Now this process works fine in principle, and we can use it to calculate all discrete Fourier transforms. But the problem is it requires too many calculations. To complete one discrete Fourier transform requires multiplying N data points by N different frequency waves. So, N squared complex multiplications. Now this is doable for small samples but if we had a larger sample like a million, that would require a million squared or one trillion calculations.

Computing the DFT directly using the above formula can be computationally intensive. Therefore, the Fast Fourier Transform (FFT) algorithm is commonly used to efficiently calculate the DFT, reducing the number of computations required.