This set of Digital Signal Processing Problems focuses on “Frequency Transformations in the Analog Domain”.

1. The following frequency characteristic is for which of the following filter?

a) Type-2 Chebyshev filter

b) Type-1 Chebyshev filter

c) Butterworth filter

d) Bessel filter

View Answer

Explanation: The frequency characteristic given in the figure is the magnitude response of a 13-order type-2 chebyshev filter.

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

View Answer

Explanation: If Ωu is the desired pass band edge frequency of new high pass filter, then the transfer function of this new high pass filter is obtained by using the transformation s→ Ωu /s. If ΩS and Ω’S are the stop band frequencies of prototype and transformed filters respectively, then the backward design equation is given by

.

3. Which of the following filter has a phase spectrum as shown in figure?

a) Chebyshev filter

b) Butterworth filter

c) Bessel filter

d) Elliptical filter

View Answer

Explanation: The phase response given in the figure belongs to the frequency characteristic of a 7-order elliptic filter.

4. What is the pass band 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

View Answer

Explanation: Let H(s) denote the transfer function of a low pass analog filter with a pass band edge frequency ΩP equal to 1 rad/sec. This filter is known as analog low pass normalized prototype.

5. 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

View Answer

Explanation: The low pass-to-high pass transformation is simply achieved by replacing s by 1/s. If the desired high pass filter has the pass band edge frequency Ωu, then the transformation is

s→ Ωu / s.

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

View Answer

Explanation: If Ωu is the desired pass band edge frequency of new low pass filter, then the transfer function of this new low pass filter is obtained by using the transformation s→ s / Ωu. If ΩS and Ω’S are the stop band frequencies of prototype and transformed filters respectively, then the backward design equation is given by

.

7. If H(s) is the transfer function of a analog low pass normalized filter and Ωu is the desired pass band edge frequency of 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

View Answer

Explanation: If Ωu is the desired pass band edge frequency of new low pass filter, then the transfer function of this new low pass filter is obtained by using the transformation s→ s / Ωu.

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

View Answer

Explanation: If Ωu and Ωl are the upper and lower cutoff pass band frequencies of the desired band pass filter, then the transformation to be performed on the normalized low pass filter is

9. Which of the following filter has a phase spectrum as shown in figure?

a) Chebyshev filter

b) Butterworth filter

c) Bessel filter

d) Elliptical filter

View Answer

Explanation: The phase response given in the figure belongs to the frequency characteristic of a 13-order type-1 Chebyshev filter.

10. If , 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|}

View Answer

Explanation: If Ωu and Ωl are the upper and lower cutoff pass band frequencies of the desired band pass filter and Ω1 and Ω2 are the lower and upper cutoff stop band frequencies of the desired band pass filter, then the backward design equation is

ΩS= Min{|A|,|B|}

where, .

11. If, 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|

View Answer

Explanation: If Ωu and Ωl are the upper and lower cutoff pass band frequencies of the desired band stop filter and Ω1 and Ω2 are the lower and upper cutoff stop band frequencies of the desired band stop filter, then the backward design equation is

ΩS= Min{|A|,|B|}

where, .

12. 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

View Answer

Explanation: The low pass-to-high pass transformation is simply achieved by replacing s by 1/s. If the desired high pass filter has the pass band edge frequency Ωu, then the transformation is

s→ Ωu / s

13. The following frequency characteristic is for which of the following filter?

a) Type-2 Chebyshev filter

b) Type-1 Chebyshev filter

c) Butterworth filter

d) Bessel filter

View Answer

Explanation: The frequency characteristic given in the figure is the magnitude response of a 37-order Butterworth filter.

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

d) None of the mentioned

View Answer

Explanation: If Ωu and Ωl are the upper and lower cutoff pass band frequencies of the desired band stop filter, then the transformation to be performed on the normalized low pass filter is

**Sanfoundry Global Education & Learning Series – Digital Signal Processing.**

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