1
GATE ECE 2005
+2
-0.6
For a signal x(t) the Fourier transform is X(f). Then the inverse Fourier transform of X(3f+2) is given by
A
$${1 \over 2}\,x\left( {{t \over 2}} \right){e^{j3\pi t}}$$
B
$${1 \over 3}\,x\left( {{t \over 3}} \right){e^{ - j4\pi t/3}}$$
C
$$3\,x(3t){e^{ - j4\pi t}}$$
D
$$x(3t + 2)$$
2
GATE ECE 2004
+2
-0.6
Let x(t) and y(t) (with Fourier transforms X(f) and Y(f) respectively) be related as shown in Fig.(1) & (2).

Then Y(f) is

A
$$- {1 \over 2}X(f/2){e^{ - j2\pi f}}$$
B
$$- {1 \over 2}X(f/2){e^{j2\pi f}}$$
C
$$- X(f/2){e^{j2\pi f}}$$
D
$$- X(f/2){e^{ - j2\pi f}}$$
3
GATE ECE 2000
+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
$$\sin {\omega _1}t + \,\sin {\omega _2}t$$
4
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
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