1
GATE ECE 2005
MCQ (Single Correct Answer)
+1
-0.3
The region of convergence of z-transform of the sequence $${\left( {{5 \over 6}} \right)^n}u(n) - {\left( {{6 \over 5}} \right)^n}u( - n - 1)$$ must be
A
$$\left| {z\,} \right| < {5 \over 6}$$
B
$$\left| {z\,} \right| > {6 \over 5}$$
C
$${5 \over 6} < \left| {z\,} \right| < {6 \over 5}$$
D
$${6 \over 5} < \left| {z\,} \right| < \infty $$
2
GATE ECE 2005
MCQ (Single Correct Answer)
+1
-0.3
Which of the following can be impulse response of a causal system?
A
GATE ECE 2005 Signals and Systems - Continuous Time Linear Invariant System Question 43 English Option 1
B
GATE ECE 2005 Signals and Systems - Continuous Time Linear Invariant System Question 43 English Option 2
C
GATE ECE 2005 Signals and Systems - Continuous Time Linear Invariant System Question 43 English Option 3
D
GATE ECE 2005 Signals and Systems - Continuous Time Linear Invariant System Question 43 English Option 4
3
GATE ECE 2005
MCQ (Single Correct Answer)
+2
-0.6
The output y(t) of a linear time invariant system is related to its input x(t) by the following equation: y(t) = 0.5 x $$(t - {t_d} + T) + \,x\,(t - {t_d}) + 0.5\,x(t - {t_d} - T)$$. The filter transfer function $$H(\omega )$$ of such a system is given by
A
$$(1 + \cos \omega T){e^{ - j\omega {t_d}}}$$
B
$$(1 + 0.5\cos \omega T){e^{ - j\omega {t_d}}}$$
C
$$(1 + \cos \omega T){e^{j\omega {t_d}}}$$
D
$$(1 - 0.5\cos \omega T){e^{ - j\omega {t_d}}}$$
4
GATE ECE 2005
MCQ (Single Correct Answer)
+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
$$x(3t + 2)$$
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