Frequency Selective Filters

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “LTI System as Frequency Selective Filters”.

1. An ideal filter should have unity gain in their stop band.
a) True
b) False

2. Which filter has a magnitude frequency response as shown in the plot given below?

a) Low pass Filter
b) High pass Filter
c) Band pass Filter
d) Band stop Filter

3. An ideal filter should have zero gain in their stop band.
a) True
b) False

4. The ‘Envelope delay’ or ‘Group delay’ is the time delay that the signal component of frequency ω undergoes as it passes from the input to the output of the system.
a) True
b) False

5. If the phase ϴ(ω) of the system is linear, then the group delay of the system?
a) Increases with frequency of signal
b) Constant
c) Decreases with frequency of signal
d) Independent of frequency of signal

6. A two pole low pass filter has a system function H(z)=b0(1−pz−1)2, What is the value of ‘p’ such that the frequency response H(ω) satisfies the condition |H(π/4)|2=1/2 and H(0)=1?
a) 0.46
b) 0.38
c) 0.32
d) 0.36

7. A two pole low pass filter has a system function H(z)=b0(1−pz−1)2, What is the value of ‘b0‘ such that the frequency response H(ω) satisfies the condition |H(π/4)|2=1/2 and H(0)=1?
a) 0.36
b) 0.38
c) 0.32
d) 0.46

8. What is the system function for a two pole band pass filter that has the centre of its pass band at ω=π/2, zero its frequency response characteristic at ω=0 and at ω=π, and its magnitude response is 1/√2 at ω=4π/9?
a) 0.151−z−21+0.7z−2
b) 0.151+z−21−0.7z−2
c) 0.151−z−21−0.7z−2
d) 0.151+z−21+0.7z−2

9. If hlp(n) denotes the impulse response of a low pass filter with frequency response Hlp(ω), then what is the frequency response of the high pass filter in terms of Hlp(ω)?
a) Hlp(ω-π/2)
b) Hlp(ω+π/2)
c) Hlp(ω-π)
d) Hlp(ω+π)

10. If the low pass filter described by the difference equation y(n)=0.9y(n-1)+0.1x(n) is converted into a high pass filter, then what is the frequency response of the high pass filter?
a) 0.1/(1+0.9e)
b) 0.1/(1+0.9e-jω)
c) 0.1/(1-0.9e)
d) None of the mentioned

11. A digital resonator is a special two pole band pass filter with the pair of complex conjugate poles located near the unit circle.
a) True
b) False

12. Which of the following filters have a frequency response as shown below?

a) Band pass filter
b) Band stop filter
c) All pass filter
d) Notch filter

13. A comb filter is a special case of notch filter in which the nulls occur periodically across the frequency band.
a) True
b) False

14. The filter with the system function H(z)=z-k is a ____________
a) Notch filter
b) Band pass filter
c) All pass filter
d) None of the mentioned

15. If the system has a impulse response as h(n)=Asin(n+1)ω0u(n), then the system is known as Digital frequency synthesizer.
a) True
b) False