Value of complex multiplier in DFT/FFT

1. What is the number of complex multiplications for DFT and FFT?
2. How many complex multiplication are there in FFT?
3. How many complex multiplication are required per output data point?
4. How many complex multiplications are required?

What is the number of complex multiplications for DFT and FFT?

In direct computation of N-point DFT, the total number of complex additions are N (N – 1) and total number of complex multiplications are N2.

How many complex multiplication are there in FFT?

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).

How many complex multiplication are required per output data point?

So, the number of complex multiplications per output data point is [Nlog₂2N]/L.

How many complex multiplications are required?

How many complex multiplications are required to compute X(k)? Explanation: We observe that the direct computation of F₁(k) requires (N/2)² complex multiplications. The same applies to the computation of F₂(k). Furthermore, there are N/2 additional complex multiplications required to compute W_N^k.