A brute force calculation of a length DFT requires a number of operations roughly proportional to . Thus, a 1024-point DFT would require about a million multiplications and about a million additions.
Luckily, the DFT algorithm can be simplified to a form in which the required number of calculations is proportional to Now, our 1024-point DFT can be calculated with only about 10,000 operations!
This simplified algorithm is referred to as the Fast Fourier Transform or FFT.