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11. The unit impulse response of a linear time invariant system is the unit step function u(t). For t > 0, the response of the system to an excitation e-at u(t), a > 0 will be

ae-at

$$left( {{1 over a}} ight)left( {1 - {e^{ - at}}} ight)$$

a(1 - e-at)

1 - e-at

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> 0, the response of the system to an excitation e-at u(t), a > 0 will be" class="read-more button" href="https://exam.pscnotes.com/mcq/the-unit-impulse-response-of-a-linear-time-invariant-system-is-the-unit-step-function-ut-for-t-0-the-response-of-the-system-to-an-excitation-e-at-ut-a-0-will-be/#more-49709">Detailed Solution

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)?

$${{ - s} over {{{left( {{s^2} + s + 1} ight)}^2}}}$$

$${s over {{{left( {{s^2} + s + 1} ight)}^2}}}$$

$${{2s + 1} over {{{left( {{s^2} + s + 1} ight)}^2}}}$$

Detailed SolutionThe 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)?

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

Zero Hz

0.75 kHz

0.5 kHz

0.25 kHz

Detailed SolutionA 1 kHz sinusoidal

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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

14. Flat top sampling of low pass signals

Gives rise to aperture effect

Implies oversampling

Leads to aliasing

Introduces delay distortion

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button" href="https://exam.pscnotes.com/mcq/flat-top-sampling-of-low-pass-signals/#more-48698">Detailed Solution

15. The Fourier series of an odd periodic function, contains only

Odd harmonics

Even harmonics

Cosine terms

Sine terms

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288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z"/> Subscribe on YouTube button" href="https://exam.pscnotes.com/mcq/the-fourier-series-of-an-odd-periodic-function-contains-only/#more-48280">Detailed Solution

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

2 - e-0.2t

50 - 49e-0.2t

50 - 49e0.2t

Detailed SolutionConsider

the differential equation $${{dx} \over {dt}} = 10 – 0.2x$$ with initial conduction x(0) = 1. The response x(t) for t > 0 is

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

100

300

500

1500

Detailed Solution

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class="screen-reader-text">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

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

$${1 over 2}$$

$${3 over 2}$$

Detailed SolutionLet 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

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

Stable but not causal

Stable and causal

Causal but unstable

Unstable and not causal

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is the unit step sequence. The above system is" class="read-more button" href="https://exam.pscnotes.com/mcq/the-impulse-response-hn-of-a-linear-time-invariant-system-is-given-by-hn-un-3-un-2-2un-7-where-un-is-the-unit-step-sequence-the-above-system-is/#more-47800">Detailed Solution

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

5 kHz

12 kHz

15 kHz

20 kHz

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448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z"/> Subscribe on YouTube sampling theorem, the sampling frequency which is not valid is" class="read-more button" href="https://exam.pscnotes.com/mcq/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/#more-47793">Detailed Solution

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