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Question 1

Marks : +2 | -2

Pass Ratio : 100%

WNk+N/2=?

WNk

-WNk

WN-k

None of the mentioned

Explanation:

According to the symmetry property, we get WNk+N/2=-WNk.

Question 2

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Pass Ratio : 100%

The computation of XR(k) for a complex valued x(n) of N points requires _____________

2N2 evaluations of trigonometric functions

4N2 real multiplications

4N(N-1) real additions

All of the mentioned

Explanation:

The expression for XR(k) is given as

Question 3

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The following butterfly diagram is used in the computation of __________

Decimation-in-time FFT

Decimation-in-frequency FFT

All of the mentioned

None of the mentioned

Explanation:

The above given diagram is the basic butterfly computation in the decimation-in-time FFT algorithm.

Question 4

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Pass Ratio : 100%

If the arrangement is of the form in which the first row consists of the first M elements of x(n), the second row consists of the next M elements of x(n), and so on, then which of the following mapping represents the above arrangement?

n=l+mL

n=Ml+m

n=ML+l

none of the mentioned

Explanation:

If we consider the mapping n=Ml+m, then it leads to an arrangement in which the first row consists of the first M elements of x(n), the second row consists of the next M elements of x(n), and so on.

Question 5

Marks : +2 | -2

Pass Ratio : 100%

Which of the following is true regarding the number of computations required to compute an N-point DFT?

N2 complex multiplications and N(N-1) complex additions

N2 complex additions and N(N-1) complex multiplications

N2 complex multiplications and N(N+1) complex additions

N2 complex additions and N(N+1) complex multiplications

Explanation:

The formula for calculating N point DFT is given as

Question 6

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What is the real part of the N point DFT XR(k) of a complex valued sequence x(n)?

\\(\\sum_{n=0}^{N-1} [x_R (n) cosâ¡\\frac{2Ï€kn}{N} – x_I (n) sinâ¡\\frac{2Ï€kn}{N}]\\)

\\(\\sum_{n=0}^{N-1} [x_R (n) sinâ¡\\frac{2Ï€kn}{N} + x_I (n) cosâ¡\\frac{2Ï€kn}{N}]\\)

\\(\\sum_{n=0}^{N-1} [x_R (n) cosâ¡\\frac{2Ï€kn}{N} + x_I (n) sinâ¡\\frac{2Ï€kn}{N}]\\)

None of the mentioned

Explanation:

For a complex valued sequence x(n) of N points, the DFT may be expressed as

Question 7

Marks : +2 | -2

Pass Ratio : 100%

How many complex multiplications are required to compute X(k)?

N(N+1)

N(N-1)/2

N2/2

N(N+1)/2

Explanation:

We observe that the direct computation of F1(k) requires (N/2)2 complex multiplications. The same applies to the computation of F2(k). Furthermore, there are N/2 additional complex multiplications required to compute WNk. Hence it requires N(N+1)/2 complex multiplications to compute X(k).

Question 8

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The total number of complex additions required to compute N point DFT by radix-2 FFT is?

(N/2)log2N

Nlog2N

(N/2)logN

None of the mentioned

Explanation:

The decimation of the data sequence should be repeated again and again until the resulting sequences are reduced to one point sequences. For N=2v, this decimation can be performed v=log2N times. Thus the total number of complex additions is reduced to Nlog2N.

Question 9

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If X(k) is the N/2 point DFT of the sequence x(n), then what is the value of X(k+N/2)?

F1(k)+F2(k)

F1(k)-WNk F2(k)

F1(k)+WNk F2(k)

None of the mentioned

Explanation:

We know that, X(k) = F1(k)+WNk F2(k)

Question 10

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Pass Ratio : 100%

Which of the following is true regarding the number of computations required to compute DFT at any one value of ‘k’?

4N-2 real multiplications and 4N real additions

4N real multiplications and 4N-4 real additions

4N-2 real multiplications and 4N+2 real additions

4N real multiplications and 4N-2 real additions

Explanation:

The formula for calculating N point DFT is given as

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