Is it possible to reduce the complexity of radix-2 FFT if the input vector contains identical elements?

1. How does FFT reduce computational complexity?
2. What is the advantage of radix 2 FFT algorithm in comparison with the classical DFT method?
3. What is the complexity of FFT algorithm?
4. What is the way to reduce number of arithmetic operations during DFT computation?

How does FFT reduce computational complexity?

Radix-2 FFT algorithm reduces the order of computational complexity of Eq. 1 by decimating even and odd indices of input samples. There are two kinds of decimation:[14] decimation in the time domain and decimation in frequency (DIF) domain.

What is the advantage of radix 2 FFT algorithm in comparison with the classical DFT method?

DFT requires no multiplies. The overall result is called a radix 2 FFT. A different radix 2 FFT is derived by performing decimation in frequency. A split radix FFT is theoretically more efficient than a pure radix 2 algorithm [73,31] because it minimizes real arithmetic operations.

What is the complexity of FFT algorithm?

Fast Fourier transform (FFT) algorithm, that uses butterfly structures, has a computational complexity of O ( N l o g ( N ) ) , a value much less than O ( N 2 ) .

What is the way to reduce number of arithmetic operations during DFT computation?

Thus for reasonably large values of N (in order of 1000) direct evaluation of the DFT requires an inordinate amount of computation. By using FFT algorithms the number of computations can be reduced.