[amp_mcq option1=”$${K \over 4}$$” option2=”Zero” option3=”Infinite” option4=”Undefined” correct=”option4″]
Signal processing
22. A system with input x[n] and output y[n] is given as $$y\left( n \right) = \left( {\sin {5 \over 6}\pi n} \right)x\left( n \right).$$ The system is
[amp_mcq option1=”Linear, stable and invertible” option2=”Non-linear, stable and non-invertible” option3=”Linear, stable and non-invertible” option4=”Linear, unstable and invertible” correct=”option1″]
23. The Fourier transform of a voltage signal x(t) is X(f). The unit of |X(f)| is
[amp_mcq option1=”Volt” option2=”Volt-sec” option3=”Volt/sec” option4=”Volt2″ correct=”option1″]
Detailed SolutionThe Fourier transform of a voltage signal x(t) is X(f). The unit of |X(f)| is
24. A rectangular pulse of duration T is applied to a filter matched to this input. The output of the filter is a
[amp_mcq option1=”Rectangular pulse of duration T” option2=”Rectangular pulse of duration 2T” option3=”Triangular pulse” option4=”Sine function” correct=”option1″]
25. If L[f(t)] = F(s), then L[f(t – T)] is equal to
[amp_mcq option1=”esTF(s)” option2=”e-sTF(s)” option3=”$${{F\left( s \right)} \over {1 + {e^{sT}}}}$$” option4=”$${{F\left( s \right)} \over {1 – {e^{ – sT}}}}$$” correct=”option4″]
Detailed SolutionIf L[f(t)] = F(s), then L[f(t – T)] is equal to
26. A signal $$2\cos \left( {{{2\pi } \over 3}t} \right) – \cos \left( {\pi t} \right)$$ is the input to an LTI system with the transfer function $$H\left( s \right) = {e^s} + {e^{ – s}}$$ If Ck denote the kth coefficient in the exponential Fourier series of the output signal, then C3 is equal to
[amp_mcq option1=”0″ option2=”1″ option3=”2″ option4=”3″ correct=”option3″]
27. If $$sL\left[ {f\left( t \right)} \right] = {\omega \over {\left( {{s^2} + {\omega ^2}} \right)}},$$ then the value of $$\mathop {\lim }\limits_{t \to \infty } f\left( t \right)$$
[amp_mcq option1=”Cannot be determined” option2=”Is zero” option3=”Is unity” option4=”Is infinite” correct=”option4″]
28. A signal containing only two frequency components (3 kHz and 6 kHz) is sampled at the rate of 8 kHz, and then passed through a low pass filter with a cut-off frequency of 8 kHz. The filter output
[amp_mcq option1=”Is an undistorted version of the original signal” option2=”Contains only the 3 kHz component” option3=”Contains the 3 kHz component and a spurious component of 2 kHz” option4=”Contains both the components of the original signal and two spurious components of 2 kHz and 5 kHz” correct=”option2″]
29. A Hilbert transformer is a
[amp_mcq option1=”Non-linear system” option2=”Non-causal system” option3=”Time-varying system” option4=”Low-pass system” correct=”option1″]
30. The transfer function of a discrete time LTI system is given by $$H\left( z \right) = {{2 – {3 \over 4}{z^{ – 1}}} \over {1 – {3 \over 4}{z^{ – 1}} + {1 \over 8}{z^{ – 2}}}}$$ Consider the following statements: S1 : The system is stable and causal for $$ROC:\left| z \right| > {1 \over 2}$$ S2 : The system is stable but not causal for $$ROC:\left| z \right| < {1 \over 4}$$ S3 : The system is neither stable nor causal for $$ROC:{1 \over 4} < \left| z \right| < {1 \over 2}$$ Which one of the following statements is valid?
[amp_mcq option1=”Both S1 and S2 are true” option2=”Both S2 and S3 true” option3=”Both S1 and S3 are true” option4=”S1, S2 and S3 are all true” correct=”option3″]