1
GATE ECE 2016 Set 1
+1
-0.3
Which one of the following is an eight function of the class of all continuous-time, linear, time- invariant systems u(t) denotes the unit-step function?
A
$${e^{j{\omega _0}t}}u(t)$$
B
$$\cos ({\omega _0}t)$$
C
$${e^{j{\omega _0}t}}$$
D
$$\sin ({\omega _0}t)$$
2
GATE ECE 2006
+1
-0.3
Let x(t) $$\leftrightarrow$$ X($$(j\omega )$$ BE Fourier transform pair. The Fourier Transform of the signal x(5t - 3) in terms of X($$(j\omega )$$ is given as
A
$${1 \over 5}{e^{ - {{j3\omega } \over 5}}}X\left( {{{j\omega } \over 5}} \right)$$
B
$${1 \over 5}{e^{{{j3\omega } \over 5}}}X\left( {{{j\omega } \over 5}} \right)$$
C
$${1 \over 5}{e^{ - j3\omega }}X\left( {{{j\omega } \over 5}} \right)$$
D
$${1 \over 5}{e^{j3\omega }}X\left( {{{j\omega } \over 5}} \right)$$
3
GATE ECE 2004
+1
-0.3
The Fourier transform of a conjugate symmetric function is always
A
imaginary
B
conjugate anti-symmetric
C
real
D
conjugate symmetric
4
GATE ECE 2002
+1
-0.3
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
A
$${e^f}u(f)$$
B
$${e^{ - f}}$$ u(f)
C
$${e^f}u(f)$$
D
$${e^{ - f}}$$u(-f)
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