11. What is the approximate transition width of the main lobe of a Hamming window?
A. 4π/M
B. 8π/M
C. 12π/M
D. 2π/M
Answer: B
The transition width of the main lobe in the case of Hamming window is equal to 8π/M where M is the length of the window.
12. What is the peak sidelobe (in dB. for a rectangular window?
A. -13
B. -27
C. -32
D. -58
Answer: A
The peak sidelobe in the case of a rectangular window has a value of -13dB.
13. What is the peak sidelobe (in dB. for a Hanning window?
A. -13
B. -27
C. -32
D. -58
Answer: C
The peak sidelobe in the case of the Hanning window has a value of -32dB.
14. How does the frequency of oscillations in the passband of a low pass filter varies with the value of M?
A. Decrease with an increase in M
B. Increase with an increase in M
C. Remains constant with an increase in M
D. None of the mentioned
Answer: B
The frequency of oscillations in the passband of a low pass filter increases with an increase in the value of M, but they do not diminish in amplitude.
15. The oscillatory behavior near the band edge of the low pass filter is known as the Gibbs phenomenon.
A. True
B. False
Answer: A
The multiplication of hd(n) with a rectangular window is identical to truncating the Fourier series representation of the desired filter characteristic Hd(ω).
The truncation of the Fourier series is known to introduce ripples in the frequency response characteristic H(ω) due to the non-uniform convergence of the Fourier series at a discontinuity. The oscillatory behavior near the band edge of the low pass filter is known as the Gibbs phenomenon.
16. 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
Answer: D
The frequency response shown in the figure is the frequency response of a low pass filter designed using a Blackman window of length M=61.
17. 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
Answer: C
The frequency response shown in the figure is the frequency response of a low pass filter designed using a Kaiser window of length M=61 and α=4.
18. What is the approximate transition width of the main lobe of a Blackman window?
A. 4π/M
B. 8π/M
C. 12π/M
D. 2π/M
Answer: C
The transition width of the main lobe in the case of the Blackman window is equal to 12π/M where M is the length of the window.
19. Which of the following windows has a time-domain sequence h(n)=\(\frac{1}{2}(1-cos\frac{2πn}{M-1})\)?
A. Bartlett window
B. Blackman window
C. Hamming window
D. Hanning window
Answer: D
The Hanning window has a time domain sequence as
h(n)=\(\frac{1}{2}(1-cos\frac{2πn}{M-1})\)
20. If the value of M increases then the main lobe in the frequency response of the rectangular window becomes broader.
A. True
B. False
Answer: B
Since the width of the main lobe is inversely proportional to the value of M if the value of M increases then the main lobe becomes narrower.
21. The large side lobes of W(ω) result in which of the following undesirable effects?
A. Circling effects
B. Broadening effects
C. Ringing effects
D. None of the mentioned
Answer: C
The larger side lobes of W(ω) result in undesirable ringing effects in the FIR filter frequency response H(ω), and also in relatively large side lobes in H(ω).
22. In the frequency sampling method for FIR filter design, we specify the desired frequency response Hd(ω) at a set of equally spaced frequencies.
A. True
B. False
Answer: A
In the frequency sampling method, we specify the frequency response Hd(ω) at a set of equally spaced frequencies, namely ωk=\(\frac{2π}{M}(k+\alphA.\)
23. To reduce side lobes, in which region of the filter do the frequency specifications have to be optimized?
A. Stopband
B. Passband
C. Transition band
D. None of the mentioned
Answer: C
To reduce the side lobes, it is desirable to optimize the frequency specification in the transition band of the filter. This optimization can be accomplished numerically on a digital computer by means of linear programming techniques.
24. What is the frequency response of a system with input h(n) and window length of M?
A. \(\sum_{n=0}^{M-1} h(n)e^{jωn}\)
B. \(\sum_{n=0}^{M} h(n)e^{jωn}\)
C. \(\sum_{n=0}^M h(n)e^{-jωn}\)
D. \(\sum_{n=0}^{M-1} h(n)e^{-jωn}\)
Answer: D
The desired output of an FIR filter with an input h(n) and using a window of length M is given as
H(ω)=\(\sum_{n=0}^{M-1} h(n)e^{-jωn}\)
25. What is the relation between H(k+α) and h(n)?
A. H(k+α)=\(\sum_{n=0}^{M+1} h(n)e^{-j2π(k+α)n/M}\); k=0,1,2…M+1
B. H(k+α)=\(\sum_{n=0}^{M-1} h(n)e^{-j2π(k+α)n/M}\); k=0,1,2…M-1
C. H(k+α)=\(\sum_{n=0}^M h(n)e^{-j2π(k+α)n/M}\); k=0,1,2…M
D. None of the mentioned
Answer: B
We know that
ωk=\(\frac{2π}{M}\)(k+α) and H(ω)=\(\sum_{n=0}^{M-1} h(n)e^{-jωn}\)
Thus from substituting the first in the second equation, we get
