[amp_mcq option1=”Is $$\left| z \right| > {1 \over 9}$$” option2=”Is $$\left| z \right| < {1 \over 3}$$" option3="Is $${1 \over 3} > \left| z \right| > {1 \over 9}$$” option4=”Does not exist” correct=”option4″]
Signal processing
2. A system with an input x(t) and output y(t) is described by the relation: y(t) = tx(t). This system is
[amp_mcq option1=”Linear and time-invariant” option2=”Linear and time varying” option3=”Non-linear & time-invariant” option4=”Non-linear and time-varying” correct=”option1″]
3. The voltage across an impedance in a network is V(s) = Z(s). I(s), where V(s), Z(s) and I(s) are the Laplace transform of the corresponding time functions v(t), z(t) and i(t). The voltage v(t) is
[amp_mcq option1=”v(t) = z(t).i(t)” option2=”$$v\left( t \right) = \int\limits_0^t {i\left( \tau \right)} z\left( {t – \tau } \right)d\tau $$” option3=”$$v\left( t \right) = \int\limits_0^t {i\left( \tau \right)} z\left( {t + \tau } \right)d\tau $$” option4=”v(t) = z(t) + i(t)” correct=”option4″]
4. The transfer function of a zero-order-hold system is
[amp_mcq option1=”$$\left( {\frac{1}{s}} \right)\left( {1 + {e^{ – sT}}} \right)$$” option2=”$$\left( {\frac{1}{s}} \right)\left( {1 – {e^{ – sT}}} \right)$$” option3=”$$1 – \left( {\frac{1}{s}} \right){e^{ – sT}}$$” option4=”$$1 + \left( {\frac{1}{s}} \right){e^{ – sT}}$$” correct=”option1″]
Detailed SolutionThe transfer function of a zero-order-hold system is
5. Two systems with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by
[amp_mcq option1=”Product of h1(t) and h2(t)” option2=”Sum of h1(t) and h2(t)” option3=”Convolution of h1(t) and h2(t)” option4=”Subtraction of h2(t) from h1(t)” correct=”option3″]
6. A periodic signal x(t) has a trigonometric Fourier series expansion $$x\left( t \right) = {a_0} + \sum\limits_{n = 1}^\infty {\left( {{a_n}\,\cos \,n{\omega _0}t + {b_n}\sin \,n{\omega _0}t} \right)} $$ If $$x\left( t \right) = – x\left( { – t} \right) = – x\left( {{{t – \pi } \over {{\omega _0}}}} \right),$$ we can conclude that
[amp_mcq option1=”an are zero for all n and bn are zero for n even” option2=”an are zero for all n and bn are zero for n odd” option3=”an are zero for n even and bn are zero for n odd” option4=”an are zero for n odd and bn are zero for n even” correct=”option1″]
7. The magnitude and phase of the complex Fourier series coefficient ak of a periodic signal x(t) are shown in the figure. Choose the correct statement from the four choices given. Notation: C is the set of complex number, R is the set of purely real numbers, and P is the set of purely imaginary numbers.
[amp_mcq option1=”$$x\left( t \right) \in R$$” option2=”$$x\left( t \right) \in P$$” option3=”$$x\left( t \right) \in \left( {C – R} \right)$$” option4=”The information given is not sufficient to draw any conclusion about x(t)” correct=”option1″]
8. For an N-point FFT algorithm with N = 2m, which one of the following statements is TRUE?
[amp_mcq option1=”It is not possible to construct a signal flow graph with both input and output in normal order” option2=”The number of butterflies in the mn state is $$\frac{N}{m}$$” option3=”In-place computation requires storage of only 2N node data” option4=”Computation of a butterfly requires only one complex multiplication” correct=”option2″]
9. A discrete time linear shift-invariant system has an impulse response h[n] with h[0] = 1, h[1] = -1, h[2] = 2, and zero otherwise. The system is given an input sequence x[n] with x[0] = x[2] = 1 and zero otherwise. The number of nonzero samples in the output sequence y[n], and the value of y[2] are, respectively
[amp_mcq option1=”5, 2″ option2=”6, 2″ option3=”6, 1″ option4=”5, 3″ correct=”option3″]
10. The trigonometric Fourier series of a periodic time function can have only
[amp_mcq option1=”Cosine terms” option2=”Sine terms” option3=”Cosine and sine terms” option4=”Dc and cosine terms” correct=”option3″]
Detailed SolutionThe trigonometric Fourier series of a periodic time function can have only