Analog Filter Characteristics MCQ [Free PDF] – Objective Question Answer for Analog Filter Characteristics Quiz

1. Low pass Butterworth filters are also called as ________

A. All-zero filter
B. All-pole filter
C. Pole-zero filter
D. None of the mentioned

Answer: B

Low pass Butterworth filters are also called all-pole filters because it has only non-zero poles.

 

2. What is the equation for the magnitude square response of a low pass Butterworth filter?

A. \(\frac{1}{\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}}\)

B. \(1+(\frac{Ω}{Ω_C})^{2N}\)

C. \(\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}\)

D. None of the mentioned

Answer: A

A Butterworth is characterized by the magnitude frequency response

|H(jΩ)| = \(\frac{1}{\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}}\)

where N is the order of the filter and ΩC is defined as the cutoff frequency.

 

3. What is the transfer function of magnitude squared frequency response of the normalized low pass Butterworth filter?

A. \(\frac{1}{1+(s/j)^{-2N}}\)

B. \(1+(\frac{s}{j})^{-2N}\)

C. \(1+(\frac{s}{j})^{2N}\)

D. \(\frac{1}{1+(\frac{s}{j})^{2N}}\)

Answer: D

We know that the magnitude squared frequency response of a normalized low pass Butterworth filter is given as

|H(jΩ)|2 =\(\frac{1}{1+Ω^{2N}}\)

=> HN(jΩ).HN(-jΩ)=\(\frac{1}{1+Ω^{2N}}\)

Replacing jΩ by ‘s’ and hence Ω by s/j in the above equation, we get

HN(s).HN(-s) = \(\frac{1}{1+(\frac{s}{j})^{2N}}\) which is called the transfer function.

 

4. Which of the following is the band edge value of |H(Ω)|2?

A. (1+ε2)
B. (1-ε2)
C. 1/(1+ε2)
D. 1/(1-ε2)

Answer: C

1/(1+ε2) gives the band edge value of the magnitude square response |H(Ω)|2.

 

5. The magnitude square response shown in the below figure is for which of the following given filters?

A. Butterworth
B. Chebyshev
C. Elliptical
D. None of the mentioned

Answer: A

The magnitude square response shown in the given figure is for the Butterworth filter.

 

6. What is the order of a low-pass Butterworth filter that has a -3dB bandwidth of 500Hz and an attenuation of 40dB at 1000Hz?

A. 4
B. 5
C. 6
D. 7

Answer: D

Given Ωc=1000π and Ωs=2000π

For an attenuation of 40dB, δ2=0.01.

We know that

N=\(\frac{log⁡[(\frac{1}{δ_2^2})-1]}{2log⁡[\frac{Ω_s}{Ω_s}]}\)

Thus by substituting the corresponding values in the above equation, we get N=6.64
To meet the desired specifications, we select N=7.

 

7. Which of the following is true about the type-1 Chebyshev filter?

A. Equi-ripple behavior in passband
B. Monotonic characteristic in stopband
C. Equi-ripple behavior in passband & Monotonic characteristic in stopband
D. None of the mentioned

Answer: C

Type-1 Chebyshev filters are all-pole filters that exhibit equi-ripple behavior in the passband and a monotonic characteristic in the stopband.

 

8. Type-2 Chebyshev filters consists of ______________

A. Only poles
B. Both poles and zeros
C. Only zeros
D. Cannot be determined

Answer: B

Type-1 Chebyshev filters are all-pole filters whereas the family of type-2 Chebyshev filters contains both poles and zeros.

 

9. Which of the following is false about the type-2 Chebyshev filters?

A. Monotonic behavior in the passband
B. Equi-ripple behavior in the stopband
C. Zero behavior
D. Monotonic behavior in the stopband

Answer: D

Type-2 Chebyshev filters exhibit equi-ripple behavior in the stopband and a monotonic characteristic in the passband.

 

10. The zeros of type-2 class of Chebyshev filters lies on ___________

A. Imaginary axis
B. Real axis
C. Zero
D. Cannot be determined

Answer: A

The zeros of this class of filters lie on the imaginary axis in the s-plane.

 

11. Which of the following defines a Chebyshev polynomial of order N, TN(x)?

A. cos(Ncos-1x) for all x
B. cosh(Ncosh-1x) for all x
C.cos(Ncos-1x), |x|≤1 cosh(Ncosh-1x), |x|>1
D. None of the mentioned

Answer: C
In order to understand the frequency-domain behavior of Chebyshev filters, it is of utmost importance to define a Chebyshev polynomial and then its properties. A Chebyshev polynomial of degree N is defined as
TN(x) = cos(Ncos-1x), |x|≤1
cosh(Ncosh-1x), |x|>1

 

12. The frequency response shown in the figure below belongs to which of the following filters?

The frequency response shown in the figure below belongs to which of the following filters?

A. Type-1 Chebyshev
B. Type-2 Chebyshev
C. Butterworth
D. Elliptical

Answer: B

Since the passband is monotonic in behavior and the stopband exhibit equi-ripple behavior, it is the magnitude square response of a type-2 Chebyshev filter.

 

13. What is the order of the type-2 Chebyshev filter whose magnitude square response is as shown in the following figure?

The frequency response shown in the figure below belongs to which of the following filters?

A. 2
B. 4
C. 6
D. 3

Answer: D

Since the magnitude square response of the type-2 Chebyshev filter, it has an odd number of maxima and minima in the stopband, the order of the filter is odd i.e., 3.

 

14. Which of the following is true about the magnitude square response of an elliptical filter?

A. Equi-ripple in passband
B. Equi-ripple in stopband
C. Equi-ripple in passband and stopband
D. None of the mentioned

Answer: C

An elliptical filter is a filter that exhibits equi-ripple behavior in both passband and stopband of the magnitude square response.

 

15. Bessel filters exhibit a linear phase response over the passband of the filter.

A. True
B. False

Answer: A

An important characteristic of the Bessel filter is the linear phase response over the passband of the filter. As a consequence, Bessel filters have a larger transition bandwidth, but their phase is linear within the passband.

 

16. 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

Answer: A

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

 

17. 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=\(\frac{Ω’_S}{Ω_u}\)

Answer: B

If Ωu is the desired passband edge frequency of the 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 stopband frequencies of prototype and transformed filters respectively, then the backward design equation is given by

ΩS=\(\frac{Ω_u}{Ω’_S}\)

 

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

A. Chebyshev filter
B. Butterworth filter
C. Bessel filter
D. Elliptical filter

Answer: D

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

 

19. 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

Answer: C

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

 

20. 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

Answer: B

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

 

21. 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=\(\frac{Ω’_S}{Ω_u}\)

Answer: D

If Ωu is the desired passband edge frequency of the 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 stopband frequencies of prototype and transformed filters respectively, then the backward design equation is given by

ΩS=\(\frac{Ω’_S}{Ω_u}\)

 

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

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

 

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

 

Answer: C

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

s→\(\frac{s^2+Ω_u Ω_l}{s(Ω_u-Ω_l)}\)

 

24. 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|}

Answer: D

If Ωu and Ωl are the upper and lower cutoff pass band frequencies of the desired bandpass filter and Ω1 and Ω2 are the lower and upper cutoff stopband frequencies of the desired bandpass 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=\(\frac{Ω_2^2-Ω_u Ω_l}{Ω_2 (Ω_u-Ω_l)}\).

 

25. 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|

Answer: B

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 stopband 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=\(\frac{Ω_2 (Ω_u-Ω_l)}{-Ω_2^2+Ω_u Ω_l}\).

 

26. 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

Answer: B

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

 

27. 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

Answer: C

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

 

28. 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

Answer: C

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→\(\frac{s(Ω_u-Ω_l)}{s^2-Ω_u Ω_l}\)

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