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.