[amp_mcq option1=”$${\left| {X\left( k \right)} \right|^2}$$” option2=”$$\frac{1}{2}\sum\limits_{r = 0}^{N – 1} {X\left( r \right)X’\left( {k + r} \right)} $$” option3=”$$\frac{1}{2}\sum\limits_{r = 0}^{N – 1} {X\left( r \right)X\left( {k + r} \right)} $$” option4=”0″ correct=”option4″]
Signal processing
52. For a function g(t), it is given that $$\int\limits_{ – \infty }^{ + \infty } {g\left( t \right){e^{ – j\omega t}}dt = \omega {e^{ – 2{\omega ^2}}}} $$ for any real value $$\omega $$ . If $$y\left( t \right) = \int\limits_{ – \infty }^t {g\left( \tau \right)} d\tau ,\,{\rm{then}}\,\int\limits_{ – \infty }^{ + \infty } {y\left( t \right)} dt$$ is. . . . . . . .
[amp_mcq option1=”0″ option2=”#NAME?” option3=”$$ – {j \over 2}$$” option4=”$${j \over 2}$$” correct=”option3″]
53. The impulse response of a system is h(t) = tu(t). For an input u(t – 1), the output is
[amp_mcq option1=”$${{{t^2}} \over 2}u\left( t \right)$$” option2=”$${{t\left( {t – 1} \right)} \over 2}u\left( {t – 1} \right)$$” option3=”$${{{{\left( {t – 1} \right)}^2}} \over 2}u\left( {t – 1} \right)$$” option4=”$${{{t^2} – 1} \over 2}u\left( {t – 1} \right)$$” correct=”option1″]
54. Let Y(s) be the unit-step response of a causal system having a transfer function $$G\left( s \right) = {{3 – s} \over {\left( {s + 1} \right)\left( {s + 3} \right)}}$$ That is, $$Y\left( s \right) = {{G\left( s \right)} \over s}.$$ The forced response of the system is
[amp_mcq option1=”u(t) – 2e-t u(t) + e-3t u(t)” option2=”2u(t)” option3=”u(t)” option4=”2u(t) – 2e-t u(t) + e-3t u(t)” correct=”option1″]
55. The Laplace transform of a continuous-time signal x(t) is $$X\left( s \right) = {{5 – s} \over {{s^2} – s – 2}}.$$ If the Fourier transform of this signal exists, then x(t) is
[amp_mcq option1=”e2tu(t) – 2e-tu(t)” option2=”-e2tu(-t) + 2e-tu(t)” option3=”-e2tu(-t) – 2e-tu(t)” option4=”e2tu(-t) – 2e-tu(t)” correct=”option1″]
56. For the discrete-time system shown in the figure, the poles of the system transfer function are located at
[amp_mcq option1=”2, 3″ option2=”$$\frac{1}{2},3$$” option3=”$$\frac{1}{2},\frac{1}{3}$$” option4=”$$2,\frac{1}{3}$$” correct=”option3″]
57. If the region of convergence of x1[n] + x2[n] is $${1 \over 3} < \left| z \right| < {2 \over 3},$$ then the region of convergence of x1[n] - x2[n] includes
[amp_mcq option1=”$${1 \over 3} < \left| z \right| < 3$$" option2="$${2 \over 3} < \left| z \right| < 3$$" option3="$${3 \over 2} < \left| z \right| < 3$$" option4="$${1 \over 3} < \left| z \right| < {2 \over 3}$$" correct="option3"]
58. A linear discrete-time system has the characteristics equation, z3 – 0.81 z = 0. The system
[amp_mcq option1=”Is stable” option2=”Is marginally stable” option3=”Is unstable” option4=”Stability cannot be assessed from the given information” correct=”option1″]
59. A real-valued signal x(t) limited to the frequency band $$\left| f \right| \le {W \over 2}$$ is passed through a linear time invariant system whose frequency response is $$H\left( f \right) = \left\{ {\matrix{ {{e^{ – j4\pi f,}}} & {\left| f \right| \le {W \over 2}} \cr {0,} & {\left| f \right| > {W \over 2}} \cr } } \right.$$ The output of the system is
[amp_mcq option1=”x(t + 4)” option2=”x(t – 4)” option3=”x(t + 2)” option4=”x(t – 2)” correct=”option1″]
60. The z-transform of a system is $$H\left( z \right) = {z \over {z – 0.2}}.$$ If the ROC is |z| < 0.2, then the impulse response of the system is
[amp_mcq option1=”(0.2)nu[n]” option2=”(0.2)nu[- n – 1]” option3=”-(0.2)nu[n]” option4=”-(0.2)nu[- n – 1]” correct=”option3″]