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### Transcript of 1 Assignment-8 (Lecture 36-40) - NPTEL 8 1 Assignment-8 (Lecture 36-40) 1. A symbol sequence...

• 1 Assignment-8 (Lecture 36-40)

1. A symbol sequence consisting of binary digit is given as,

In = bn + 4bn−1

where, bn = −1, 1 with equal probability then the power spectral density of the lowpass modulated signal is, A. 1

T |G(f)|22cos2πfT

B. 4|G(f)|2cos2πfT C. 1

T |G(f)|2

( 17 + 8cos(2πfT )

) D. 1

T |G(f)|2

( 1 + 4cos(2πfT )

) 2. A symbol sequence consisting of binary digit is given as,

In = bn + 4bn−1

Where bn = 0, 1 with equal probability. The power spectral density of the baseband signal is, A. 1

T |G(f)|2(1 + 4cos2πfT )

B. 1 T |G(f)|2(8.5 + 4cos2πfT )

C. 1 T |G(f)|2(1 + 2cos2πfT )

D. None of these

3. A symbol sequence consisting of binary digit is given as,

In = bn + 4bn−1

if g(t) is raised-cosine pulse, how will the output look like?

• A.

B.

C.

D. None of these

4. For a Wide sense cyclostationary signal A. The mean is periodic and autocorrelation function is aperiodic. B. The mean is aperiodic and autocorrelation function is periodic. C. Both the mean and autocorrelation functions are periodic. D. Both the mean and autocorrelation functions are aperiodic.

5. A WSS random process X(t) is applied to the input of an LTI system with impulse response h(t) = 3e−2tu(t). The mean value if the output Y(t) is, A. 3

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• B. 1 C. 4 D. 2

6. Let X(t) and Y (t) be defined by,

X(t) = Acosωt+Bsinωt

Y (t) = Bcosωt− Asinωt

Where ω is a constant and A and B are independent random variables both having zero mean and variance σ2. Then, the cross-correlation of X(t) and Y (t) is, A. σ2cosω(t1 − t2) B. −σ2sinω(t1 − t2) C. 1

σ2 sinω(t1 − t2)

D. − 1 σ2 cosω(t1 − t2)

7. If X(t) and Y (t) are WSS random processes then the upper limit of |RXY (τ)| is, A. RXX(0) B. RXX(0)RY Y (0) C. √ RXX(0)RY Y (0)

D. None of these

8. A WSS random process X(t) with autocorrelation

RXX(τ) = Ae −a|τ |

Where A and a are real positive constants, is applied to the input of an LTI system with impulse response

r(t) = e−btu(t)

where b is a real positive constant, the autocorrelation of the output Y (t) of the system is, A. aA

(a2−b2)be −b|τ | − A

a2−b2 e −a|τ |

B. A b e−a|τ | − b

a2−b2 e −b|τ |

C. aA (a2−b2)be

−b|τ | + A a2−b2 e

−a|τ |

D. None of these

9. A bit stream is given as, 110101101011

then the inphase and quadrature phase signal components of the MSK signal is given as,

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• A.

B.

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• C.

D.

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• 10. Which of the following statements are true regarding the spectra of OQPSK and MSK? A. Main lobe width of MSK is same as OQPSK and sidelobe of OQPSK fall off faster. B. Main lobe width of MSK is less than OQPSK and sidelobe of MSK fall off faster. C. Main lobe width of MSK is larger than OQPSK and sidelobes of both fall off at the same rate. D. Main lobe width of MSK is larger than OQPSK and sidelobe of MSK fall off faster.

1. C

2. B

3. A

4. C

5. A

6. B

7. C

8. A

9. B

10. D

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