Computational Efficiency in FFT :a)Total Real Multiplications = 2N Log2Nb)Total Real Additions = 3N Log2NSelect one:FALSETRUE
Question
Computational Efficiency in FFT :a)Total Real Multiplications = 2N Log2Nb)Total Real Additions = 3N Log2NSelect one:FALSETRUE
Solution
The statement is TRUE.
In the Fast Fourier Transform (FFT), the number of computations is significantly reduced compared to the Discrete Fourier Transform (DFT).
a) The total number of real multiplications in FFT is indeed 2N log2N. This is because each stage of the FFT requires N/2 complex multiplications, and each complex multiplication involves 4 real multiplications. However, one of these can be eliminated, leaving 2 real multiplications per complex multiplication. Since there are log2N stages, the total number of real multiplications is 2N log2N.
b) Similarly, the total number of real additions in FFT is 3N log2N. Each stage of the FFT requires N/2 complex additions, and each complex addition involves 2 real additions. Therefore, there are N real additions per stage. However, there is also an additional N/2 real additions per stage due to the twiddle factor. This results in a total of 1.5N real additions per stage. Since there are log2N stages, the total number of real additions is 3N log2N.
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