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

Answer: A

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=\(\frac{Ω’_S}{Ω_u}\)

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=\(\frac{Ω_u}{Ω’_S}\)

3. 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.

4. 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.

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

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.

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=\(\frac{Ω’_S}{Ω_u}\)

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=\(\frac{Ω’_S}{Ω_u}\)

7. 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.

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→\(\frac{s^2-Ω_u Ω_l}{s(Ω_u+Ω_l)}\)

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→\(\frac{s^2+Ω_u Ω_l}{s(Ω_u-Ω_l)}\)

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|}

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