The function f(t) has the Fourier Transform g($$\omega $$). The Fourier Transform of $$$g(t) = \left( {\int\limits_{ - \infty }^\infty {g(t){e^{ - j\omega t}}} } \right)\,is$$$

The power spectral density of a deterministic signal is given by $${\left[ {\sin (f)/f} \right]^2}$$, where 'f' is frequency. The autocorrelation function of this signal in the time domain is

If the Fourier Transfrom of a deterministic signal g(t) is G (f), then

Item-1
(1) The Fourier transform of g (t - 2) is
(2) The Fourier transform of g (t/2) is

Item - 2
(A) G(f) $$e^{-j\left(4\mathrm{πf}\right)}$$
(B) G(2f)
(C) 2G(2f)
(D) G(f-2)

Match each of the items 1, 2 on the left with the most appropriate item A, B, C or D on the right.

The Laplace Transform of e_at .cos$$\left( {\alpha t} \right).u\left( t \right)$$ is equal to