1
GATE ECE 2000
MCQ (Single Correct Answer)
+2
-0.6
The Hilbert transform of $$\left[ {\cos \,{\omega _1}t + \,\sin {\omega _2}t\,} \right]$$ is
A
$$\sin \,{\omega _1}t + \,\cos {\omega _2}t$$
B
$$\sin \,{\omega _1}t + \,\cos {\omega _2}t$$
C
$$\cos \,{\omega _1}t + \,\sin {\omega _2}t$$
D
$$\sin {\omega _1}t + \,\sin {\omega _2}t$$
2
GATE ECE 1997
MCQ (Single Correct Answer)
+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
3
GATE ECE 1997
MCQ (Single Correct Answer)
+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)
4
GATE ECE 1996
MCQ (Single Correct Answer)
+2
-0.6
The autocorrelation function of an energy signal has
A
no symmetry
B
conjugate symmetry
C
odd symmetry
D
even symmetry
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