Signals and Systems Practice Test

In an LTI (linear time-invariant) system, the impulse response h(t) is defined as the output when the input is a Dirac delta signal δ(t). This is because, for any input x(t), the output is the convolution x(t) * h(t). The Dirac delta acts as the identity for convolution, so feeding δ(t) directly reveals h(t) itself: y(t) = δ(t) * h(t) = h(t).

The other inputs produce different responses: a unit step gives the step response (the integral of h(t) if the system is causal), a sine wave produces a steady-state response related to the system’s frequency response, and a ramp yields a response tied to the system’s integration properties. None of these equal the impulse response itself.