Digital Signal Processing Questions and Answers – Frequency Transformations in the Analog Domain

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?
Frequency characteristic figure is magnitude response of 13-order type-2 chebyshev filter
a) Type-2 Chebyshev filter
b) Type-1 Chebyshev filter
c) Butterworth filter
d) Bessel filter
View Answer

Answer: a
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?
a) ΩS=\(\frac{Ω_S}{Ω_u}\)
b) ΩS=\(\frac{Ω_u}{Ω’_S}\)
c) Ω’S=\(\frac{Ω_S}{Ω_u}\)
d) ΩS=\(\frac{Ω’_S}{Ω_u}\)
View Answer

Answer: b
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
ΩS=\(\frac{Ω_u}{Ω’_S}\)
.

3. Which of the following filter has a phase spectrum as shown in figure?
Phase response in figure belongs to frequency characteristic of 7-order elliptic filter
a) Chebyshev filter
b) Butterworth filter
c) Bessel filter
d) Elliptical filter
View Answer

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

Answer: c
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

Answer: b
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.
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6. Which of the following is the backward design equation for a low pass-to-low pass transformation?
a) ΩS=\(\frac{Ω_S}{Ω_u}\)
b) ΩS=\(\frac{Ω_u}{Ω’_S}\)
c) Ω’S=\(\frac{Ω_S}{Ω_u}\)
d) ΩS=\(\frac{Ω’_S}{Ω_u}\)
View Answer

Answer: d
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
ΩS=\(\frac{Ω’_S}{Ω_u}\)
.

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

Answer: a
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.
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8. 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→\(\frac{s^2-Ω_u Ω_l}{s(Ω_u+Ω_l)}\)
View Answer

Answer: c
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
s→\(\frac{s^2+Ω_u Ω_l}{s(Ω_u-Ω_l)}\)

9. Which of the following filter has a phase spectrum as shown in figure?
Phase response belongs to frequency characteristic of 13-order type-1 Chebyshev filter
a) Chebyshev filter
b) Butterworth filter
c) Bessel filter
d) Elliptical filter
View Answer

Answer: a
Explanation: The phase response given in the figure belongs to the frequency characteristic of a 13-order type-1 Chebyshev filter.
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10. 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|}
View Answer

Answer: d
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, A=\(\frac{-Ω_1^2+Ω_u Ω_l}{Ω_1 (Ω_u-Ω_l)}\) and B=\(\frac{Ω_2^2-Ω_u Ω_l}{Ω_2 (Ω_u-Ω_l)}\).

11. 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|
View Answer

Answer: b
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, =\(\frac{Ω_1 (Ω_u-Ω_l)}{-Ω_1^2+Ω_u Ω_l}\) and B=\(\frac{Ω_2 (Ω_u-Ω_l)}{-Ω_2^2+Ω_u Ω_l}\).

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

Answer: b
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?
Frequency characteristic in figure is magnitude response of 37-order Butterworth filter
a) Type-2 Chebyshev filter
b) Type-1 Chebyshev filter
c) Butterworth filter
d) Bessel filter
View Answer

Answer: c
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?
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
View Answer

Answer: c
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
s→\(\frac{s(Ω_u-Ω_l)}{s^2-Ω_u Ω_l}\)

Sanfoundry Global Education & Learning Series – Digital Signal Processing.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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