The impulse response h(t) of a linear time-invariant continuous time system is described by $$h\left( t \right) = \,\,\exp \left( {\alpha t} \right)u\left( t \right)\,\,\, + \,\,\exp \left( {\beta t} \right)u\left( { - t} \right),$$ where u(t) denotes the unit step function, and $$\alpha $$ and $$\beta $$ are real constants. This system is stable if

Which of the following can be impulse response of a causal system?

Let x(t) be the input to a linear, time-invariant system. The required output is 4x(t - 2). The transfer function of the system should be

Convolution of x(t + 5) with impulse function $$\delta \left( {t\, - \,7} \right)$$ is equal to