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# Test: FIR Filters Windows Design - 1

## 10 Questions MCQ Test Digital Signal Processing | Test: FIR Filters Windows Design - 1

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This mock test of Test: FIR Filters Windows Design - 1 for Electrical Engineering (EE) helps you for every Electrical Engineering (EE) entrance exam. This contains 10 Multiple Choice Questions for Electrical Engineering (EE) Test: FIR Filters Windows Design - 1 (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: FIR Filters Windows Design - 1 quiz give you a good mix of easy questions and tough questions. Electrical Engineering (EE) students definitely take this Test: FIR Filters Windows Design - 1 exercise for a better result in the exam. You can find other Test: FIR Filters Windows Design - 1 extra questions, long questions & short questions for Electrical Engineering (EE) on EduRev as well by searching above.
QUESTION: 1

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

Solution:

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.

QUESTION: 2

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

Solution:

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).

QUESTION: 3

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

Solution:

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

QUESTION: 4

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

Solution:

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.

QUESTION: 5

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

Solution:

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.

QUESTION: 6

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

Solution:

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

QUESTION: 7

Which of the following windows has a time domain sequence Solution:

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

QUESTION: 8

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

Solution:

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.

QUESTION: 9

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

Solution:

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.

QUESTION: 10

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

Solution:

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 