The Fourier transform F $$\left\{ {{e^{ - t}}u(t)} \right\}$$ is equal to $${1 \over {1 + j2\pi f}}$$. Therefore, $$F\left\{ {{1 \over {1 + j2\pi t}}} \right\}$$ is

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

The Laplace transform of a continuous - time signal x(t) is $$X\left( s \right) = {{5 - s} \over {{s^2} - s - 2}}$$. If the Fourier transform of tyhis signal exists, then x(t) is

If the impulse response of a discrete-time system is $$h\left[ n \right]\, = \, - {5^n}\,\,u\left[ { - n\, - 1} \right],$$ then the system function $$H\left( z \right)\,\,\,$$ is equal to