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Test: FIR Filters Windows Design - 1


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10 Questions MCQ Test Signals and Systems | Test: FIR Filters Windows Design - 1

Test: FIR Filters Windows Design - 1 for Electrical Engineering (EE) 2022 is part of Signals and Systems preparation. The Test: FIR Filters Windows Design - 1 questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: FIR Filters Windows Design - 1 MCQs are made for Electrical Engineering (EE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: FIR Filters Windows Design - 1 below.
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Test: FIR Filters Windows Design - 1 - Question 1

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

Detailed Solution for Test: FIR Filters Windows Design - 1 - Question 1

Explanation: We know that the rectangular window of length M-1 is defined as
w(n)= 1, n=0,1,2…M-1
=0, else where.

Test: FIR Filters Windows Design - 1 - Question 2

The multiplication of the window function w(n) with h(n) is equivalent to the multiplication of H(w) and W(w).

Detailed Solution for Test: FIR Filters Windows Design - 1 - Question 2

Explanation: According to the basic formula of convolution, the multiplication of two signals w(n) and h(n) in time domain is equivalent to the convolution of their respective Fourier transforms W(w) and H(w).

Test: FIR Filters Windows Design - 1 - Question 3

What is the width of the main lobe of the frequency response of a rectangular window of length M-1?

Detailed Solution for Test: FIR Filters Windows Design - 1 - Question 3

Explanation: The width of the main lobe width is measured to the first zero of W(ω)) is 4π/M.

Test: FIR Filters Windows Design - 1 - Question 4

 The width of each side lobes decreases with an increase in M.

Detailed Solution for Test: FIR Filters Windows Design - 1 - Question 4

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. In fact, the width of each side lobes decreases with an increase in M.

Test: FIR Filters Windows Design - 1 - Question 5

 With an increase in the value of M, the height of each side lobe:

Detailed Solution for Test: FIR Filters Windows Design - 1 - Question 5

Explanation: The height of each side lobes increase with an increase in M such a manner that the area under each side lobe remains invariant to changes in M.

Test: FIR Filters Windows Design - 1 - Question 6

As M is increased, W(ω) becomes wider and the smoothening produced by the W(ω) is increased.

Detailed Solution for Test: FIR Filters Windows Design - 1 - Question 6

Explanation: As M is increased, W(ω) becomes narrower and the smoothening produced by the W(ω) is reduced.

Test: FIR Filters Windows Design - 1 - Question 7

Which of the following windows has a time domain sequence   

Detailed Solution for Test: FIR Filters Windows Design - 1 - Question 7

Explanation: The Bartlett window which is also called as triangular window has a time domain sequence as
, 0≤n≤M-1.

Test: FIR Filters Windows Design - 1 - Question 8

The width of each side lobes decreases with an decrease in M.

Detailed Solution for Test: FIR Filters Windows Design - 1 - Question 8

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. In fact, the width of each side lobes decreases with an increase in M.

Test: FIR Filters Windows Design - 1 - Question 9

What is the approximate transition width of main lobe of a Hamming window?

Detailed Solution for Test: FIR Filters Windows Design - 1 - Question 9

Explanation: 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.

Test: FIR Filters Windows Design - 1 - Question 10

What is the Fourier transform of the rectangular window of length M-1?

Detailed Solution for Test: FIR Filters Windows Design - 1 - Question 10

Explanation: We know that the Fourier transform of a function w(n) is defined as

For a rectangular window, w(n)=1 for n=0,1,2….M-1
Thus we get

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