Comparing arithmetic complexity of FFT radix-2 and convolution

1. What is the advantage of radix 2 FFT algorithm in comparison with the classical DFT method?
2. What is difference between radix 2 and radix 4 FFT?
3. What is radix 2 in FFT?
4. How many multiplications and addition are involved in radix 2 FFT?

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 difference between radix 2 and radix 4 FFT?

Radix-4 FFT Algorithm

A stage is half of radix-2. The radix-4 DIF FFT divides an N-point discrete Fourier transform (DFT) into four N 4 -point DFTs, then into 16 N 16 -point DFTs, and so on. In the radix-2 DIF FFT, the DFT equation is expressed as the sum of two calculations.

What is radix 2 in FFT?

Radix-2 algorithm is a member of the family of so called Fast Fourier transform (FFT) algorithms. It computes separately the DFTs of the even-indexed inputs (x0,x2,...,xN−2) and of the odd-indexed inputs (x1,x3,...,xN−1), and then combines those two results to produce the DFT of the whole sequence.

How many multiplications and addition are involved in radix 2 FFT?

The number of multiplications and additions required to compute N-point DFT using redix-2 FFT are N log2N and N/2 log 2N respectively.