If the step response of a causal, linear time-invariant system is a(t), then the response of the system to a general input x(t) would be

A. $$\int\limits_{{0^ + }}^t {\frac{{da\left( \tau \right)}}{{d\tau }}x\left( {t - \tau } \right)d\tau } $$

B. $$a\left( 0 \right)x\left( t \right) + \int\limits_{{0^ + }}^t {\frac{{da\left( \tau \right)}}{{d\tau }}x\left( {t - \tau } \right)d\tau } $$

C. $$x\left( 0 \right)a\left( t \right) + \int\limits_{{0^ + }}^t {x\left( \tau \right)a\left( {t - \tau } \right)d\tau } $$

D. $$x\left( 0 \right)a\left( t \right) + \int\limits_{{0^ + }}^t {\frac{{da\left( \tau \right)}}{{d\tau }}x\left( {t - \tau } \right)d\tau } $$

Answer: Option A