1
GATE ECE 2001
MCQ (Single Correct Answer)
+1
-0.3
The region of convergence of the z- transform of a unit step function is
A
$$\left| {z\,} \right| > 1$$
B
$$\left| {z\,} \right| < 1$$
C
(Real part of z )> 0
D
(Real part of z )< 0
2
GATE ECE 2001
MCQ (Single Correct Answer)
+1
-0.3
The transfer function of a system is given by $$H\left( s \right) = {1 \over {{s^2}\left( {s - 2} \right)}}$$. The impulse response of the system is
A
$$\left( {{t^2} * {e^{ - 2t}}} \right)U\left( t \right)$$
B
$$\left( {t * {e^{2t}}} \right)U\left( t \right)$$
C
$$\left( {{t^2}{e^{ - 2t}}} \right)U\left( t \right)$$
D
$$\left( {t{e^{ - 2t}}} \right)U\left( t \right)$$
3
GATE ECE 2001
MCQ (Single Correct Answer)
+2
-0.6
The impulse response function of four linear system S1, S2, S3, S4 are given respectively by

$${h_1}$$(t), = 1;

$${h_2}$$(t), = U(t);

$${h_3}(t)\, = \,{{U(t)} \over {t + 1}}$$;

$${h_4}(t)\, = {e^{ - 3t}}U(t)$$ ,

where U (t) is the unit step function. Which of these system is time invariant, causal, and stable?

A
SI
B
S2
C
S3
D
S4
4
GATE ECE 2001
Subjective
+5
-0
The Fourier transform $$G(\omega )$$ of the signal g(t) in Fig.(1) is given as
$$G(\omega ) = {1 \over {{\omega ^2}}}({e^{j\omega }} - j\omega {e^{j\omega }} - 1)$$.

Using this information, and the time-shifting and time-scaling properties, determine and Fourier transform of signals in Fig (2), (3) and (4).

GATE ECE 2001 Signals and Systems - Fourier Transform Question 4 English 1 GATE ECE 2001 Signals and Systems - Fourier Transform Question 4 English 2 GATE ECE 2001 Signals and Systems - Fourier Transform Question 4 English 3 GATE ECE 2001 Signals and Systems - Fourier Transform Question 4 English 4
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