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Which of the following is true regarding the number of computations required to compute an N-point DFT?
- a)N2 complex multiplications and N(N-1) complex additions
- b)N2 complex additions and N(N-1) complex multiplications
- c)N2 complex multiplications and N(N+1) complex additions
- d)N2 complex additions and N(N+1) complex multiplications
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Which of the following is true regarding the number of computations re...
Explanation: The formula for calculating N point DFT is given as
From the formula given at every step of computing we are performing N complex multiplications and N-1 complex additions. So, in a total to perform N-point DFT we perform N2 complex multiplications and N(N-1) complex additions.
From the formula given at every step of computing we are performing N complex multiplications and N-1 complex additions. So, in a total to perform N-point DFT we perform N2 complex multiplications and N(N-1) complex additions.
Most Upvoted Answer
Which of the following is true regarding the number of computations re...
Number of computations required to compute an N-point DFT:
The Discrete Fourier Transform (DFT) is a mathematical algorithm used to transform a discrete sequence of N complex numbers into another sequence of N complex numbers. It is commonly used in signal processing and data analysis.
The number of computations required to compute an N-point DFT depends on the specific algorithm used. The most commonly used algorithm is the Fast Fourier Transform (FFT), which significantly reduces the number of computations compared to a direct implementation of the DFT.
The number of computations can be calculated as follows:
1. Complex Multiplications:
- In the DFT algorithm, for each output sample, N complex multiplications are required. This is because each output sample is a linear combination of all the input samples, and the coefficients of the linear combination are complex numbers.
- Therefore, the total number of complex multiplications required for an N-point DFT is N^2.
2. Complex Additions:
- In the DFT algorithm, for each output sample, N-1 complex additions are required. This is because the linear combination of input samples involves adding up N complex numbers.
- Therefore, the total number of complex additions required for an N-point DFT is N(N-1).
Considering the above calculations, the correct answer is option 'A': N^2 complex multiplications and N(N-1) complex additions.
In summary:
- The number of complex multiplications required for an N-point DFT is N^2.
- The number of complex additions required for an N-point DFT is N(N-1).
- The total number of computations for an N-point DFT is the sum of complex multiplications and complex additions.
The Discrete Fourier Transform (DFT) is a mathematical algorithm used to transform a discrete sequence of N complex numbers into another sequence of N complex numbers. It is commonly used in signal processing and data analysis.
The number of computations required to compute an N-point DFT depends on the specific algorithm used. The most commonly used algorithm is the Fast Fourier Transform (FFT), which significantly reduces the number of computations compared to a direct implementation of the DFT.
The number of computations can be calculated as follows:
1. Complex Multiplications:
- In the DFT algorithm, for each output sample, N complex multiplications are required. This is because each output sample is a linear combination of all the input samples, and the coefficients of the linear combination are complex numbers.
- Therefore, the total number of complex multiplications required for an N-point DFT is N^2.
2. Complex Additions:
- In the DFT algorithm, for each output sample, N-1 complex additions are required. This is because the linear combination of input samples involves adding up N complex numbers.
- Therefore, the total number of complex additions required for an N-point DFT is N(N-1).
Considering the above calculations, the correct answer is option 'A': N^2 complex multiplications and N(N-1) complex additions.
In summary:
- The number of complex multiplications required for an N-point DFT is N^2.
- The number of complex additions required for an N-point DFT is N(N-1).
- The total number of computations for an N-point DFT is the sum of complex multiplications and complex additions.
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Which of the following is true regarding the number of computations required to compute an N-point DFT?a)N2complex multiplications and N(N-1) complex additionsb)N2complex additions and N(N-1) complex multiplicationsc)N2complex multiplications and N(N+1) complex additionsd)N2complex additions and N(N+1) complex multiplicationsCorrect answer is option 'A'. Can you explain this answer?
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