1
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$$\left[ {j({\omega _c} + \Delta \omega )t} \right]$$
2
GATE ECE 1999
+1
-0.3
A signal x(t) has a Fourier transform X ($$\omega$$). If x(t) is a real and odd function of t, then X($$\omega$$) is
A
a real and even function of $$\omega$$
B
an imaginary and odd function of $$\omega$$
C
an imaginary and even function of $$\omega$$
D
a real and odd function of $$\omega$$
3
GATE ECE 1998
+1
-0.3
The amplitude spectrum of a Gaussian pulse is
A
uniform
B
a sine function
C
Gaussian
D
an impulse function
4
GATE ECE 1998
+1
-0.3
The Fourier transform of a function x(t) is X(f). The Fourier transform of $${{dx(t)} \over {dt}}$$ will be
A
$${{dX(f)} \over {dt}}$$
B
$$j2\pi fX(f)$$
C
$$jfX(f)$$
D
$${{X(f)} \over {jf}}$$
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