[amp_mcq option1=”$$F\left( s \right) = \frac{1}{{1 + {e^{ – \frac{{sT}}{2}}}}}$$” option2=”$$F\left( s \right) = \frac{1}{{s\left( {1 + {e^{ – \frac{{sT}}{2}}}} \right)}}$$” option3=”$$F\left( s \right) = \frac{1}{{s\left( {1 – {e^{ – \frac{{sT}}{2}}}} \right)}}$$” option4=”$$F\left( s \right) = \frac{1}{{1 – {e^{ – sT}}}}$$” correct=”option3″]
Signal processing
42. A function is given by f(t) = sin2t + cos 2t. Which of the following is true?
[amp_mcq option1=”$$f$$ has frequency components at 0 and $${1 \over {2\pi }}Hz$$” option2=”$$f$$ has frequency components at 0 and $${1 \over \pi }Hz$$” option3=”$$f$$ has frequency components at $${1 \over {2\pi }}$$ and $${1 \over \pi }Hz$$” option4=”$$f$$ has frequency components at 0, $${1 \over {2\pi }}$$ and $${1 \over \pi }Hz$$” correct=”option1″]
Detailed SolutionA function is given by f(t) = sin2t + cos 2t. Which of the following is true?
43. Letx(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2 and P3 with system relations R1, R2, P3, P4. Properties P1 : Linear but NOT time-invariant P2 : Time-invariant but NOT linear P3 : Linear and time-invariant Relations R1 : y(t) = t2x(t) R2 : y(t) = t |x(t)| R3 : y(t) = |x(t)| R4 : y(t) = x(t – 5)
[amp_mcq option1=”(P1, R1), (P2, R3), (P3, R4)” option2=”(P1, R2), (P2, P3), (P3, R4)” option3=”(P1, R3), (P2, R1), (P3, R2)” option4=”(P1, R1), (P2, R2), (P3, R3)” correct=”option1″]
44. If G(f) represents the Fourier transform of a signal g(t) which is real and odd symmetric in time, then
[amp_mcq option1=”G(f) is complex” option2=”G(f) is imaginary” option3=”G(f) is real” option4=”G(f) is real and non-negative” correct=”option1″]
45. The z-transform X[z] of a sequence x[n] is given by $$X\left[ z \right] = {{0.5} \over {1 – 2{z^{ – 1}}}}.$$ It is given that the region of convergence of X[z] includes the unit circle. The value of x[0] is
[amp_mcq option1=”-0.5″ option2=”0″ option3=”0.25″ option4=”0.5″ correct=”option4″]
46. A system is described by the following differential equation, where u(t) is the input to the system and y(t) is the output of the system. y(t) + 5y(t) = u(t) When y(0) = 1 and u(t) is a unit step function, y(t) is
[amp_mcq option1=”0.2 + 0.8e-5t” option2=”0.2 – 0.2e-5t” option3=”0.8 + 0.2e-5t” option4=”0.8 – 0.8e-5t” correct=”option1″]
47. Consider a system whose input r and output y are related by the equation $$y\left( t \right) = \int\limits_{ – \infty }^\infty {x\left( {t – \tau } \right)} h\left( {2\tau } \right)d\tau $$ Where h(t) is shown in the graph Which of the following four properties are possessed by the system? BIBO: Bounded input gives a bounded output Causal: The system is causal. LP : The system is low pass. LTI: The system is linear and time-invariant.
[amp_mcq option1=”Causal, LP” option2=”BIBO, LTI” option3=”BIBO, Causal, LTI” option4=”LP, LTI” correct=”option2″]
48. If the impulse response of a discrete-time system is h[n] = -5nu[- n – 1], then the system function H(z) is equal to
[amp_mcq option1=”$${{ – z} \over {z – 5}}$$ and the system is stable” option2=”$${z \over {z – 5}}$$ and the system is stable” option3=”$${{ – z} \over {z – 5}}$$ and the system is unstable” option4=”$${z \over {z – 5}}$$ and the system is unstable” correct=”option3″]
49. 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]?
[amp_mcq option1=”It is a finite duration signal” option2=”It is a causal signal” option3=”It is a non-causal signal” option4=”It is a periodic signal” correct=”option1″]
50. The ACF of a rectangular pulse of duration T is
[amp_mcq option1=”A rectangular pulse of duration T” option2=”A rectangular pulse of duration 2T” option3=”A triangular pulse of duration T” option4=”A triangular pulse of duration 2T” correct=”option1″]
Detailed SolutionThe ACF of a rectangular pulse of duration T is