Question

The running integrator, given by y(t) = \(∫_{-∞}^∞ x(t) \,dt\) has ____________

(a) No finite singularities in it’s double sided Laplace transform Y(s)

(b) Produces an abounded output for every causal bounded input

(c) Produces a bounded output for every anti-causal bounded input

(d) Has no finite zeroes in it’s double sided Laplace transform Y (s)

This question was posed to me in an online interview.

My question comes from Fourier Analysis topic in portion Fourier Analysis on Complex Spaces of Signals and Systems

Answer 1

Correct option is (b) Produces an abounded output for every causal bounded input

Explanation: The running integrator \(∫_{-∞}^t x(t)\,dt = 0\) for every causal system. As causal systems have no memory and the initial value is zero, the output is followed by input. So, y (t) will always be bounded if this function is a causal bounded system.