How many multiplications and additions does it take to compute an FFT of a signal?

Each pair requires 4 additions and 4 multiplications, giving a total number of computations equaling 8N4=N2. This number of computations does not change from stage to stage. Because the number of stages, the number of times the length can be divided by two, equals log2N, the complexity of the FFT is O(NlogN).

1. How many multiplications and how many additions are needed are needed to compute the DFT?
2. How many complex additions are required for FFT algorithm?
3. How many multiplications and additions are required to perform a 8 point FFT?
4. How many multiplications and additions are required to compute n-point DFT using radix 2 FFT?

How many multiplications and how many additions are needed are needed to compute the DFT?

We observe that for each value of k, direct computation of X(k) involves N complex multiplications (4N real multiplications) and N-1 complex additions (4N-2 real additions). Consequently, to compute all N values of the DFT requires N ² complex multiplications and N ²-N complex additions.

How many complex additions are required for FFT algorithm?

So, the total number of complex additions to be performed in linear filtering of a sequence using FFT algorithm is 2Nlog₂N.

How many multiplications and additions are required to perform a 8 point FFT?

The 8-point DFT therefore requires 8×8 = 82 = 64 complex multiplications and 8×7 = 8(8 - 1) = 56 additions. In general, for an N-point DFT, N2 multiplications and N (N – 1) additions are required.

How many multiplications and additions are required to compute n-point DFT using radix 2 FFT?

Questions 2

Diagram of "radix-2" FFT computing 8-pt DFT. If we use summation formula to compute DFT, for each k, we need N times complex multiplications and N-1 times complex additions. In total, we need N*N=64 times of complex multiplications and N*(N-1)=56 times of complex additions.