# Digital Signal Processing Questions and Answers – Design of Linear Phase FIR Filters Using Windows – 2

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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

Explanation: The peak side lobe in the case of rectangular window has a value of -13dB.

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

Explanation: The peak side lobe in the case of Hanning window has a value of -32dB.

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

Explanation: The frequency of oscillations in the pass band of a low pass filter increases with an increase in the value of M, but they do not diminish in amplitude.

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

Explanation: 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 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 Gibbs phenomenon.

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

Explanation: 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.

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

Explanation: 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.

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

Explanation: The transition width of the main lobe in the case of Blackman window is equal to 12π/M where M is the length of the window.

8. 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

Explanation: The Hanning window has a time domain sequence as
h(n)=$$\frac{1}{2}(1-cos⁡\frac{2πn}{M-1})$$, 0≤n≤M-1

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

Explanation: 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.

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