1)

I had been asked this question in an international level competition.

I'd like to ask this question from Convolution : Impulse Response Representation for LTI Systems in chapter Time Domain Representation for LTI Systems of Signals and Systems

Answer 1

The correct answer is (a) y(t)=t.u(t)

To elaborate: By taking x (t) = u (t) and h (t) = u (t) and substituting in the integral

 On solving the given integral we get y (t) = t u (t).