Examveda

The impulse response of a causal, linear, time-invariant, continuous-time system is h(t). The output y(t) of the same system to an input x(t), where x(t) = 0 for t < -2, is

A. $$\int\limits_0^t {h\left( \tau \right)x\left( {t - \tau } \right)d\tau } $$

B. $$\int\limits_{ - 2}^t {h\left( \tau \right)x\left( {t - \tau } \right)d\tau } $$

C. $$\int\limits_{ - 2}^{t - 2} {h\left( \tau \right)x\left( {t - \tau } \right)d\tau } $$

D. $$\int\limits_0^{t + 2} {h\left( \tau \right)x\left( {t - \tau } \right)d\tau } $$

Answer: Option D


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