1
GATE ECE 1997
+2
-0.6
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
A
a rectangular pulse
B
a delta function
C
a sine pulse
D
a triangular pulse
2
GATE ECE 1997
+2
-0.6
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.
A
(1 - A), (2 - C)
B
(I - B), (2 - C)
C
(1 - D), (2 - C)
D
(1 - A), (2 - D)
3
GATE ECE 1997
+1
-0.3
The Laplace Transform of eat .cos$$\left( {\alpha t} \right).u\left( t \right)$$ is equal to
A
$${{\left( {s - \alpha } \right)} \over {{{\left( {s - \alpha } \right)}^2} + {\alpha ^2}}}$$
B
$${{\left( {s + \alpha } \right)} \over {{{\left( {s + \alpha } \right)}^2} + {\alpha ^2}}}$$
C
$${1 \over {{{\left( {s - \alpha } \right)}^2}}}$$
D
none of the above
4
GATE ECE 1997
Subjective
+2
-0
Match each of the items 1, 2 on the left with the most appropriate item A, B, C or D on the right.

In the case of a linear time invariant system

List - 1
(1) Poles in the right half plane implies.
(2) Impulse response zero for $$t \le 0$$ implies.

List - 2
(A) Exponential decay of output
(B) System is causal
(C) No stored energy in the system
(D) System is unstable

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