[amp_mcq option1=”It is causal and stable” option2=”It is causal but not stable” option3=”It is not causal but stable” option4=”It is neither causal nor stable” correct=”option1″]
Signal processing
42. A system with transfer function H(z) has impulse response h(n) defined as h(2) = 1, h(3) = -1 and h(k) = 0 otherwise. Consider the following statements. S1 : H(z) is a low-pass filter. S2 : H(z) is an FIR filter. Which of the following is correct?
[amp_mcq option1=”Only S2 is true” option2=”Both S1 and S2 are false” option3=”Both S1 and S2 are true, and S2 is a reason for S1″ option4=”Both S1 and S2 are true, but S2 is not a reason for S1″ correct=”option3″]
43. The Fourier Transform of the signal $$x\left( t \right) = {e^{ – 3{t^2}}}$$ is of the following form, where A and B are constants
[amp_mcq option1=”$$A{e^{ – B{f^2}}}$$” option2=”$$A{e^{ – B{t^2}}}$$” option3=”$$A + B{\left| f \right|^2}$$” option4=”$$A{e^{ – Bf}}$$” correct=”option4″]
44. The Fourier transform of a signal h(t) is $$H\left( {j\omega } \right) = {{\left( {2\cos \omega } \right)\left( {\sin \omega } \right)} \over \omega }$$ The value of h(0) is
[amp_mcq option1=”$${1 \over 4}$$” option2=”$${1 \over 2}$$” option3=”1″ option4=”2″ correct=”option4″]
45. The input and output of a continuous time system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a casual system?
[amp_mcq option1=”y(t) = x(t – 2) + x(t + 4)” option2=”y(t) = (t – 4)x(t + 1)” option3=”y(t) = (t + 4)x(t – 1)” option4=”y(t) = (t + 5)x(t + 5)” correct=”option1″]
46. The first five points of the 8-point DFT of a real valued sequence are 5, 1 – j3, 0, 3 – j4 and 3 + j4. The last two points of the DFT are respectively
[amp_mcq option1=”0, 1 – j3″ option2=”0, 1 + j3″ option3=”1 + j3, 5″ option4=”1 – j3, 5″ correct=”option1″]
47. The trigonometric Fourier series of an even function of time does not have
[amp_mcq option1=”The dc term” option2=”Cosine terms” option3=”Sine terms” option4=”Odd harmonic terms” correct=”option4″]
Detailed SolutionThe trigonometric Fourier series of an even function of time does not have
48. The signal $$\cos \left( {10\pi t + \frac{\pi }{4}} \right)$$ is ideally sampled at a sampling frequency of 15 Hz. The sampled signal is passed through a filter with impulse response $$\left( {\frac{{\sin \left( {\pi t} \right)}}{{\pi \tau }}} \right)\cos \left( {40\pi t – \frac{\pi }{2}} \right).$$ The filter output is
[amp_mcq option1=”$$\frac{{15}}{2}\cos \left( {40\pi t – \frac{\pi }{4}} \right)$$” option2=”$$\frac{{15}}{2}\left( {\frac{{\sin \left( {\pi t} \right)}}{{\pi t}}} \right)\cos \left( {10\pi t + \frac{\pi }{4}} \right)$$” option3=”$$\frac{{15}}{2}\cos \left( {10\pi t – \frac{\pi }{4}} \right)$$” option4=”$$\frac{{15}}{2}\left( {\frac{{\sin \left( {\pi t} \right)}}{{\pi t}}} \right)\cos \left( {10\pi t – \frac{\pi }{2}} \right)$$” correct=”option1″]
49. The Fourier series representation of an impulse train denoted by $$s\left( t \right) = \sum\limits_{n = – \infty }^\infty {\delta \left( {t – n{T_0}} \right)} \,{\rm{is}}\,{\rm{given}}\,{\rm{by}}$$
[amp_mcq option1=”$${1 \over {{T_0}}}\sum\limits_{n = – \infty }^\infty {\exp \left( { – {{j2\pi nt} \over {{T_0}}}} \right)} $$” option2=”$${1 \over {{T_0}}}\sum\limits_{n = – \infty }^\infty {\exp } \left( { – {{j\pi nt} \over {{T_0}}}} \right)$$” option3=”$${1 \over {{T_0}}}\sum\limits_{n = – \infty }^\infty {\exp } \left( {{{j\pi nt} \over {{T_0}}}} \right)$$” option4=”$${1 \over {{T_0}}}\sum\limits_{n = – \infty }^\infty {\exp } \left( {{{j2\pi nt} \over {{T_0}}}} \right)$$” correct=”option1″]
50. If the Laplace transform of a signal y(t) is $$Y\left( s \right) = {1 \over {s\left( {s – 1} \right)}},$$ then its final value is
[amp_mcq option1=”-1″ option2=”0″ option3=”1″ option4=”Unbounded” correct=”option3″]