The impulse response of a system is h(t) = tu(t). For an input u(t - 1), the output is

A. $${{{t^2}} \over 2}u\left( t \right)$$

B. $${{t\left( {t - 1} \right)} \over 2}u\left( {t - 1} \right)$$

C. $${{{{\left( {t - 1} \right)}^2}} \over 2}u\left( {t - 1} \right)$$

D. $${{{t^2} - 1} \over 2}u\left( {t - 1} \right)$$

Answer: Option C