[amp_mcq option1=”ef u(f)” option2=”e-f u(f)” option3=”ef u(-f)” option4=”e-f u(-f)” correct=”option4″]
Signal processing
32. Let $$g\left( t \right) = {e^{ – \pi {t^2}}}$$ and h(t) is a filter matched to g(t). If g(t) is applied as input to h(t), then the Fourier transform of the output is
[amp_mcq option1=”$${e^{ – \pi {t^2}}}$$” option2=”$${e^{ – {{\pi {t^2}} \over 2}}}$$” option3=”$${e^{ – \pi \left| f \right|}}$$” option4=”$${e^{ – 2\pi {t^2}}}$$” correct=”option3″]
33. Consider the following statements for continuous-time linear time invariant (LTI) systems. 1. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane. 2. There is no causal and BIBO stable system with a pole in the right half of the complex plane. Which one among the following is correct?
[amp_mcq option1=”Both 1 and 2 are true” option2=”Both 1 and 2 are not true” option3=”Only 1 is true” option4=”Only 2 is true” correct=”option1″]
34. Let x(t) and y(t) (with Fourier transforms X(f) and Y(f) respectively) be related as shown in the figure. Then Y(f) is
[amp_mcq option1=”$$ – \frac{1}{2}X\left( {\frac{f}{2}} \right){e^{ – j2\pi f}}$$” option2=”$$ – \frac{1}{2}X\left( {\frac{f}{2}} \right){e^{j2\pi f}}$$” option3=”$$ – X\left( {\frac{f}{2}} \right){e^{j2\pi f}}$$” option4=”$$ – X\left( {\frac{f}{2}} \right){e^{ – j2\pi f}}$$” correct=”option4″]
35. Two sequences [a, b, c] and [A, B, C] are related as, \[\left[ {\begin{array}{*{20}{c}} A \\ B \\ C \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1&1&1 \\ 1&{W_3^{ – 1}}&{W_3^{ – 2}} \\ 1&{W_3^{ – 2}}&{W_3^{ – 4}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} a \\ b \\ c \end{array}} \right]\] where, $${W_3} = {e^{i\frac{{2\pi }}{3}}}.$$ If another sequence [p, q, r] is derived as, \[\left[ {\begin{array}{*{20}{c}} a \\ b \\ c \end{array}} \right] = \] \[\left[ {\begin{array}{*{20}{c}} 1&1&1 \\ 1&{W_3^1}&{W_3^2} \\ 1&{W_3^2}&{W_3^4} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 1&0&0 \\ 0&{W_3^2}&0 \\ 0&0&{W_3^4} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {A/3} \\ {B/3} \\ {C/3} \end{array}} \right]\] then the relationship between the sequences [p, q, r] and [a, b, c] is
[amp_mcq option1=”[p, q, r] = [b, a, c]” option2=”[p, q, r] = [b, c, a]” option3=”[p, q, r] = [c, a, b]” option4=”[p, q, r] = [c, b, a]” correct=”option1″]
36. The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity 4. The impulse response of the system is h[n]. If h[0] = 1, we can conclude
[amp_mcq option1=”h[n] is real for all n” option2=”h[n] is purely imaginary for all n” option3=”h[n] is real for only even n” option4=”h[n] is purely imaginary for only odd n” correct=”option1″]
37. The pole-zero pattern of a certain filter is shown in figure. The filter must be of the following type
[amp_mcq option1=”Low-pass” option2=”High-pass” option3=”All-pass” option4=”Band-pass” correct=”option1″]
38. Specify the filter type if its voltage transfer function H(s) is given by $$H\left( s \right) = {{K\left( {{s^2} + 1\omega _0^2} \right)} \over {{s^2} + \left( {{{{\omega _0}} \over Q}} \right)s + \omega _0^2}}$$
[amp_mcq option1=”All pass filter” option2=”Low pass filter” option3=”Band pass filter” option4=”Notch filter” correct=”option2″]
39. Consider the system shown in the figure below. The transfer function $$\frac{{Y\left( z \right)}}{{X\left( z \right)}}$$ of the system is
[amp_mcq option1=”$$\frac{{1 + a{z^{ – 1}}}}{{1 + b{z^{ – 1}}}}$$” option2=”$$\frac{{1 + b{z^{ – 1}}}}{{1 + a{z^{ – 1}}}}$$” option3=”$$\frac{{1 + a{z^{ – 1}}}}{{1 – b{z^{ – 1}}}}$$” option4=”$$\frac{{1 – b{z^{ – 1}}}}{{1 – a{z^{ – 1}}}}$$” correct=”option1″]
40. The complex envelope of the bandpass signal $$x\left( t \right) = \sqrt 2 \left( {{{\sin \left( {{{\pi t} \over 5}} \right)} \over {{{\pi t} \over 5}}}} \right)\sin \left( {\pi t – {\pi \over 4}} \right),$$ centered about $$f = {1 \over 2}Hz,$$ is
[amp_mcq option1=”$$\left( {{{\sin \left( {{{\pi t} \over 5}} \right)} \over {{{\pi t} \over 5}}}{e^{j{\pi \over 4}}}} \right)$$” option2=”$$\left( {{{\sin \left( {{{\pi t} \over 5}} \right)} \over {{{\pi t} \over 5}}}{e^{ – j{\pi \over 4}}}} \right)$$” option3=”$$\sqrt 2 \left( {{{\sin \left( {{{\pi t} \over 5}} \right)} \over {{{\pi t} \over 5}}}{e^{j{\pi \over 4}}}} \right)$$” option4=”$$\sqrt 2 \left( {{{\sin \left( {{{\pi t} \over 5}} \right)} \over {{{\pi t} \over 5}}}{e^{ – j{\pi \over 4}}}} \right)$$” correct=”option3″]