51. The impulse response functions of four linear systems S1, S2, S3, S4 are given respectively by
$${h_1}\left( t \right) = 1,$$ $${h_2}\left( t \right) = u\left( t \right),$$ $${h_3}\left( t \right) = \frac{{u\left( t \right)}}{{t + 1}},$$ $${h_4}\left( t \right) = {e^{ - 3t}}u\left( t \right)$$
Where u(t) is the unit step function. Which of these systems is time invariant, causal, and stable?
$${h_1}\left( t \right) = 1,$$ $${h_2}\left( t \right) = u\left( t \right),$$ $${h_3}\left( t \right) = \frac{{u\left( t \right)}}{{t + 1}},$$ $${h_4}\left( t \right) = {e^{ - 3t}}u\left( t \right)$$
Where u(t) is the unit step function. Which of these systems is time invariant, causal, and stable?
52. For an all-pass system $$H\left( z \right) = \frac{{\left( {{z^{ - 1}} - b} \right)}}{{\left( {1 - a{z^{ - 1}}} \right)}},$$ where | H(e-jω) | = 1, for all ω. If Re(a) ≠ 0, lm(a) ≠ 0, then b equals
53. If $$L\left[ {f\left( t \right)} \right] = {{2\left( {s + 1} \right)} \over {{s^2} + 2s + 5}},$$ then f(0+) and f(∞) are given by
54. Suppose x[n] is an absolutely summable discrete- time signal. Its z-transform is a rational function with two poles and two zeroes. The poles are at z = ±2j. Which one of the following statements is TRUE for the signal x[n]?
55. Let h(t) denote the impulse response of a causal system with transfer function $${1 \over {s + 1}}.$$ Consider the following three statements:
S1 : The system is stable.
S2 : $${{h\left( {t + 1} \right)} \over {h\left( t \right)}}$$ independent of t for t > 0.
S3 : A non-causal system with the same transfer function is stable.
For the above system,
S1 : The system is stable.
S2 : $${{h\left( {t + 1} \right)} \over {h\left( t \right)}}$$ independent of t for t > 0.
S3 : A non-causal system with the same transfer function is stable.
For the above system,
56. The amplitude spectrum of a Gaussian pulse is
57. Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)} d\tau $$ is
58. A discrete-time all-pass system has two of its poles at 0.25<0° and 2<30°. Which one of the following statements about the system is TRUE?
59. The transfer function of a zero-order-hold system is
60. The first five points of the 8-point DFT of a real valued sequence are 5, 1 - j3, 0, 3 - j4 and 3 + j4. The last two points of the DFT are respectively
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