[amp_mcq option1=”ae-at” option2=”$$\left( {{1 \over a}} \right)\left( {1 – {e^{ – at}}} \right)$$” option3=”a(1 – e-at)” option4=”1 – e-at” correct=”option1″]
Signal processing
12. The unilateral Laplace transform of f(t) is $${1 \over {{s^2} + s + 1}}.$$ Which one of the following is the unilateral Laplace transform of g(t) = t.f(t)?
[amp_mcq option1=”$${{ – s} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$” option2=”$${{ – \left( {2s + 1} \right)} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$” option3=”$${s \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$” option4=”$${{2s + 1} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$” correct=”option3″]
13. A 1 kHz sinusoidal signal is ideally sampled at 1500 samples/sec and the sampled signal is passed through an ideal low-pass filter with cutoff frequency 800 Hz. The output signal has the frequency
[amp_mcq option1=”Zero Hz” option2=”0.75 kHz” option3=”0.5 kHz” option4=”0.25 kHz” correct=”option1″]
14. Flat top sampling of low pass signals
[amp_mcq option1=”Gives rise to aperture effect” option2=”Implies oversampling” option3=”Leads to aliasing” option4=”Introduces delay distortion” correct=”option1″]
15. The Fourier series of an odd periodic function, contains only
[amp_mcq option1=”Odd harmonics” option2=”Even harmonics” option3=”Cosine terms” option4=”Sine terms” correct=”option1″]
Detailed SolutionThe Fourier series of an odd periodic function, contains only
16. Consider the differential equation $${{dx} \over {dt}} = 10 – 0.2x$$ with initial conduction x(0) = 1. The response x(t) for t > 0 is
[amp_mcq option1=”2 – e-0.2t” option2=”2 – e-0.2t” option3=”50 – 49e-0.2t” option4=”50 – 49e0.2t” correct=”option1″]
17. For a periodic signal $$v\left( t \right) = 30\sin 100t + 10\cos 300t + 6\sin \left( {500t + {\pi \over 4}} \right),$$ the fundamental frequency in rad/s is
[amp_mcq option1=”100″ option2=”300″ option3=”500″ option4=”1500″ correct=”option3″]
18. Let y[n] denote the convolution of h[n] and g[n], where h[n] = $${\left( {\frac{1}{2}} \right)^n}$$ u[n] and g[n] is a causal sequence. If y[0] = 1 and y[1] = $$\frac{1}{2},$$ then g[1] equals
[amp_mcq option1=”0″ option2=”$${1 \over 2}$$” option3=”1″ option4=”$${3 \over 2}$$” correct=”option4″]
19. The impulse response h[n] of a linear time-invariant system is given by h[n] = u[n + 3] + u[n – 2] – 2u[n – 7], where u[n] is the unit step sequence. The above system is
[amp_mcq option1=”Stable but not causal” option2=”Stable and causal” option3=”Causal but unstable” option4=”Unstable and not causal” correct=”option2″]
20. A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency which is not valid is
[amp_mcq option1=”5 kHz” option2=”12 kHz” option3=”15 kHz” option4=”20 kHz” correct=”option4″]