Signal processing

1. Let $$x\left[ n \right] = {\left( { – {1 \over 9}} \right)^n}u\left( n \right) – {\left( { – {1 \over 3}} \right)^n}u\left( { – n – 1} \right).$$ The Region of Convergence (ROC) of the z-transform of x[n]

”Is
”Is
”Does

Detailed SolutionLet $$x\left[ n \right] = {\left( { – {1 \over 9}} \right)^n}u\left( n \right) – {\left( { – {1 \over 3}} \right)^n}u\left( { – n – 1} \right).$$ The Region of Convergence (ROC) of the z-transform of x[n]

2. A system with an input x(t) and output y(t) is described by the relation: y(t) = tx(t). This system is

Linear and time-invariant
Linear and time varying
Non-linear & time-invariant
Non-linear and time-varying

Detailed SolutionA system with an input x(t) and output y(t) is described by the relation: y(t) = tx(t). This system is

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

v(t) = z(t).i(t)
$$vleft( t ight) = intlimits_0^t {ileft( au ight)} zleft( {t - au } ight)d au $$
$$vleft( t ight) = intlimits_0^t {ileft( au ight)} zleft( {t + au } ight)d au $$
v(t) = z(t) + i(t)

Detailed SolutionThe 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

4. The transfer function of a zero-order-hold system is

$$left( { rac{1}{s}} ight)left( {1 + {e^{ - sT}}} ight)$$
$$left( { rac{1}{s}} ight)left( {1 - {e^{ - sT}}} ight)$$
$$1 - left( { rac{1}{s}} ight){e^{ - sT}}$$
$$1 + left( { rac{1}{s}} ight){e^{ - sT}}$$

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

Product of h1(t) and h2(t)
Sum of h1(t) and h2(t)
Convolution of h1(t) and h2(t)
Subtraction of h2(t) from h1(t)

Detailed SolutionTwo 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

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

an are zero for all n and bn are zero for n even
an are zero for all n and bn are zero for n odd
an are zero for n even and bn are zero for n odd
an are zero for n odd and bn are zero for n even

Detailed SolutionA 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

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.

$$xleft( t ight) in R$$
$$xleft( t ight) in P$$
$$xleft( t ight) in left( {C - R} ight)$$
The information given is not sufficient to draw any conclusion about x(t)

Detailed SolutionThe 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.

8. For an N-point FFT algorithm with N = 2m, which one of the following statements is TRUE?

It is not possible to construct a signal flow graph with both input and output in normal order
The number of butterflies in the mn state is $$ rac{N}{m}$$
In-place computation requires storage of only 2N node data
Computation of a butterfly requires only one complex multiplication

Detailed SolutionFor an N-point FFT algorithm with N = 2m, which one of the following statements is TRUE?

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

5, 2
6, 2
6, 1
5, 3

Detailed SolutionA 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

10. The trigonometric Fourier series of a periodic time function can have only

Cosine terms
Sine terms
Cosine and sine terms
Dc and cosine terms

Detailed SolutionThe trigonometric Fourier series of a periodic time function can have only

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