Electronics and Communication Engineering (ECE) Exam  >  Electronics and Communication Engineering (ECE) Tests  >  Test: DFT Algorithm Computation - 2 - Electronics and Communication Engineering (ECE) MCQ

Test: DFT Algorithm Computation - 2 - Electronics and Communication Engineering (ECE) MCQ


Test Description

10 Questions MCQ Test - Test: DFT Algorithm Computation - 2

Test: DFT Algorithm Computation - 2 for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Test: DFT Algorithm Computation - 2 questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: DFT Algorithm Computation - 2 MCQs are made for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: DFT Algorithm Computation - 2 below.
Solutions of Test: DFT Algorithm Computation - 2 questions in English are available as part of our course for Electronics and Communication Engineering (ECE) & Test: DFT Algorithm Computation - 2 solutions in Hindi for Electronics and Communication Engineering (ECE) course. Download more important topics, notes, lectures and mock test series for Electronics and Communication Engineering (ECE) Exam by signing up for free. Attempt Test: DFT Algorithm Computation - 2 | 10 questions in 10 minutes | Mock test for Electronics and Communication Engineering (ECE) preparation | Free important questions MCQ to study for Electronics and Communication Engineering (ECE) Exam | Download free PDF with solutions
Test: DFT Algorithm Computation - 2 - Question 1

 If we split the N point data sequence into two N/2 point data sequences f1(n) and f2(n) corresponding to the even numbered and odd numbered samples of x(n), then such an FFT algorithm is known as decimation-in-time algorithm. 

Detailed Solution for Test: DFT Algorithm Computation - 2 - Question 1

Explanation: Let us consider the computation of the N=2v point DFT by the divide and conquer approach. We select M=N/2 and L=2. This selection results in a split of N point data sequence into two N/2 point data sequences f1(n) and f2(n) corresponding to the even numbered and odd numbered samples of x(n), respectively, that is
f1(n)=x(2n)
f2(n)=x(2n+1) ,n=0,1,2…N/2-1
Thus f1(n) and f2(n) are obtained by decimating x(n) by a factor of
2, and hence the resulting FFT algorithm is called a decimation-in-time algorithm.

Test: DFT Algorithm Computation - 2 - Question 2

If we split the N point data sequence into two N/2 point data sequences f1(n) and f2(n) corresponding to the even numbered and odd numbered samples of x(n) and F1(k) and F2(k) are the N/2 point DFTs of f1(k) and f2(k) respectively, then what is the N/2 point DFT X(k) of x(n)? 

Detailed Solution for Test: DFT Algorithm Computation - 2 - Question 2

Explanation: From the question, it is given that
f1(n)=x(2n)
f2(n)=x(2n+1) ,n=0,1,2…N/2-1

1 Crore+ students have signed up on EduRev. Have you? Download the App
Test: DFT Algorithm Computation - 2 - Question 3

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

Detailed Solution for Test: DFT Algorithm Computation - 2 - Question 3

Explanation: We know that, X(k) = F1(k)+WNk F2(k)
We know that F1(k) and F2(k) are periodic, with period N/2, we have F1(k+N/2)= F1(k) and F2(k+N/2)= F2(k). In addition, the factor WNk+N/2= -WNk.
Thus we get, X(k+N/2)= F1(k)- WNk F2(k).

Test: DFT Algorithm Computation - 2 - Question 4

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

Detailed Solution for Test: DFT Algorithm Computation - 2 - Question 4

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).

Test: DFT Algorithm Computation - 2 - Question 5

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

Detailed Solution for Test: DFT Algorithm Computation - 2 - Question 5

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 multiplications is reduced to (N/2)log2N.

Test: DFT Algorithm Computation - 2 - Question 6

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

Detailed Solution for Test: DFT Algorithm Computation - 2 - Question 6

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.

Test: DFT Algorithm Computation - 2 - Question 7

 The following butterfly diagram is used in the computation of:

Detailed Solution for Test: DFT Algorithm Computation - 2 - Question 7

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

Test: DFT Algorithm Computation - 2 - Question 8

 For a decimation-in-time FFT algorithm, which of the following is true?

Detailed Solution for Test: DFT Algorithm Computation - 2 - Question 8

Explanation: In decimation-in-time FFT algorithm, the input is taken in bit reversal order and the output is obtained in the order.

Test: DFT Algorithm Computation - 2 - Question 9

The following butterfly diagram is used in the computation of:

Detailed Solution for Test: DFT Algorithm Computation - 2 - Question 9

Explanation: The above given diagram is the basic butterfly computation in the decimation-in-frequency FFT algorithm.

Test: DFT Algorithm Computation - 2 - Question 10

 For a decimation-in-time FFT algorithm, which of the following is true?

Detailed Solution for Test: DFT Algorithm Computation - 2 - Question 10

Explanation: In decimation-in-frequency FFT algorithm, the input is taken in order and the output is obtained in the bit reversal order.

Information about Test: DFT Algorithm Computation - 2 Page
In this test you can find the Exam questions for Test: DFT Algorithm Computation - 2 solved & explained in the simplest way possible. Besides giving Questions and answers for Test: DFT Algorithm Computation - 2, EduRev gives you an ample number of Online tests for practice

Top Courses for Electronics and Communication Engineering (ECE)

Download as PDF

Top Courses for Electronics and Communication Engineering (ECE)