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 ‘b_{0}‘ 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 h_{lp}(n) denotes the impulse response of a low pass filter with frequency response H_{lp}(ω), then what is the frequency response of the high pass filter in terms of H_{lp}(ω)?

a) H_{lp}(ω-π/2)

b) H_{lp}(ω+π/2)**c) H _{lp}(ω-π)**

d) H

_{lp}(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^{jω})**b) 0.1/(1+0.9e ^{-jω})**

c) 0.1/(1-0.9e

^{jω})

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)ω_{0}u(n), then the system is known as Digital frequency synthesizer.**a) True**

b) False