1. What is the passband edge frequency of an analog low pass normalized filter?

A. 0 rad/sec

B. 0.5 rad/sec

C. 1 rad/sec

D. 1.5 rad/sec

2. If H(s) is the transfer function of an analog low pass normalized filter and Ωu is the desired passband edge frequency of the new low pass filter, then which of the following transformation has to be performed?

A. s → s/Ωu

B. s → s.Ωu

C. s → Ωu/s

D. none of the mentioned

3. Which of the following is a low pass-to-high pass transformation?

A. s → s / Ωu

B. s → Ωu / s

C. s → Ωu.s

D. none of the mentioned

4. Which of the following is the backward design equation for a low pass-to-low pass transformation?

A. \(\Omega_S=\frac{\Omega_S}{\Omega_u}\)

B. \(\Omega_S=\frac{\Omega_u}{\Omega’_S}\)

C. \(\Omega’_S=\frac{\Omega_S}{\Omega_u}\)

D. \(\Omega_S=\frac{\Omega’_S}{\Omega_u}\)

5. Which of the following is a low pass-to-band pass transformation?

A. s→\(\frac{s^2+Ω_u Ω_l}{s(Ω_u+Ω_l)}\)

B. s→\(\frac{s^2-Ω_u Ω_l}{s(Ω_u-Ω_l)}\)

C. s→\(\frac{s^2+Ω_u Ω_l}{s(Ω_u-Ω_l)}\)

D. s→\(\frac{s^2-Ω_u Ω_l}{s(Ω_u+Ω_l)}\)

6. Which of the following is the backward design equation for a low pass-to-high pass transformation?

A. \(\Omega_S=\frac{\Omega_S}{\Omega_u}\)

B. \(\Omega_S=\frac{\Omega_u}{\Omega’_S}\)

C. \(\Omega’_S=\frac{\Omega_S}{\Omega_u}\)

D. \(\Omega_S=\frac{\Omega’_S}{\Omega_u}\)

7. Which of the following is a low pass-to-band stop transformation?

A. s→\(\frac{s(Ω_u-Ω_l)}{s^2+Ω_u Ω_l}\)

B. s→\(\frac{s(Ω_u+Ω_l)}{s^2+Ω_u Ω_l}\)

C. s→\(\frac{s(Ω_u-Ω_l)}{s^2-Ω_u Ω_l}\)

D. none of the mentioned

8. If A=\(\frac{-Ω_1^2+Ω_u Ω_l}{Ω_1 (Ω_u-Ω_l)}\) and B=\(\frac{Ω_2^2-Ω_u Ω_l}{Ω_2 (Ω_u-Ω_l)}\), then which of the following is the backward design equation for a low pass-to-band pass transformation?

A. ΩS=|B|

B. ΩS=|A|

C. ΩS=Max{|A|,|B|}

D. ΩS=Min{|A|,|B|}

9. If A=\(\frac{Ω_1 (Ω_u-Ω_l)}{-Ω_1^2+Ω_u Ω_l}\) and B=\(\frac{Ω_2 (Ω_u-Ω_l)}{Ω_2^2-Ω_u Ω_l}\), then which of the following is the backward design equation for a low pass-to-band stop transformation?

A. ΩS=Max{|A|,|B|}

B. ΩS=Min{|A|,|B|}

C. ΩS=|B|

D. ΩS=|A|

10. Which of the following is a low pass-to-high pass transformation?

A. s → s / Ωu

B. s → Ωu/s

C. s → Ωu.s

D. none of the mentioned

11. Which of the following operation has to be performed to increase the sampling rate by an integer factor I?

A. Interpolating I+1 new samples

B. Interpolating I-1 new samples

C. Extrapolating I+1 new samples

D. Extrapolating I-1 new samples

12. In one of the interpolation processes, we can preserve the spectral shape of the signal sequence x(n).

A. True

B. False

13. If v(m) denotes a sequence with a rate Fy=I.Fx which is obtained from x(n), then which of the following is the correct definition for v(m)?

A.x(mI), m=0,±I,±2I…. 0, otherwise

B. x(mI), m=0,±I,±2I…. x(m/I), otherwise

C. x(m/I), m=0,±I,±2I….

0, otherwise

D. None of the mentioned

14. If X(z) is the z-transform of x(n), then what is the z-transform of interpolated signal v(m)?

A. X(zI)

B. X(z+I)

C. X(z/I)

D. X(zI)

15. If x(m) and v(m) are the original and interpolated signals and ωy denotes the frequency variable relative to the new sampling rate, then V(ωy)= X(ωyI).

A. True

B. False

16. What is the relationship between ωx and ωy?

A. ωy= ωx.I

B. ωy= ωx/I

C. ωy= ωx+I

D. None of the mentioned

17. The following sampling rate conversion technique is an interpolation by a factor I.

A. True

B. False

18. The following sampling rate conversion technique is an interpolation by a factor I.

A. True

B. False

19. Which of the following is true about the interpolated signal whose spectrum is V(ωy)?

A. (I-1)-fold non-periodic

B. (I-1)-fold periodic repetition

C. I-fold non periodic

D. I-fold periodic repetition

20. C=I is the desired normalization factor.

A. True

B. False

21. Sampling rate conversion by the rational factor I/D is accomplished by what connection of interpolator and decimator?

A. Parallel

B. Cascade

C. Convolution

D. None of the mentioned

22. Which of the following has to be performed in sampling rate conversion by rational factor?

A. Interpolation

B. Decimation

C. Either interpolation or decimation

D. None of the mentioned

23. Which of the following operation is performed by the blocks given in the figure below?

A. Sampling rate conversion by a factor I

B. Sampling rate conversion by a factor D

C. Sampling rate conversion by a factor D/I

D. Sampling rate conversion by a factor I/D

24. The Nth root of unity WN is given as ______

A. e^{j2πN}

B. e^{-j2πN}

C. e^{-j2π/N}

D. e^{j2π/N}