Fast Fourier transform

The fast Fourier transform (FFT) is an efficient algorithm to calculate the discrete Fourier transform (DFT). FFT improves on more naïve algorithms and is of order O(NlogN). DFT has applications in signal processing, image processing, solving partial differential equations, and more. NumPy has a module called fft that offers fast Fourier transform functionality. A lot of the functions in this module are paired; this means that, for many functions, there is a function that does the inverse operation. For instance, the fft and ifft functions form such a pair.