Is there an equation for efficiency of a 2-radix FFT as you raise $k$?

1. What is a radix 2 FFT?
2. What is FFT formula?
3. Does FFT have to be power of 2?
4. What is difference between radix 2 and radix-4 FFT?

What is a radix 2 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.

What is FFT formula?

The fast Fourier transform has become a major DSP tool since being popularized by Cooley and Tuckey in 1965. In the FFT formula, the DFT equation X(k) = ∑x(n)W_N^nk is decomposed into a number of short transforms and then recombined.

Does FFT have to be power of 2?

Sure, you can use a radix-2 FFT to compute FFTs for lengths not a power of 2 (but it is not as efficient as using methods specifically tailored to the factors of the sequence length).

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.