# FIR Filters Windows Design

This set of Digital Signal Processing MCQs focuses on “Design of Linear Phase FIR Filters Using Windows-2”.

1. What is the peak side lobe (in dB) for a rectangular window?
a) -13
b) -27
c) -32
d) -58

2. What is the peak side lobe (in dB) for a Hanning window?
a) -13
b) -27
c) -32
d) -58

3. How does the frequency of oscillations in the pass band of a low pass filter varies with the value of M?
a) Decrease with increase in M
b) Increase with increase in M
c) Remains constant with increase in M
d) None of the mentioned

4. The oscillatory behavior near the band edge of the low pass filter is known as Gibbs phenomenon.
a) True
b) False

5. Which of the following window is used in the design of a low pass filter to have a frequency response as shown in the figure?

a) Hamming window
b) Hanning window
c) Kaiser window
d) Blackman window

6. Which of the following window is used in the design of a low pass filter to have a frequency response as shown in the figure?

a) Hamming window
b) Hanning window
c) Kaiser window
d) Blackman window

7. What is the approximate transition width of main lobe of a Blackman window?
a) 4π/M
b) 8π/M
c) 12π/M
d) 2π/M

8. Which of the following windows has a time domain sequence h(n)=12(1−cos2πnM−1)?
a) Bartlett window
b) Blackman window
c) Hamming window
d) Hanning window

9. If the value of M increases then the main lobe in the frequency response of the rectangular window becomes broader.
a) True
b) False

10. The large side lobes of W(ω) results in which of the following undesirable effects?
a) Circling effects
b) Broadening effects
c) Ringing effects
d) None of the mentioned

11. Which of the following defines the rectangular window function of length M-1?
a)

```w(n)=1, n=0,1,2...M-1
=0, else where```

b)

```w(n)=1, n=0,1,2...M-1
=-1, else where```

c)

```w(n)=0, n=0,1,2...M-1
=1, else where```

d) None of the mentioned

12. The multiplication of the window function w(n) with h(n) is equivalent to the multiplication of H(w) and W(w).
a) True
b) False

13. What is the Fourier transform of the rectangular window of length M-1?
a) ejω(M−1)/2sin(ωM2)sin(ω2)
b) ejω(M+1)/2sin(ωM2)sin(ω2)
c) e−jω(M+1)/2sin(ωM2)sin(ω2)
d) e−jω(M−1)/2sin(ωM2)sin(ω2)

14. What is the magnitude response |W(ω)| of a rectangular window function?
a) |sin(ωM/2)||sin(ω/2)|
b) |sin(ω/2)||sin(ωM/2)|
c) |cos(ωM/2)||sin(ω/2)|
d) None of the mentioned

15. What is the width of the main lobe of the frequency response of a rectangular window of length M-1?
a) π/M
b) 2π/M
c) 4π/M
d) 8π/M

16. The width of each side lobes decreases with an increase in M.
a) True
b) False

17. With an increase in the value of M, the height of each side lobe ____________
a) Do not vary
b) Does not depend on value of M
c) Decreases
d) Increases

18. As M is increased, W(ω) becomes wider and the smoothening produced by the W(ω) is increased.
a) True
b) False

19. Which of the following windows has a time domain sequence h(n)=1−2|n−M−12|M−1?
a) Bartlett window
b) Blackman window
c) Hanning window
d) Hamming window

20. The width of each side lobes decreases with an decrease in M.
a) True
b) False

21. What is the approximate transition width of main lobe of a Hamming window?
a) 4π/M
b) 8π/M
c) 12π/M
d) 2π/M
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