Analog Domain Frequency Transformations

Digital Communications Systems

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

2. Which of the following is the backward design equation for a low pass-to-high pass transformation?
a) ΩS=ΩSΩu
b) ΩS=ΩuΩ′S
c) Ω’S=ΩSΩu
d) ΩS=Ω′SΩu

.

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

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

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

6. Which of the following is the backward design equation for a low pass-to-low pass transformation?
a) ΩS=ΩSΩu
b) ΩS=ΩuΩ′S
c) Ω’S=ΩSΩu
d) ΩS=Ω′SΩu

.

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

8. Which of the following is a low pass-to-band pass transformation?
a) s→s2+ΩuΩls(Ωu+Ωl)
b) s→s2−ΩuΩls(Ωu−Ωl)
c) s→s2+ΩuΩls(Ωu−Ωl)
d) s→s2−ΩuΩls(Ωu+Ωl)

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

10. If A=−Ω21+ΩuΩlΩ1(Ωu−Ωl) and B=Ω22−ΩuΩlΩ2(Ωu−Ωl), 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|}

11. If A=Ω1(Ωu−Ωl)−Ω21+ΩuΩl and B=Ω2(Ωu−Ωl)−Ω22+ΩuΩl, 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|

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

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

14. Which of the following is a low pass-to-band stop transformation?
a) s→s(Ωu−Ωl)s2+ΩuΩl
b) s→s(Ωu+Ωl)s2+ΩuΩl
c) s→s(Ωu−Ωl)s2−ΩuΩl
d) None of the mentioned

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