Fast Fourier Transform

Fast Fourier transform (FFT) is an efficient algorithm for calculating the discrete Fourier transform (DFT). The FFT produces the same results as a DFT but it reduces the execution time by hundreds in some cases. Whereas DFT takes an order of $O(n^{2})\,$ computations, FFT takes an order of $O(n\,\log \,n)$, and is definitely the preferred algorithm to be used in all applications in terms of computational complexity. The FFT in most implementations consistent of samples that are exactly a power of 2, this is commonly known as a FFT Radix 2 algorithm where $n=64,128,256,512,1024,2048$ etc.

Unlike the DFT, the frequency spacing nor window size per-bin can't be adjusted because FFT bins aren't calculated individually.

External links

• Fast Fourier transform on Wikipedia