1
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)
2
GATE ECE 2001
+1
-0.3
If a signal f(t) has energy E, the energy of the signal f(2t) is equal to
A
E
B
E/2
C
2E
D
4E
3
GATE ECE 2000
+1
-0.3
The Fourier Transform of the signal $$x(t) = {e^{ - 3{t^2}}}$$ is of the following form, where A and B are constants:
A
$$A{e^{ - B\left| f \right|}}$$
B
$$A{e^{ - Bf}}$$
C
$$A + B{\left| f \right|^2}$$
D
$$A{e^{ - B{f^2}}}$$
4
GATE ECE 1999
+1
-0.3
A modulated signal is given by s(t)= $${e^{ - at}}$$ cos $$\left[ {({\omega _c} + \Delta \omega )t} \right]$$ u (t), where a, $${\omega _c}$$ and $${\Delta \omega }$$ are positive constants, and $${\omega _c}$$ >>$${\Delta \omega }$$. The complex envelope of s(t) is given by
A
exp(-at)exp$$\left[ {({\omega _c} + \Delta \omega )t} \right]$$ u(t)
B
exp (-at)exp(j$${\Delta \omega t )}$$ u(t)
C
exp(j$${\Delta \omega t )}$$ u (t)
D
exp$$\left[ {j({\omega _c} + \Delta \omega )t} \right]$$
EXAM MAP
Medical
NEET