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

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

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

A deterministic signal x(t) = $$\cos (2\pi t)$$ is passed through a differentiator as shown in Figure.
(a) Determine the autocorrelation R_xx ($$\tau $$) and the power spectral density S_xx(f).
(b) Find the output power spectral density S_yy( f ).
(c) Evaluate R_xy(0) and R_xy(1/4).